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_{This is a working paper version of my thesis. The underlying question is: How much information should you collect before making a decision. More specifically this involves arguments about whether it is logically possible to collect an optimal amount of information (since you need to collect information about information about information and so on forever) and several other problems involved in estimating the value of information. The footnotes and some other details were lost in the conversion to HTML, so potential readers might want to download the paper in Word format (at www.oocities.org/hmelberg/papers/infinite.doc) (click here to download). Comments are, as always, very much appreciated as I am planning to revise the paper one more time before it is submitted (before May 1999).}

1 Introduction *

2 What is rational choice? *

3 Collecting an optimal amount of information? *

4 Evaluating the infinite regress argument? *

5 The problem of estimation *

6 Implications *

7 Conclusion *

8 References *

1.  
2. Introduction

 

1. What is the question?

The starting point of this paper is the following question: How much information should we collect before we make a decision? The short answer is that we should collect information as long as the expected value of spending more resources on collecting information is greater than the expected cost. But, how do we know the expected value and cost of more information? To answer this we need to collect information i.e. we have to collect information to determine how much information to collect. As the reader may already have understood, this apparently leads to an infinite regress. We must collect information on how much information to collect before we decide how much information we should collect and so on forever. This is the problem of infinite regress in the collection of information, and some authors - for instance Jon Elster and Sidney G. Winter - argue that it is a serious problem in the theory of rational choice.

The infinite regress problem is only one possible source of indeterminate answers when trying to decide how much information to collect. For instance, when we are in a unique situation we cannot determine the value of information from historical experience of similar situations, and hence there is - using the classical view of probability - no rational basis for estimating the value of information. I have labelled all the problems in this (residual) category the estimation problem.

The question is then whether it is correct that the infinite regress argument and the problem of estimation makes it impossible to act rationally.

 

2. Why try to answer this question?

What makes a question worth asking and answering? First of all, the answer should not be obvious or the obvious answer must be incorrect. Second, the question must be important. Third, it must be possible in principle to give an answer. In this section I will try to relate these requirements to the problem of deciding how much information to collect. The aim is both to demonstrate that I am not flogging dead horses (i.e. there is disagreement today) or arguing against straw men (i.e. I show that there are people who think the collection of information does not represent a problem).

 

1. The answer should not be obvious, or the obvious answer should be incorrect

One good way of demonstrating that the answer is not obvious is to show that the "experts" disagree. For instance, on the question under consideration Roy Radner (1996, p. 1363) seems to believe that the gathering of information can be solved rationally. As he writes:

It is convenient to classify the costly (resource-using) activities of decision-making into three groups:

1. observation, or the gathering of information;

2. memory, or the storage of information;

3. computation, or the manipulation of information. [...]

4. communication, or the transmission of information.

Of these activities, and their related costs, the first, second, and fourth can be accommodated by the Savage paradigm with relative little strain, although they do have interesting implications.

In apparent contradiction to this view, we may quote Jon Elster (1985, p. 69) who believes the problem of information collection is significant. He writes:

In most cases it will be equally irrational to spend no time on collecting evidence and to spend most of one's time doing so. In between there is some optimal amount of time that should be spent on information-gathering. This, however, is true only in the objective sense that an observer who knew everything about the situation could assess the value of gathering information and find the point at which the marginal value of information equals marginal costs. But of course the agent who is groping towards a decision does not have the information needed to make an optimal decision with respect to information-collecting.[23] He knows, from first principles, that information is costly and that there is a trade-off between collecting information and using it, but he does not know what that trade-off is.

The term contradiction may be too strong to describe the difference between the two quotations. Radner claims that information collection can be "accommodated by the Savage Paradigm" by he does not discuss whether mere consistency of subjective beliefs (which is what is required within the Savage paradigm) is sufficient to label the decision "rational." Thus, the difference between Radner and Elster may be that Radner is willing to label a decision rational as long as it is based on consistent beliefs, while Elster places stronger demands on beliefs, such that they should be rationally constructed for a given set of information. This is a topic I will discuss closer in the second chapter, which is a general introduction to rational decision-making. In any case, the quotations prove that there is a difference in the degree to which decision theorists view the collection of information as a problem (see chapter 4.1 for more examples of conflicting views on this issue). Whether it is a substantial disagreement or a mere problem of labelling remains to be discussed.

 

2. The answer should have important implications

Not all non-obvious questions are worth asking. For instance, assume you have spent much time and effort finding the answer to a non-obvious question ("What is the twenty-first decimal of p ?"), but that few or no important consequences follow from answering the question. It seems like you could have made better use of your time trying to answer a different and more important question. Sometimes people react in this way to the opening paragraph of this paper. "So what"; "Who cares?" and "This is simply too abstract to be of practical use" were some of the comments. I disagree, but before I can explain why it is necessary to discuss the meaning of "importance."

Clearly, "importance" is a subjective term so what is important to you need not be important to me. Although the previously mentioned reaction ("who cares?") could be dismissed on this ground ("I don't care what you say, it is important to me!"), I think this would be wrong. It is wrong because I believe the reaction stems not from thinking that the implications are unimportant, but from being unaware of the implications. Hence, I will try to persuade the reader by making some of the implications explicit.

We should distinguish between implications that derive their importance from being directly policy-relevant versus those implications that have intellectual importance. If I could give a good answer to the question of how to reduce the problem of unemployment, this would immediately be of importance to the welfare of many people (which may be one commonly agreed meaning of "importance"). I admit that my question - or more precisely my discussion of the question - is not important in this sense. However, sometimes a question is academically important because the answer may change the way we explain many phenomena. New directions of research may be opened and some theories may be weakened. In what way is this the case with the question of how much information we should collect?

The answer to the question of how much information to collect may change the way we explain many economic phenomena. To understand why, it is necessary to locate the two problems I want to discuss within a larger map of possible questions and problems, and I have tried to do so in Figure 1.1. Please be aware that in the paragraphs below I have only tried to provide the absolute minimum explanation necessary to explain the structure. It is the task of the other chapters (especially chapter two) to put more meat on the bones.

First of all, there is a very general disagreement about the assumptions on which economists should base their theories, that is the discussion between those who define economics as the application of rational choice analysis vs. those who focus on more psychological or behavioural foundational assumptions. The two problems discussed in this paper - the problem of infinite regress in the collection of information and the problem of estimating the net value of information - are two of very many possible issues in this general debate.



 

There are two possible general arguments against rational choice theory: First, it may be impossible to act rationally, for instance because the theory demands that the agent must have information which it is in principle impossible to have. (I have followed Elster terminology and labelled the problem as "indeterminacy"). Second, the theory may be invalid in the sense that even if it is possible to act rationally, people fail to do so. I have limited my attention to problems of indeterminacy i.e. the argument to be evaluated is not of the type "this is not how people act", but rather "it is impossible to act according to the theory because the theory does not present a solution."

Whether the theory is indeterminate or invalid depends, of course, on the definition of rationality (to be discussed in chapter two). The complexity of this definition and the extent to which it can be followed also depends on the assumptions we make about the environment, that is whether we assume a representative individual in a world of certainty, or whether we assume a decision in a multi-person world with uncertainty. For some time I worked on the problems of indeterminacy both in a multi-person and a one-person world. There is, for instance, a problem of finding a solution concept in game theory that is strong enough to generate unique predictions. In the end, however, I decided that the focus was too broad, and I ended up discussing only the problem of indeterminacy within the collection of information that might exist in a one-person world with uncertainty, without considering the additional difficulties that result from a multi-person environment.

The two general reasons for the failure of rational choice theory (invalid or indeterminate) can be divided into two sub-groups. The theory can be invalid because people do not try to behave rationally (believing, for instance, that adherence to norms and moral rules is the correct way of deciding how to act). The second reason for judging the theory invalid could be that people but do not manage to behave rationally even when they try (due to, for instance, cognitive limitations). Indeterminacy may exist when the problem has no solution and when there are many solutions (for instance many Nash equilibria. I have already limited my topic to "indeterminacy," but I will further limit myself to the problem of "no solution" as opposed to "many solutions."

There may well be diminishing return to even further classification, but I believe that the two problems discussed in this paper do not really belong to the same class. True, they are both about why it may be impossible to collect an optimal amount of information, but the infinite regress argument - unlike the problem of estimation - may exist even if we have all the information we could desire. That is why I have labelled one "logical problems" and the other "empirical problems." I do not attach much prestige to these last two labels as long as the two problems are kept separate the reader is free to label them as he want (if he wants).

Finally, I discuss only one (of many) "logical" and only one (of many) "empirical" problems that (supposedly) makes it impossible to collect an optimal amount of information. It is here - at last - that the problem of infinite regress in the collection of information and the problem of estimation can be located. Even more specifically, my main (but not exclusive) argument is focused on Jon Elster's interpretation of the problem of infinite regress and estimation.

In summary, besides the inherent intellectual satisfaction in satisfying our curiosity about the answer to a question, I believe that the question is important because its role in the debate on the basic building blocks of economic theories: Is it the assumption of rational choice or is psychological theories about behaviour. It is, however, important to note that I do not pretend to give general answers to that question. All I do is to discuss two issues that are relevant to the larger debate, without claiming that these two alone determine the argument.

 

3. Is it possible to answer the question and if so how?

Some questions are interesting (or non-obvious) and important, but there is very little hope of determining the answers with any degree of reliability and this greatly reduces the utility of spending time on them. Hence, the third demand for it to be worth trying to answer a question is that it is at least in principle possible to give an answer. This demand may be strengthened to say that we should only focus on those questions and answers that can be relatively reliably answered given inherent limitations of knowledge (both personal and in general), time, resources and so on.

Some questions do not have objectively true answers. For instance, it is in principle impossible to give an objectively true answer to the question of whether vanilla or chocolate ice cream is the best ice-cream flavour. More seriously the question "What is just?" does not have a unique and objectively true answer. As for the topic of this paper, it is true that there is no single definition of rationality that everybody accepts. This does not mean that it is impossible to discuss the question of rational collection of information in a scientific manner.

Imagine that I claim to have the correct definition of rational choice. Another person may then criticise this definition by pointing to some of its logical implications that I had not considered or by showing that the definition is not coherent (because all its elements cannot be true at the same time). I may then agree that the definition was wrong, and revise it accordingly. Alternatively, I may claim that his logical implication does not represent a counterintuitive example that should lead us to revise the theory. Finally, I may try to prove that the claimed implication does not follow from my definition. There is nothing "unscientific" about this debate. It is true that the process of confronting each other with the implications of the definition need not lead to a unique definition of rationality, but that is different from arguing that the process itself is unscientific (for more on this, see Melberg 1996, pp. 475-477 and Elster 1993, pp. 180-181).

Having established that it is in principle possible to at least discuss the problem in a scientific manner, it remains to be argued exactly how we should proceed to answer the question. I have previously admitted that I shall proceed by dividing the question into smaller parts and then select only some of these for closer investigation. Moreover, I have chosen to do an in depth examination of a few arguments from a few authors instead of a short discussion (or survey) of many arguments using unnamed ("some economists say") - or worse: imagined - opponents. As a small compensation for the restricted scope, I have included several footnotes, as well as a bibliographical appendix, which directs the interested reader to further literature. Finally, on the question of the use of formal and abstract mathematics vs. verbal reasoning, I have opted for a mainly verbal style. These choices were made mostly out of necessity. I would have liked to be able to give a more formal and comprehensive answer, but limited personal abilities prevent me from doing so.

One final aspect should be commented on since it may seem peculiar to some. I think it is important to state the weaknesses of my own arguments and sometimes I will indicate the degree to which I am unsure. This is not only a question of academic honesty. By telling the reader about my own uncertainty, I make it easier for those who want to scrutinize and build on my arguments. I also prevent them from taking what I weakly believe too seriously. This is important because, as mentioned in the preface, science is a cumulative effort and there is no reason to make this cumulative work more difficult than it already is by hiding uncertainties behind confident language.

3.  
4. What is rational choice?

 

1. Introduction

If we disagree on the definition of rationality we may also give different answer to the question of whether it is possible to make a rational decision about how much information to collect. To avoid misunderstandings of this sort, it is necessary to discuss the concept of rationality in general. It is not necessary, however, to discuss all aspects of every possible definition of rational choice. I will limit myself to a short presentation of the standard theory in economics (expected utility theory) and a closer discussion of only those elements that are relevant to the problem of infinite regress and the problem of estimation. It is, for instance, very important to discuss whether we should require that the collection of information and the construction of beliefs be optimal before we label the decision rational. It is not important to discuss whether rationality also demands that we exclude certain types of preferences - such as acting on preferences the agent "knows are impossible to fulfill" (Nozick 1993, p. 144). These discussions are often said to be about substantive rationality, as opposed to the economists more instrumental concept of rationality (i.e. they are about what we should want, not only what we should do to get something we want). Although interesting, these deeper philosophical issues are not relevant to the infinite regress argument or the problem of estimation..

 

2. The role of rationality and uncertainty in economics in general

 

1. Rationality

What is the role of the rationality assumption in economics? For some economists rational maximization is one of a few defining features of economics. As Gary Becker writes:

"The combined assumptions of maximizing behavior, market equilibrium, and stable preferences, used relentlessly and unflinchingly, form the heart of the economic approach." (Quoted in Hirschleifer 1985, 301. Originally in Becker 1976, p. 4)

In this approach economics is by definition the analysis of the implications of rational choice.

On the other side, there are economists who emphasise the limitations of rationality. As Kenneth J. Arrow (1987, p. 25) writes:

It [the assumption of rationality] is most plausible under very ideal assumptions. When these conditions cease to hold, the rationality assumptions become strained and possibly even self-contradictory. They certainly imply an ability at information processing and calculation that is far beyond the feasible and that cannot well be justified as the result of learning and adaptation.

Moreover, "there is no general principle that prevents the creation of an economic theory based on hypotheses other than rationality" (Arrow 1987, p. 25). For instance, one could create a theory of consumption based on the psychological mechanism of habit-formation.

The quotations clearly reflect a disagreement about the role of the assumption of rational behaviour in economics. Although I shall make a few comments on the debate in a later chapter, I have doubts about the fruitfulness of trying to answer the general question of "for or against the use of the assumption of rationality." In any case the question is too large for me and I have chose to focus on a critical evaluation of only two arguments for the indeterminacy of rational choice in one area (the collection of information).

 

2. Uncertainty

The meaning and role of uncertainty in economics is controversial. For some uncertainty is a situation in which it is impossible to attach probabilities to the outcomes. Others deny this impossibility and argue that for all practical purposes uncertainty and risk are synonyms. Risk is here defined as a situation in which you do not know which outcome ("state of the world") will obtain, but you do have beliefs that can be expressed as numerical probabilities.

Depending on the two different meanings of uncertainty economists have tended to take different positions on its importance. Those who believe radical uncertainty exists (like the Post Keynesians), also believe the concept is extremely important especially in demonstrating that the economy is not self-regulating (see, for instance, Davidson 1991). On the other hand there are those who try to show that the assumption of certainty is not vital to many of the core results in economics (such as the existence of a Pareto optimal and stable general equilibrium).

Let me make the above general comments slightly more precise. General equilibrium theory requires a complete set of markets; there must be a price vector such that for each commodity demand is equal to supply. Without claiming to understand the proofs, I must accept that economists have rigorously demonstrated both the existence of this general equilibrium and that it is Pareto optimal. This proof requires certain assumptions and although certainty may be dispensed with as an assumption, it is usually assumed. In what way does uncertainty make the problem more difficult?

A commodity may be defined by at least four features: (1) Its physical description; (2) The place of delivery; (3) The time of delivery; And (4) The state of nature obtaining. In short, an ice-cream at a beach in 1997 in sunny weather is a different from an ice-cream in a forest in 1994 when it is raining. This definition of a commodity drastically increases the number of markets that have to exist to have a complete set of markets. Moreover, uncertainty seems to create large problems for (3) and (4) since they require a complete set of future contingent markets. For instance, it is possible to buy "options" (a right to buy something in the future at a specified price), but empirically speaking not all commodities have existing options markets. The same goes for (4); it is possible to buy insurance for some states of nature (car-crash), but uncertainty/risk may to destroy the existence of some of these markets (unemployment insurance). In this way uncertainty makes it more likely that a complete set of markets does not exist and that the Pareto optimality of a decentralized self-regulating economy no longer holds. This is one of the key theoretical significances of uncertainty in economics.

 

3. Sub-conclusion

In sum, whatever your opinion on the meaning of uncertainty and rationality it is clear that the debate about its meaning and implications are central to economics. The general significance may derive from what some consider to be the ultimate economics question: "Does the free-market produce a stable and efficient economy?" This question may linger far, far in the background in this paper. It is not the one I try to answer, but questions about the possibility of rational behaviour in an uncertain world are certainly relevant to the proofs behind the first theorem of welfare economics since the existing proofs assume both rationality and (often) certainty.

 

3. Rational Choice in Economics: Expected Utility Theory

Imagine that you have to select one action (x_i) from a set of feasible actions (X). Assume, moreover, that you are in a situation of uncertainty. Which action should you choose?

In its prescriptive variant expected utility theory says that we should choose that action which maximizes expected utility. As Schoemaker (1982) points out the theory can also be used descriptively ("this is how people choose"), predictively ("I expect him to chose x since it is the act that maximizes expected utility") and postdictively i.e. it is used as a non-falsifiable assumption that guides research. Anomalies do not destroy the theory, but stimulates search for the "unknown" variable that makes the behaviour conform to the theory. My interest here is mainly in the normative aspects of the theory i.e. whether it can tell us what to do. In the following I shall thus present the basics of the theory with special emphasis on exactly what is required before the theory can be put to use.

How do we calculate the expected utility? To answer this we first specify our uncertainty as a list of possible "states of the world" (each state is denoted s_i and is a member of the set of possible states S). We then have a list of possible actions and possible states that together form the set of possible consequences (c_xs). A simple example is the following: You have to chose whether to bring an umbrella or not when you go for a walk (x₁= bring umbrella, x₂= not bring umbrella). There are two possible "states of the world": s₁= it will rain, s₂= it will not rain. Cross-tabulating this we have the following four possible consequences:

 

Figure 2.1: Calculation of Expected Utility

		Possible states (S)
		s1 Rain (probability p1)	s2 No rain (probability p2)
Possible actions (X)	x1 (Bring umbrella)	c11 (it rains and you have an umbrella)	c12 (you brought the umbrella, but is does not rain)
	x2 (Do not bring umbrella)	c21 (it rains and you did not bring an umbrella)	c22 (you did not bring the umbrella and it did not rain)

 

The expected utility of an action is calculated by multiplying the utility of each possible consequence of an action with the (subjective or given) probability that the consequence will occur. Formally in our example:

EU (x₁) = v(c₁₁) p₁ + v(c₁₂) p₂

EU (x₂) = v(c₂₁) p₁ + v(c₂₂) p₂

Or, more generally:

EU (x) = S v(c_xs) p_s

Maximization of expected utility then simply means that you choose that alternative which has the highest expected utility when it is calculated in the way described above.

So far all I have done is to describe exactly how one calculates the expected utility from an action. How can this procedure be justified as the rational way of making a choice? The answer is that the decision rule "maximize expected utility" (MEU) follows from what some people think are appealing axioms. More specifically, we must assume that the preference function v(× ) must (or should) satisfy the following:

1. Completeness (all possible consequences are ranked)

2. Continuity (increasing a probability will eventually make you switch from one alternative to another)

3.Transitivity (if you prefer x₁ to x₂ and x₂ to x₃, the you must also prefer x₁ to x₃)

4. Independence (my choice between x₁ and x₂ is not changed if each alternative is changed by the same amount, say x₃ is added to both alternative) (this is comparable to Savage's sure-thing principle).

von Neumann and Morenstern showed that if we accept these assumptions, then it follows that we should use the MEU rule to choose between the possible actions. The intuitive idea may have been around for a long time (at least since Bernoulli's solution to the St. Petersburg Paradox), but it was von Neuman and Morgenstern who rigorously proved that the MEU rule followed from certain appealing axioms. In the words of Hirschleifer and Riley (1992: 15):

The great contribution of Neumann and Morgenstern was to show that, given plausible assumptions about individual preferences, it is possible to construct a v(c) function - "cardinal" in that only positive linear transformations thereof are permissible - whose joint use with the Expected Utility Rule ... will lead to the correct ordering of actions.

They made the connection between the ranking of outcomes and the choice of action and proved that as long as certain restrictions on the preference function was accepted, the maximization of expected utility would necessarily follow.

The Expected Utility Hypothesis has been extensively discussed, and especially the fourth assumption (independence) has been questioned. The purpose of this section, however, was not to present a detailed review of the debates around the hypothesis (see, for instance, Machina 1987 or Sugden 1991). Instead I simply wanted to describe the basics of the theory and make its assumptions explicit.

 

4. Should we demand more or less than Expected Utility theory

What is the source of the probabilities used in calculation of expected utility and what - if any - restrictions should be place on the construction of probability estimates before we are willing to label the decision rational? von Neumann and Morgenstern's theory says little about this and they simply take probabilities as objectively given. In contrast to the few restrictions placed on beliefs, they include some demands that are in no way are obvious "demands of rationality." It is not rationality that requires us to have complete and continuous preferences (there is, for instance, nothing inherently irrational about non-continuous - lexicographic - preferences). However, this criticism should not be draw too far since von Neumann and Morgenstern did not present their axioms as "demands of rationality." They are rather "conditions that must be satisfied if the MEU rule is justified as the rational way of making a decision."

If we focus on the construction of beliefs, we find that different authors disagree on the degree to which the construction of beliefs should be made a part of the definition of rationality. The debate has at least two aspects: One intuitive, the other methodological. First, what does our intuition tell us about the rationality of including the formation of beliefs and the collection of information in the definition of rationality. Second, one could use methodological criteria like parsimony and fruitfulness to justify (or deny) the claim that rationality should be the working-hypothesis at all levels - be it the choice of action for given beliefs or the formation of beliefs.

To examine the first issue I have chosen to discuss two opposing views, that of Jon Elster and Russell Hardin. My argument is, in short, that Elster is right about the intuitiveness of demanding that our knowledge be rationally constructed before we label the decision rational.

 

1. The intuitive argument: Elster vs. Hardin

Elster's views on the definition of rational choice is can be summarized by the following quotation:

Ideally, a fully satisfactory rational-choice explanation of an action would have the following structure. It would show that the action is the (unique) best way of satisfying the full set of the agent's desires, given the (uniquely) best beliefs the agent could form, relatively to the (uniquely determined) optimal amount of evidence. We may refer to this as the optimality part of the explanation. In addition the explanation would show that the action was caused (in the right way) by the desires and beliefs, and the beliefs caused (in the right way) by consideration of the evidence. We may refer to this as the causal part of the explanation. These two parts together yield a first-best rational-choice explanation of the action. The optimality part by itself yields a second-best explanation, which, however, for practical purposes may have to suffice, given the difficulty of access to the psychic causality of the agent. (Elster 1985, p. 71)

According to this view there are two general demands that have to be met before we can use rational choice to explain an action: First, the demands of optimality. Second the demands of causality. The demands of optimality can be divided into three requirements: optimality in the choice of action from the feasible set, optimality of beliefs for a given set of information, and optimality in the collection of information. The two causal demands require that action and beliefs be caused "in the right way" given preferences, beliefs and evidence. For instance, assume it is rational for me to press a green button (not the red), and I do so. We would not call this a rational action is the reason I pressed the green button was that somebody pushed me and I accidentally hit it. The same goes for beliefs. I may, for example, make two errors when I calculate probabilities, but these two errors may cancel each other out so the final belief is optimal. This is an example of evidence causing the beliefs in the wrong (non-rational) way.

I now turn to a critical examination of the opposing view i.e. the view that we should not demand that our estimates be constructed in a rational fashion before we label the action rational. To do so I shall use Russell Hardin's arguments from his book One for All: The Logic of Group Conflict. Some may believe it is a bit on the side to discuss the rationality of individual action in ethnic conflicts in a paper on economics, but I believe there are good reasons for focusing on Hardin: He is a well respected academic (so I am not attacking a soft target); he knows the general topic well (he is an authority on game theory, collective action and rationality); and he discusses the specific question head on (should we require beliefs and the collection of information to be rational before we label the decision rational?). The fact that the context is ethnic violence and not, say, investment, makes little difference to the principles involved.

The aim of Hardin's book, expressed in his own words, is "to go as far as possible with a rational choice account of reputedly primordial, moral, and irrational phenomena of ethnic identification and action" (Hardin, 1995, p. 16). A short summary of his theory of ethnic violence goes as follows. It is rational to identify with a group since it provides both security, material benefits and satisfies a psychic need to belong somewhere. Being a member of a group affects your beliefs since it tends to reduce awareness of alternative ways of doing things, as well as inducing the belief that what "we" do is the right thing to do (is-ought fallacy). Given these beliefs, it becomes rational for people who want power to play on people's ignorance and the belief that we are "better" that the other groups. Finally, group violence happens when the leaders find it the best way of maintaining power (for instance to distract people from economic failure). Using nationalist propaganda, they create a belief that it is in people's self interest to engage in a pre-emptive attack against the other group. Once violence starts there is a spiral that only increases violence, since it creates hate as well as an even stronger belief that we must destroy the other side before they kill us (and there is no way the parties can credibly promise not to discriminate the other).

Although this to some extent is a plausible story, we have to ask whether it is intuitive to label it rational. More specifically, is the formation of beliefs behind nationalism and ethnic violence rational? Hardin admits that beliefs used to explain group conflict are "not convincing, even patently not so in the sense that it would not stand serious scrutiny..." (Hardin 1995, p. 62, emphasis removed). But how can it be rational to act on beliefs that are obviously wrong? Hardin's answer is worth quoting in at length:

One might say that the supposed knowledge of ethnic or national superiority is corrupt at its foundation. Unfortunately this is true also of other knowledge, perhaps of almost all knowledge of factual matters. [...] Hence, at their foundations there is little to be distinguish supposed knowledge of normative from that of factual matters [...] Should we say that anyone who acts on such knowledge is irrational? We could, but then we would be saying that virtually everyone's actions are always irrational. It seems more reasonable to say that one's beliefs may have corrupt foundations but that, given those beliefs, it is reasonable to act in certain ways rather than others is one wishes to achieve particular goals.

[...]

Someone who carries through on an ethnic commitment on the claim that her ethnic group is in fact superior, even normatively superior, to others, may not be any more irrational than I am in following my geographic knowledge. She merely follows the aggregated wisdom of her ethnic group. (Hardin 1995, p. 62-63)

In short, because all knowledge is corrupted at its base it "would be odd [...] to conclude that the action was irrational when taken if it was fully rational given the available knowledge" (Hardin 1995, p. 16, my emphasis).

Who is correct, Hardin or Elster? First of all, there are several internal inconsistencies in Hardin's argument. For instance, even if we agree that rationality demands only optimality for given information, it is difficult to see how people can believe that the individuals in their ethnic group descend from one "original" group-Eve. This is a common belief among nationalist (see Connor 1994). Hence, "patently false beliefs" do not require us to collect information to be falsified, they may be irrational even for a given knowledge. Another major inconsistency is revealed by his attack on communitarianism. Hardin writes:

The chief epistemological problem with particularistic communitarianism is that it violates the dictum of the epigraph of this chapter: The important thing is not to stop questioning [...] To question such beliefs is to increase the chance of bettering them. (Hardin 1995, p. 192)

Commonsense epistemology allows for variations in our confidence of our knowledge. My belief that concern for human welfare dominates concern for various community values or even community survival is radically different from my belief that certain rough physical laws hold sway over us. (Hardin 1995, p. 210)

If it is true that all knowledge is corrupt at its foundation (his justification for not making the construction of one's belief a part of the definition of rationality), then we should put little faith in the proposition that we can increase the reliability of our beliefs and values by questioning them.

Second, we might question the argument that all knowledge is equally corrupt at its foundation. As I shall discuss later, Jon Elster and Leif Johansen have made similar claims, but they do not go this far. Is it really true that all our knowledge is so weak that none of the differences are worth seeking out or acting on?

Third, and perhaps most important, is the suggestion that to demand that we should construct the set of knowledge in a rational way must lead us to conclude that "virtually everyone's actions are always irrational." My immediate response would be that his argument leads to an equally odd conclusion: To reject the demand for rational construction of beliefs makes almost all behaviour rational. A better solution, I believe, is to at least make some demands on the collection of information. It may be true that we do not know the optimal level, but it is still possible to know that we should at least collect some information and not collect everything. In short, the demand is: "One should collect an amount of evidence that lies between the upper and lower bounds that are defined by the problem situation ..." (Elster 1985, p. 71). This may leave a large zone of indeterminacy in between, but at least it excludes some options as irrational. Moreover, this demand on information collection does not commit me to the position that almost all action is irrational, as Hardin claims. Finally, his argument makes it far too easy (and uninteresting) to prove that a phenomenon is caused by individually "rational" action.

In the end it boils down to our intuition. Is it intuitive to buy a house or a car without first collecting some information about its quality? If the answer is no, then you accept some kind of demands on the collection of information before you label the decision rational. Would you say that a man who went out today to walk on water because he believed he was God, is rational? If no, then you accept that the beliefs have to have some relation to the evidence before the action is defined as rational.

 

2. The methodological arguments

In addition to the arguments about the intuitive appeal of including belief formation and information collection in the definition of rationality, we may add several methodological arguments. To understand these methodological arguments, it is useful to take a short look at the history of economic thought.

Roger E. Backhouse has described the modern trend in economics as follows:

In the post-war period economic theory has been dominated by the attempt to explain economic phenomena in terms of rational behaviour. In macroeconomic this has taken the form of providing a microeconomic foundation for macroeconomic theories: deriving macroeconomic relationships as the outcome of individuals' optimizing subject to the constraints imposed by their endowments, markets and technology. There has been an aversion to what Lucas has termed 'free parameters': parameters describing individual or market behaviour that are not derived from the assumption of utility or profit maximization. (Backhouse 1995, p. 118)

Another trend is the invasion of economic reasoning into subjects previously thought to be outside the scope of economics. Political science, Sociology and even psychology has been increasingly influenced by rational choice theories. Marriage, divorce, crime, ethnic violence and even suicide have all been subject to rational choice analysis.

In sum, there are at least three developments. First, the increasing emphasis on microfoundations. Second, the argument that the best microfoundation is rational choice. Third, the tendency towards economic imperialism. Taken together these three developments say something about what kind of methodological criteria academics, and particularly economists, regard as valuable.

The underlying methodological view is one that conceives of progress in a discipline as explaining as much as possible using as little as possible at the deepest level possible and in a way that can be quantified (and hence tested). Or to use the terminology of methodologists: We want: universalism, parsimony, reductionism and quantifiability. Searching for microfoundations means going deeeper, using rational choice is - arguably - due to a commitment to quantifiability and economic imperialism represent the attempt to explain more.

What is the relevance of this discussion for the definition of rational choice? Recall Elster's demand that a decision is not rational unless there is optimality in (1) the choice of action, (2) the formation of beliefs for given information, and (3) the collection of information. Hardin argued against at least (3), and possibly (2). My argument here is that Hardin is wrong since the very same principles that inspires those who favour the use and extension of rational choice theory, also means that the definition of rational choice should include both (2) and (3). The application of the principle of maximization to both the formation of beliefs and the collection of information increases parsomony, increases the scope of a single principle, provides deeper microfoundations and increases quantifiability.

The rational expectation revolution is itself an implicit indication that many economists have accepted a stronger definition of rationality. Before this revolution, one 'free parameters' was the assumption of either rigid or only backwards looking adaptive expectations. In the 1970s Lucas, again in the words of Backhouse (1995, p. 123) argued that optimizing behaviour "should be systematically applied to all aspects of macroeconomic models, including the formation of expectations." The same methodological argument applies to the collection of information.

 

3. Sub-conclusion

I have argued in favour of Elster's definition of rationality and against Hardin. The argument had two main aspects. First, there is the theoretical presupposition based on parsimony that if we assume maximizing behavior in the choice of action for given beliefs, then we should also assume it when people form beliefs and when they collect information. Second, when faced with some concrete examples it sounded intuitively wrong to exclude optimal beliefs and optimal collection of information from the definition of rationality.

 

5. Collecting an optimal amount of information?

 

1. Introduction

1. The standard economic theory: Hirschleifer and Riley

The choice about whether to collect information or not can be viewed as any other choice: We should try to collect more information when the expected utility of this alternative is higher than the expected utility of the other possible alternatives. But how do we work out the expected value of more information? And, what are the relevant variables?

To illustrate their general answers these question, Hirschleifer and Riley (1992, p. 173) use the example of an agent who believes there might be oil in a field. In this situation the agent has to decide whether to drill a test well or go ahead with a major investment without collecting more information. The structure of the prior beliefs is given by the agent's beliefs about the geological structure of the soil and there are three such structures (favourable geological structure: 0.9 probability of hitting oil, moderate: probability 0.3 of oil, hopeless: impossible to find oil). In the terminology of expected utility theory there are three "states of the world." Before drilling the agent believes that the probability of favourable geological structure is 0.1, the probability of a moderate structure is 0.5 and the probability of a hopeless structure is 0.4. Finally, they assume that the result of the test drill is not conclusive i.e. the result is only "wet" or "dry." Whether the result is "wet" or "dry" depends on the geological structure, and the probability of "wet" if the true state is "favourable geological structure" is 0.9, compared to 0.3 probability of wet for "moderate" and 0 probability of wet if the true state is "hopeless." Given all this rather condensed information, we now ask three questions. First, how should you estimate the probability of oil given the result from a test-drill. Second, what is the value of doing the test-drill (i.e. gather information). Third, how much should you be willing to pay for an information service (e.g. about the geological structure of the land).

To impose some order on the information, Hirschleifer and Riley use three different matrixes: the likelihood matrix (L), the joint probability matrix (J), and the posterior matrix (O). The likelihood matrix specifies the probability of each message given the state of the world, P(m|s); The joint probability matrix gives the probability of each combination of states and messages P(sm); Lastly, the posterior gives the probability of a state of the world give a message. Using the information above we have:

 

Table 3.1: The likelihood, joint probability and posterior matrix

	The likelihood matrix				The joint probability matrix					The posterior matrix
		Message
		Wet (m1)	Dry (m2)			Wet (m1)	Dry (m2)	Prior beliefs			Wet (m1)	Dry (m2)
States of the world (Geological structure)	Favorable (s1)	0.9	0.1		Favorable (s1)	0.09	0.01	0.1		Favorable (s1)	0.375	0.013
	Moderate (s2)	0.3	0.7		Moderate (s2)	0.15	0.35	0.5		Moderate (s2)	0.625	0.461
	Hopeless (s3)	0	1		Hopeless (s3)	0	0.40	0.4		Hopeless (s3)	0	0.526
						0.24	0.76

Note: Combining the likelihood matrix with the prior beliefs about the geological structure, we find the joint probability matrix. The posterior matrix is found by combining the information from the likelihood matrix and the joint probability matrix.

 

At this point a short summary of the intuition in these calculations may be in order. After the test drill you have two pieces of information relevant to the estimation of the probability of the various geological structures. First, the results of the test drill. Second, the prior beliefs about the geological structure. The final rational estimate is a combination of the two. For instance, initially the agent believed that the probability of a favourable geological structure was 0.1, but after receiving a message of "wet" the new probability estimate becomes 0.375. The method used to derive this result is called Bayesian updating and can be stated in words as follows: "The posterior probability that an individual should attach to state s, after receiving a message m, is equal to the prior probability pis multiplied by the likelihood qms of message m and then divided by a normalizing factor which is the overall probability of receiving the message" (p. 175)

Having considered the answer to the first question (how information "should" affect your beliefs") in some detail, it remains to answer the question of how much the information is worth. Hirschleifer and Riley (1992: 180) first define this as the difference between the expected utility of doing you will receive when choosing an action based on current information vs. the expected utility of choosing an action after receiving information.

w_n=U(x_m; p_s.m) - U(x₀; p_s.m)

However, the answer is slightly more complicated since the authors assume that people can only buy an "information service" and not one piece of information. Hence, in the oil-case we could buy a test, but we could not buy the result "wet" - the result of the test may be both wet and dry! The expected difference is the between the utility you will receive when choosing an action based on current information vs. the expected utility of choosing an action after receiving information (the sum of each expected difference multiplied by its probability).

W( m) = E w_n = S q_m U(x_m; p_.m) - U(x₀; p_.m)

W( m) = S q_m S p_s.m v(c*_s.m) - S S p_s.m q_m v(c*_s0),

W( m) = S S p_s.m q_m v(c*_s.m) - S p_s v(c*_s0)

To work out the precise answer in terms of oil, we have to make some assumptions about the costs and gains. Assume the following payoffs:

Drilling and wet: $1 000 000

Drilling and dry: -$ 400 000

Not drilling: -$50 000 (relocation costs)

If we also assume that the agent is risk-neutral, the preference scaling function is linear in income, v(c) = c. Hirschleifer and Riley then asks how much one would pay for a geological analysis before the test drill. In any case, if we follow their example, they assume that the likelihood matrix of the geological analysis is as follows

 

Table 3.2: The likelihood and posterior matrix (of the geological analysis)

	The likelihood matrix				The posterior matrix
		Message				Message
		Wet (m1)	Dry (m2)			Wet (m1)	Dry (m2)
States of the world (Geological structure)	wet	0.6	0.4		wet	0.486	0.136
	dry	0.2	0.8		dry	0.514	0.864

 

The expected gain from drilling (x₁) is -$64,000 [(0.24 * 1 000 000) + (0.76 * 400 000)]. This is less than the expected loss of not drilling (-$50,000). Hence, the optimal action before receiving information is "not drilling" with an expected payoff of -$50,000.

The next step is to calculate the expected utility of the optimal action after receiving information. If the message is "dry", the optimal action is "no drilling" with payoff -$50 000. If the message is wet, the best action is "drilling" with the expected payoff of $140,400. "So the expected value of the information is $140,400 + $50,000 = $190,400. This is the value of the message service" (p. 183).

More generally, the maximum a person should be willing to pay for an information service is the x that solves the following:

S S p_s.m q_m v(c*_{s.m -} x) = S p_s v(c*_s0)

The value of information can also be visualized in a diagram (pp. 181-182 in Hirschleifer and Riley).

This concludes my treatment of the standard theory of rational choice in economics and the standard frame for determining how much information to collect. The presentation in Hirschleifer and Riley is relatively sophisticated, but it is does not discuss the underlying problems involved. It is to these I now turn. Or, more specifically, I want to investigate two problems as they have been described by one author. In the section below I simply present the arguments, leaving the task of evaluation to the next two chapters.

 

2. Elster's arguments

 

1. A list of quotations

To enable the reader to follow the discussion, I have made the following table which summarizes Elster's writings on the impossibility of collecting an optimal amount of information.

 

Table 3.3: Elster's arguments about the possibility of collecting the optimal amount of information

Year	Source	Key pages	Is "infinite regress" mentioned?	Reference to Winter?	Quotation
1978	Logic and Society (book)	162 (173)	Yes	Yes	One might argue that "... satisfaction emerges as a variety of maximization once the costs of acquiring and evaluating information are taken into account. [176] Winter, then, in a surprisingly ignored paper, argued that this retort creates an infinite regress, for how do you solve the problem of finding the optimal amount of information? The 'choice of a profit maximizing information structure requires information, and it is not apparent how the aspiring profit maximizer acquires this information, or what guarantees that he does not pay an excessive price for it'." p. 162 (quoting Winter 1964)
1979	Ulysses and the Sirens (book)	58-60, 135	Yes	Yes	"Take the case of a multinational firm that decides not to enter the forward exchange market because the information costs of the operation would exceed the benefits. Then we shall have to ask how the firm decided how much information to acquire before taking the decision not to acquire the information needed in the forward exchange market. Unless one could prove (and I do not see how one could prove) that the deviation from the 'real' optimum converges to zero or at any rate rapidly becomes smaller for each new level in the hierarchy of information structures, this argument not only has the implication that in every decision there must be a cut-off point where calculation stops and you simply have to make an unsupported choice, but also that this point might as well be as close to the action as possible. Why, indeed, seek for precision in the second decimal if you are uncertain about the first?" p.59
1982	"Rationality" (a chapter in Fløistad (1982), A survey of contemporary philosophy)	112-113	Yes	Yes	Some "argue that firms are profit maximizers because otherwise they go bankrupt. The argument is particularly powerful because it is backed (Winter [6b] by an infinite regress argument against the very possibility of planned profit-maximizing. The argument, briefly, is this. In order to maximize, say, profits, you need information. As information is costly, it would be inefficient to gather all the potentially available information. One should rather settle for the optimal amount of information. But this means that the original maximization problem has not been solved, only replaced by a new one, that immediately raises the same problem." p. 112 (sic.)
1983	"The crisis in economic theory" (Review of Nelson and Winter (1982) in London Review of Books)	5, 6	Yes	Yes	"The Nelson-Winter attack on optimality is therefore a two-pronged one. The argument from satisficing is that firms cannot optimise ex ante, since they do not have and cannot get the information that would be required. Specifically, they would need an optimal amount information, but this leads to a new optimisation problem and hence into an infinite regress. On the other hand, we cannot expect firms to maximise ex post, since the elimination of the unfit does not operate with the same, speed and accuracy as it does in natural selection. Taken together, these two arguments strike at the root of neo-classical orthodoxy." p. 6
1983	Explaining Technical Change (book)	139-140	Yes	Yes	"One of his [S. Winter] contributions is of particular interest and importance: the demonstration that the neoclassical notion of maximizing involves an infinite regress and should be replaced by that of satisficing. The argument appears to me unassailable, yet it is not universally accepted among economists, no doubt because it does not lead to uniquely defined behavioral postulates." p. 139
1983	Sour Grapes (book)	17-18	Yes	Yes	"The demand for an optimal amount of evidence immediately leads to an infinite regress" p. 18
1985	"The nature and scope of rational choice explanations" (book chapter)	69	No	Yes	"In most cases it will be equally irrational to spend no time on collecting evidence and to spend most of one's time doing so. In between there is some optimal amount of time that should be spent on information-gathering. This, however, is true only in the objective sense that an observer who knew everything about the situation could assess the value of gathering information and find the point at which the marginal value of information equals marginal costs. But of course the agent who is groping towards a decision does not have the information needed to make an optimal decision with respect to information-collecting.[23] He knows, from first principles, that information is costly and that there is a trade-off between collecting information and using it, but he does not know what that trade-off is." (Elster 1985, p. 69)
1986	"Introduction" to the edited book: Rational Choice	14, 19	No	No	"It is not possible, however, to give general optimality criteria for the gathering of information." p. 14 "The non-existence of an optimal amount of evidence arises ... from our inability to assess the expected marginal value of information." p. 19
1989	Solomonic Judgements (book)	15-16	No	No	"Sometimes it is impossible to estimate the marginal cost and benefits of information. Consider a general in the midst of battle who does not know the exact disposition of the enemy troops. The value of more information, while potentially great, cannot be ascertained. Determining the expected value would require a highly implausible ability to form numerical estimates concerning the possible enemy positions." p. 16
1989	Nuts and Bolts (book)	35-38	No	Yes (bibliographical essay).	"Deciding how much evidence to collect can be tricky. If the situation is highly stereotyped, as medical diagnosis is we know pretty well the costs and benefits of additional information. In situations that are unique, novel and urgent , like fighting a battle or helping the victim in a car accident, both costs and benefits are highly uncertain ..." p. 35
1993	"Some unresolved problems in the theory of rational behaviour" (article in Acta Sociologica)	182-183	No	No	"Suppose than I am about to choose between going to law school or to a school of forestry - a choice not simply of career but of life style. I am attracted to both professions, but I cannot rank and compare them. If I had tried both for a lifetime, I might have been able to make an informed choice between them. As it is, I know too little about them to make a rational decision." p. 182

 

2. Distinguishing the two main arguments

First of all, the quotations indicate that there has been a shift in Elster's emphasis. From 1978 to 1983 the argument against the possibility of collecting an optimal amount of information was based on the infinite regress argument. After the important article from 1985, the focus turns to the empirical problems of estimating the value of information when we are in novel situations and when the environment is fast changing. As mentioned in the introduction I have labelled the first argument "the infinite regress problem" and the second "the estimation problem." Both arguments are used by Elster to argue that it is impossible to collect an optimal amount of information.

 

3. S.G. Winter and Elster's argument

The infinite regress argument is clearly inspired by S.G. Winter. The key quotation is:

The "choice of a profit maximizing information structure itself requires information, and it is not apparent how the aspiring profit maximizer acquires this information, or what guarantees that he does not pay an excessive price for it "(Winter 1964, quoted from Elster 1983, p. 139-140.)

Three things should be noted about this quotation. First, Winter does not use the term "infinite regress," nor does he do so in any of the articles I have read (Winter 1964a, 1964b, 1971, 1975). In fact, in Winter's article from 1975 the problem is said to be a potential "self-reference," not infinite regress. The distinction is important because the problem of self-reference need not involve the problem of infinite regress. Moreover, he explicitly admits that he has not proven that the problem is one of self-reference. As he writes:

the optimization whose scope covers all consideration including its own costs -- sounds like it may involve the logical difficulties of self-reference. To demonstrate this -- to prove logically that there is no superoptimization -- would require the development of a formal framework within which the statement could be interpreted. That would be an interesting project. But, whatever the outcome of that project, it is clear that 'optimization' as ostensively defined by pointing at appropriate portions of decision theory literature does not involve self-reference. (Winter, 1975, p. 83)

Second, the focus in the quotation from 1964 is on how somebody can acquire information about the value of more information. The term "not apparent" indicates some reservation whether the argument really is purely logical (it is impossible) or empirical (it is difficult). Third, there is something odd about the last sentence ("what guarantees that he does not pay an excessive price for it"). It seems to me that rationality does not demand that we never pay more than the true value of something. The question is whether we were justified in believing that the information was worth the costs when the decision was made. It may turn out that the information was less valuable than we believed, but - as Elster argues in Sour Grapes (p. 15-19) - it is possible to make rational mistakes.

Thus, an investigation into the sources leads me to question the appropriateness of Elster's reference to Winter when discussing the problem of infinite regress. True, Winter has frequently written about problems around the collection of information, but on the specific question of infinite regress he only mentions that there may be a problem of self-reference. He does not prove formally that this is the case (nor he does he try to do so).

And even if Winter had proved that there was a self-reference, it is not enough since he must also take a second step to prove that the self-reference involves a vicious infinite regress.

 

3. Are the arguments consistent?

1.  
2. Evaluating the infinite regress argument?

 

1. Infinite regress: A general overview

The problem of infinite regress in the theory of decision making has a curious history. Several decision theorists mention the problem briefly, but few discuss it in any detail. Some dismiss it as a fruitless problem, others believe it has the power to overturn traditional neo-classical economics. Some are unsure about whether there is an infinite regress problem at all, other think it is obvious that the problem exist, and some of these believe the problem has an obvious solution.

Among those who mention the problem but dismiss it as fruitless, are Raiffa and Savage:

Raiffa: "People often ask: 'How do you know whether or not it is worth the effort to make a formal analysis of the decision problem? Is this a decision problem itself? Can you do a decision analysis of whether it is worth doing a decision analysis?' I don't know anyone who can give definite answers to these questions, and I suspect one runs into a messy and explosive infinite regression if he tries to incorporate considerations of these questions into the formal structure of a decision theoretic model" (quoted from Smith 1991, 195). Originally 1968, p. 266.

Savage: "It might ... be stimulating, and it is certainly more realistic, to think of consideration or calculation as itself an act on which the person must decide. Though I have not explored the latter possibility carefully, I suspect that the attempt to do so leads to a fruitless and endless regression." (quoted from Conlisk (JEL), 1996, p. 687), originally in Savage 1954

Modern theorists have followed this example, either ignoring the problem or dismissing it briefly. For instance, M.C.W. Janssen says that "In order to avoid a discussion of the conceptual difficulties, I will not be concerned with the information-gathering process in what follows." (Janssen 1993, p. 14).

Some take the problem seriously, without really entering into a detailed discussion. For instance, Leif Johansen has written than:

The question of how far to go ... is in itself an optimization problem, but a peculiar one in that it can itself not be subjected to analysis ... at least in the last instance. Should one try to analyse the question of how to strike an optimal balance ... then the same question could be raised in relation to this question an so on. At some point a decision has to be taken on intuitive grounds. (1977, 144, quoted in Conlisk 1996, 687)

In fact, after extensive search I found only four major papers with a detailed discussion of the problem of infinite regress: Mongin and Walliser (1986), Smith (1987), Lipman (1991) and Vassilakis (1992). There is some related work on "beliefs about beliefs" and common knowledge problems (see Sargent 1991 and Mertens & Zamir 1985), but I did not enter into this literature as I restricted myself to one-person decision theory. There is also some relevant work within search theory, for instance Baumol and Quandt (1964). Finally, there is an extensive philosophical literature on the problem of induction and infinite regress. These issues, however, are somewhat peripheral and the four papers above are the only detailed discussions of the core problem. Altogether I therefore have to agree with John Conlisk when he writes that "Given the vast number of exposition of choice theory, it is remarkable how infrequently the regress issue is mentioned ..." (Conlisk 1996, p. 687).

Moreover, an examination of the four articles reveal that they are discussing slightly different topics as well as taking very different approaches. Elster's focus is on infinite regress as a cause of the impossibility of collecting an optimal amount of information. Smith's focus is not on the collection of information, but on how to decide how to decide. The same is true of Mongin and Walliser, but they approach the question in a much more formal manner than Smith. Lipman also tries to tackle the same question, but he notes that his approach is very different from Mongin and Walliser. In sum, given the lack of papers, the importance of the problem and the difference in the existing papers, the issue of infinite regress is virtually crying out for a detailed and possibly unified treatment.

Unfortunately, I do not possess the abilities to provide this. Of the three possible levels of the infinite regress problem and the various approaches, I have chosen to focus on mainly on Elster, less on Winter, and even less on Lipman, Mongin&Walliser and Smith.

 

2. Elster's argument: A visualization

The infinite regress problem is presented as follows by Elster in an article from 1982:

In order to maximize, say, profits, you need information. As information is costly, it would be inefficient to gather all the potentially available information. One should rather settle for the optimal amount of information. But this means that the original maximization problem has not been solved, only replaced by a new one, that immediately raises the same problem (Elster 1982, p. 112)

Visualized the argument may look like this:

Figure 4.1: Elster's infinite regress argument

Figure 1

1. Collect an optimal amount of information (the first maximization problem)
2. To do (1) we must first collect information about how much information it would be optimal to collect (the second maximization problem).
3. To do (3) we have to collect an optimal amount of information about how much information we should collect before we decide how much information to collect (the third maximization problem).
...
...
and so on forever

 

 

 

Since the chain goes on forever, the argument is that the original problem has no rational solution. My question is this: Is it really true that we have to collect information before we decide how much information to collect? Is this not to demand that the agent always should know something that he does not know?

 

3. The first counterargument: Do the best you can!

Imagine the following reply to Elster's infinite regress argument as visualized in Figure 4.1: At any point in time you simply have to base your decision on what you know at that time. This includes the decision about how much information to gather. Previous experience in making decisions and gathering information may give you some basis for estimating how much information to collect (or it may not, but this is an empirical question). In any case, the rational decision is simply to choose the best alternative - act or collect more information - that has the highest expected utility given your beliefs at time zero. The situation could be visualized as in Figure 4.2. At time t=0 you want to make a rational decision about what to do, either to "act now" or to "collect more information."

Figure 4.2: The choice situation

Figure 2

   Act
0

 

Collect ...

 

When the problem is visualized in this way, one infinite regress problem is simply that the branching could go on forever. This, in turn, means that it may be impossible to work out the expected utility of collecting more information, and/or that the value of collecting more information may always be greater than "act." In practice, however, there is little reason to expect an infinite regress problem in the collection of information. Many decisions simply cannot be postponed forever i.e. in the words of Holly Smith (1987) the decision is non-deferral. In fact, as he also notes, all decisions are non-deferral since all humans eventually die. As long as this is the case, it seems rational to me simply to start at t=0 and base your choice of whether to collect more information on your beliefs about the net value of collecting more information. We avoid the infinite regress since it would not be rational to include the options after your death (or after the time limit) in the calculation.

Second, even if the decision could be postponed forever, the benefits of collecting more information might decrease and as such the problem has a solution in the limit. Of course, the real question is not only whether the problem has a solution in the limit, but whether it is possible for the agent to know this and the precise trade-off that enables him to make the rational choice about whether to collect more information or not. The answer is to base your decision on the best possible beliefs about the value of more information at time t=0. Should I collect more information? Yes, if my beliefs (based on all my past experiences up to t=0) tell me that more information has a higher expected utility than acting now. Is it possible to estimate the expected net value of more information? The intuitive answer is simply to use your previous experience up to t=0 to form beliefs about how much more information is worth. Of course, this is easier said than done, but sometimes you may compare with similar situations in the past (classical view of probability); sometimes you may use a theory which is developed using past data to predict the value of more information); and, finally, some would argue that it is rational to base your decision simply on your subjective beliefs regarding the value of more information.

In sum, the only way Elster's infinite regress in the collection of information could get off the ground (if the visualization in Figure 4.1 is correct) would be that we have an agent who is immortal (or acting on behalf on something which is immortal), the decision can be postponed forever and the value of information does not eventually converge. A problems based on these assumptions do not appear very significant in the real world.

 

4. Arguing against the counterargument: Radical scepticism and costly deliberation

A number of counterarguments can be made to the above argument that it is rational to base your choice of whether to collect more information on your current beliefs and that this "solves" the infinite regress problem. Some of these arguments are "internal" to Elster in the sense that he discusses the issues, and these will be dealt with later (for instance that the beliefs are too weak, that the numerical beliefs do not exist or that the beliefs are biased). Some of the other arguments, however, are "external" i.e. arguments that may make the problem reappear but only in ways that - I shall argue - are not consistent with Elster's arguments. Two of these will be dealt with here. First, the argument that it is never rational to base your beliefs on past experience since it is impossible to "prove" the rationality of induction. Second, there is the problem that we are not logically omnipotent, so even "forming the best beliefs" is a costly process that we should consider in the optimization process.

The problem of induction and the possibility of radical scepticism was introduced by David Hume and have been extensively discusses among philosophers ever since. Once again we find that an infinite regress is the cause of the problem: We need to justify the method by which we go from the past to the future, and this justification, in turn, needs to be justified and this also needs to be justified and so on (for more on the philosophy of knowledge and the problem of infinite regress, see Nozick 1981, ch. 3, especially p. 268-280). For instance, in the case of medical diagnostic we may try to justify the inference that the third test costs $49 150 for each life saved. The radical sceptic then argues that even if this cost is a true description of the past, you do not know whether it will hold in the future. Trying to defend yourself you claim that the general method behind your statistical method of processing information from the past to predict the future has succeeded quite well in the past for a great many different cases, not only medical diagnosis. But the sceptic counters this by the repeating his argument: Even if the general method has performed well in the past you cannot prove that it will continue to perform well in the future. There is, the sceptic claims, no rational basis for induction.

We may deny the paradox at the very start (denying the regress) or we may say that it is possible to stop the regress at some level (Nozick claims that this is possible, p. 275-280). In the current context, however, it is not necessary to go further. It is true that radical scepticism is one possible counterargument to the statement that "it is rational to base you decision on the expectations formed on the basis of your beliefs at t=0", but the argument is not available to Elster. He accepts that it is sometimes possible to collect close to an optimal amount of information (as in the example of medical diagnosis). By so doing he rejects radical scepticism and since the current context is an evaluation of Elster's arguments we do not need to spend more time on radical scepticism as a cause of indeterminacy in the rational collection of information.

To discuss the second possible counterargument, we need to follow Smith (1987) and distinguish between deliberation and search. Deliberation is costly because we have limited cognitive abilities and it takes time and effort to work out the best beliefs for a given set of knowledge. Search is the activity of gathering more information. The advice "base your action (on whether to collect more information) on the best possible beliefs you can form given your knowledge at t=0" ignores the costs of deliberation. It may not even be rational to form "the best possible beliefs" once we take into account the cost of deliberation. Moreover, deciding how much deliberation to conduct also raises an infinite regress problem - you have to deliberate on how much deliberation to do on how much deliberation .... Thus, the infinite regress is once again resurrected.

Once again I will claim that this resurrection does not correspond to Elster's presentation of infinite regress. Elster explicitly writes about infinite regress in search and not deliberation. I do not know whether it is true - as Smith claims - that most authors who discuss the problem of infinite regress do so in the context of deliberation. I am reasonably sure, however, that he misleads us by quoting Elster to exemplify an author who discusses infinite regress in deliberation. Thus, while there may be an infinite regress in deliberation, this is not the problem Elster focuses on and I do not have to deal with "infinite regress in deliberation" to argue against him.

 

5. An alternative interpretation: Information about information about ...

There is, however, a more plausible interpretation which may make the problem appear in a way that is consistent with Elster. Consider the visualization presented in Figure 4.3. Here the problem at t=0 is that the set of possible actions is infinite. The choice is not only between "act now" and "collect more information" since the "collect more information is really a general category which includes an infinite set of alternatives. Hence, at t=0, one option is to act right away, another is to collect information directly relevant to the problem; A third option is to collect information about how much information you should collect. Fourth, you may collect information about how much information to collect before you decide how much information you are going to collect. And so we could go on forever.

Figure 4.3: The infinite set of alternatives

Figure 3

Possible alternatives at time 0:
1. Act
2. Collect information
3. Collect information about how much information you should collect
4. Collect information about how much information you should collect to decide how much information to collect.
...
...

 

 

If the problem is visualized in this way it is less obvious that the non-deferral of decisions can solve the problem. Among all the feasible alternatives at t=0 we want to choose the one that has the highest expected utility. If the set of feasible actions is not well defined (i.e. it is infinite), then we do not know for certain whether some alternative "far down" would be of higher expected value.

 

6. Trying to argue against the alternative interpretation

One possible counterargument against the infinite regress in Figure 3, could be that it is not feasible (given limitations in the human mind) to go very deep. For instance Lipman's "solution" of the infinite regress involves a restriction on the feasible set of computations which in his words "can be viewed as a restriction the complexity of the calculation the agent can carry out" (Lipman 1991, p.1112). Most people are not able to go beyond three or at most four levels of reasoning of the type "I know that you know that he knows ..." Even experts in strategic thinking cannot go further than about seven levels. This might indicate either that this information is not so valuable, or that it is difficult to utilize it given our cognitive limitations, which in turn makes the information less valuable. If we then define rationality as "doing the best we can", then considering your own cognitive limitations may "solve" the infinite regress problem. Given your own cognitive limitations it becomes rational not to go very deep! How convincing is this argument?

I am unsure, but I do not think we should allow the argument about limited human cognitive abilities much weight in the current context. The key question in this paper is whether it is possible to collect an optimal amount of information. "Possible" may be interpreted to mean "is it feasible given unavoidable constraints?" The reason I am reluctant to use "limited human cognitive abilities" as an argument against the infinite regress argument, is that we may overcome (at least some) of our cognitive weaknesses (i.e. they are not unavoidable). And, as Savage (1967) argued, we want to use the theory of rationality to police our own decisions - as a tool to find the best possible decision. There is a question of degrees here, but including human limitations makes it too easy to label actions rational, reduces the utility of the theory as a guide to what we should do, and - finally - it seems to me to be a case of mislabelling to argue that human cognitive weaknesses represent a logical problem. In sum, I do not want to use this argument against the infinite regress problem.

There is, however, a second possible argument against the infinite regress in Figure 3. It is the same argument that was used to "solve" the problem as visualized in Figure 2. That is, if the decision is non-deferral the set of relevant alternatives is also constrained. True, one could always choose to collect information at some very deep level at time t=0, but as long as we know that time is limited the value of doing so is zero since after collecting this information we have to go through all the other levels before we finally make a decision. After collecting information about how much information to collect we have to go out and collect the information. Since this process is time-consuming, time constraints limits the depth of the feasible set than needs to be considered.

Unfortunately, the argument has a weakness. Collecting information about how much information to collect may in fact reduce the overall time spent collecting information. For example, after collecting information about how much information to collect, you may find that the optimal amount of information one level down is very low, even zero. I am unsure about the implications of this problem for the existence of the infinite regress argument.

 

7. Sub-conclusion

I have so far tried to understand Elster's argument on the impossibility of collecting an optimal amount of information because of the infinite regress problem. My conclusion is that the argument probably does not demonstrate a significant problem in rational choice theory. Empirically the conditions under which it may arise are very restrictive and I do not think it constitutes a logical proof against the very possibility of choosing an optimal amount of information. I want to note, however, that I have only discussed this problem in the context of how much information to gather. There are at least two other categories of infinite regress problems that I have not discussed. That is, first, to decide how to decide. And, second, to form beliefs using a fixed set of information (for instance, the problems involved in reasoning like "I know that you know that I know ..."). Moreover, I have excluded some possible interpretations that make the problem reappear because they were inconsistent with Elster's interpretation. There may be significant problems here for rational choice theory, but that was not the topic of the section above. Ignoring the other problems I focused on possible interpretations of Elster views and found them - with one exception - that the problem was not significant. The one possible exception is what we should do when gathering information at a deep level also may reduce the optimal amount of information at lower levels.

 

3.  
4. The problem of estimation

 

1. Introduction

It may be impossible to collect an optimal amount of information even if even if there is no logical problem of infinite regress. For instance, when we are in a unique situation we cannot determine the value of information from historical experience of similar situations, and hence there is (on the classical view of probability) no rational basis for estimating the value of information. I have labeled these problems the estimation problem and I have characterized it as Elster's second main argument against the possibility of collecting an optimal amount of information. As argued in chapter three there is a shift towards this line of argument after Elster's article from 1985. In that article, and later, Elster does not use the term "inifinite regress" and he does not quote S.G. Winter. Instead, the argument focuses on the problems involved in the formation of probabilities. The purpose of this section is to examine this view more closely.

 

2. What are the arguments?

Elster's general position is that "beliefs are indeterminate when the evidence is insufficient to justify a judgment about the likelihood of the various outcomes of action. This can happen in two main ways: through uncertainty, especially about the future, and through strategic action" (Nuts and Bolts, p. 33). More specifically the following two quotations illustrate some of the causes of the problem according to Elster:

Deciding how much evidence to collect can be tricky. If the situation is highly stereotyped, as medical diagnosis is we know pretty well the costs and benefits of additional information. In situations that are unique, novel and urgent, like fighting a battle or helping the victim in a car accident, both costs and benefits are highly uncertain ... (Nuts and Bolts, p. 35, my emphasis)

In many everyday decisions, however, not to speak of military or business decisions, a combination of factors conspire to pull the lower and upper bounds [on how much information it would be rational to collect] apart from one another. The situation is novel, so that past experience is of limited help. It is changing rapidly, so that information runs the risk of becoming obsolete. If the decision is urgent and important, one may expect both the benefits and the opportunity costs of information-collecting to be high, but this is not to say that one can estimate the relevant marginal equalities. (Elster 1985, p. 70, my emphasis)

To impose some order on the following discussion, I want to make a distinction between three types of probability, three types of problems and three types of implications.

On probability, we may follow Elster (ETC, p. 195-199) and distinguish between the following concepts of probability according to their source: objective probabilities (using relative frequency as source), theoretical probability (the source of the estimate is a theory such as a weather prediction), and subjective probability (degrees of belief as measured by willingness to make bets on the belief).

As for the three problems, I want to make a conceptual distinction between non-existent probabilities, weak (but unbiased) probabilities and biased probabilities. Elster seems to argue that both non-existence and weak probabilities represent indeterminacy (see the first quotation, NB p. 33), but I believe it is important to distinguish between the two since the question in this chapter is whether it is impossible to form beliefs about the value of information.

Finally, I want to separate the following three implications related to the arguments about probabilities. First, the advice that uncertainty makes it rational to use the maximin strategy. Second, that it is intellectually honest to use a strategy of randomizations in situations of radical uncertainty. Third, that uncertainty implies that we should not seek more information since it is wasteful to spend resources deciphering the second decimal when we cannot know the first. The paragraphs below elaborate on each of these three distinctions.

In Explaining Technical Change Elster (1983, p. 185) argues that "there are two forms of uncertainty [risk and ignorance] that differ profoundly in their implications for action. [...]. To this analytical distinction there corresponds a distinction between two criteria for rational choice, which may be roughly expressed as 'maximize expected utility' and 'maximize minimal utility'." More specifically, the argument is that the choice between fossile, nuclear and hydroelectric energy source should be determined not by trying to assign numerical probabilities to the outcomes, but by selecting that alternative which has the least worst consequence (minimax). To justify this principle, Elster appeals to a paper by Arrow and Hurwicz (1972). Hence, one implication of the impossibility of estimating probabilities - Elster claims - is that we should use minimax instead of maximizing expected utility (see also ETC p. 76).

In a different context, the argument is that intellectual honesty implies that we should use a strategy of randomization when we are in situations of ignorance:

"The basic reason for using lotteries to make decisions is honesty. Honesty requires us to recognize the persvasiveness of uncertainty and incommensurability, rather than deny or avoid it. Some decisions are going to be arbitrary and epistemically random no matter what we do, no matter how hard we try to base them on reasons." (SJ, p. 121)

 

The idea is followed up in a chapter discussing rules about child custody after a divorce in which Elster argues that it may be better to toss a coin than to make an impossible attempt to determine who of the parents will be best for the child.

A third implication of uncertainty, according to Elster, is that it is wasteful to collect a lot of information: "it is often more rational to admit ignorance than to strive for numerical quasi-precision in the measurement of belief" (US, p. 128).

In sum, Elster presents a number of arguments about our inability to form reliable estimates and the implications of this inability. Probabilities can be non-existent, weak or biased and this implies that it may be rational to use maximin when this is possible, and it is more honest to use randomization (when maximin is impossible) than try to maximize expected utility, and that it is irrational to collect information about the second decimal in a problem when the first decimal is unknown.

 

Table 5.1: An overview of Elster's arguments about the problem of estimation and their implications

Probability concept	Problem	Cause	Implication a	Justification	Example
Objective/ Theoretical	Non-existent probabilities	Brute and strategic uncertainty	Maximin b	Arrow+Hurwicz proof (Best end result?).	Choice between fossile, nuclear and hydroelectric energy
Objective/ Subjective/ Theoretical	Weak probabilities	Brute and strategic uncertainty	Randomization/ Maximin	Intellectual honesty	Choice of career (forester or lawyer)
Subjective	Biased probabilities	Hot and cold cognitive mechanisms	Randomization?	Better end result	Investment choices?

(a) Implication for all: We should not waste time seeking information when such information is impossible to find or only weakly significant.

(b) Assuming we know the best/worst possible outcome.

 

3. Are the arguments valid?

I have chosen to discuss the validity of Elster's arguments under three headings. First, how strong is the argument about the non-existence of probabilities (which involves a discussion of subjective and objective probability). Second, how sound is the argument that randomization is preferable (since it is more honest) in situations of weak probabilities. Third, what is the relevance of biased probabilities to the indeterminacy of rational choice? Within these three headings I want to discuss both the validity of the arguments in isolation, and their consistency with Elster's other arguments.

1. On the existence of probability estimates - subjective or objective?

The principle of maximization of expected utility (MEU) presuppose that the agent has or can form probabilities about the possible consequences of an action. Hence, if it can be shown that these probabilities do not exist, it implies that MEU cannot be used in that situation. This means, As Elster argues, that uniqueness, novelty and fast changing environments are problematic for expected utility theory because we cannot use previous experience of similar situations to estimate the relevant probabilities. One possible counterargument is that Elster's arguments about uniqueness and non-existence of probabilities is heavily dependent on the classical view of probability as relative frequency. If, for instance, we use the concept of theoretical probability it seems perfectly possible to get reasonable estimates even from unique combinations of weather observations. Another, and in this context more significant counterargument, is the view that probabilities should be interpreted as measures of subjective uncertainty, in which case it is perfectly possible to speak about probability even in unique situations.

 

1. Subjective probabilities

1. Weak probabilities and the argument for randomization

First of all, we must ask in what sense probabilities are weak. Since I want to distinguish between bias and weakness, I shall reserve the label weak for beliefs that are unbiased. Conceptually the distinction is important. For instance, we may form a belief about the colour of the balls in an urn based on a sample of three balls (say we know that the balls are either blue or yellow, but that we do not know how many are blue and how many are yellow). This belief is not very strong, but - if the proper statistical formulas are applied - it is not biased.

As mentioned Elster argues that some beliefs are too weak to justify inclusion in a rational calculation of net expected utility (and that we for this reason should refrain from choosing actions based on such calculations).

In my ignorance about the first decimal - whether my life will go better as a lawyer or as a forester - I look to the second decimal. Perhaps I opt for law school because that will make it easier for me to visit my parents. This way of deciding is as good as any - but it is not one that can be underwritten by rational choice as superior to, say, just tossing a coin. (SJ, p. 10)

I think the argument is weak. Assume you have to choose between the following two alternatives:

A: 10 000 USD with an estimated probability of 50.01 (and 0 with probability 49.99)

B: 10 000 USD with an estimated probability of 49.99 (and 0 with probability 50.01)

I would choose A even if my I knew that the variance in my estimated probability was high. True, my choice is not accompanied with great conviction that a is much better than B, but why toss coins as long as I have an option that gives a higher expected payoff? Elster might reply that this choice is an example of hyperrationality ("defined as the failure to recognize the failure of rational choice theory to yield unique prescriptions or predictions." SJ, p.17). I agree that it would be irrational to spend much time and money trying to estimate the second decimal if we were ignorant about the first in the case above, but that is not the question. We do not ask whether it is profitable to collect more information, but which choice you should make for a given set of information.

One might argue that the difference is small in the example above, but the true comparison is not simply between the difference in probability, but the difference in expected utility when the probabilities are multiplied by the payoffs. In the case above the difference is $200, which seems to me to be a non-negligible sum. The larger the payoff the more significant the small difference in probability is. This argument seems to reveal a tension in Elster's view: In the quotations at the beginning of this chapter he argues that both weak probabilities and large payoffs (importance) pull in the direction of "coin-tossing", but the factors (at least in my example) pull in separate directions.

There is, however, an even more serious problem with Elster's suggestion. In the real world we will encounter many choices in which we may rely on probabilities of varying reliability. Sometimes we are very uncertain, sometimes we are more certain. Let us compare the following two rules for choosing what to do (decision-guides):

A: If our beliefs are very weak, you should (or weaker: might as well) toss a coin to decide the matter; if the beliefs are reliable, you should choose the alternative with the highest expected utility (Elster's strategy)

B: Choose the action with the highest expected utility both in situations with weak and strong beliefs. (Bayesian strategy)

The fact that we have to make many choices means that the many small differences becomes large in aggregate. As a Bayesian says in response to why we should choose B:

... life is full of uncertainties - in a given week, you may buy insurance, bet on a football game, make a guess on an exam question, and so forth. As you add up the uncertainties of the events, the law of large numbers come into play, and the expected value determine your long-run gains (Gelman 1998, p. 168).

Another problem with Elster's decision-rule, is the fact that before we make a decision we have to determine whether the situation is one of "enough" certainty to use chose the action that maximizes expected utility, or whether we are so uncertain that we should randomize (or something else, like maximin). Where is the limit, and is it not costly to do examine the circumstances in this way every time we have to make a decision? Of course, we could go all the way and say that all our knowledge is always so weak that we always should toss coins. In this way we could avoid the problem of choosing when using Elster's strategy. Sometimes Elster is attracted to this argument, but at other times he seems to want to "have the cake and eat it." For instance, he is sympathetic to Descartes when he claims that our knowledge is limited in a way that can be compared to being lost in the forest. Yet, when discussing child custody after a divorce he does not want to go all the way and argue that it might as well always be decided using randomization. In some "obvious" cases the court should not toss a coin (SJ, p. 170-171). But then the court first has to examine whether the case is obvious and this process is costly in the same way (but maybe not to the same extent) that a trial about child-custody would be. In short, either decision-rule A has a problem in terms of deciding when to toss a coin, or one has to believe that we are so lost that we might as well always toss coins.

 

2. The relevance of biased probabilities

1. Sub-conclusion: Elster on the problem of estimation

Sometime Elster argues that some people have good judgement (see e.g. SG, p. 16, ETC p. 87). It seems to me that this implicitly reveals that it is often possible to form rational beliefs about the value of information. If we really lived in a world in which we were lost in the forest, there would be no judgment - only luck and unluck. I am still unsure about the extent to which we are inherently "lost" (i.e. for reasons other than our limited abilities), but I do think this section has demonstrated some weaknesses in the argument that the estimation problems implies that it is often impossible to form rational estimates about the value of information.

 

2. How much do you have to know to conduct an optimal search?

Expected utility theory is about choice in general, while this paper is about one particular type of choice viz. the choice of how much information to collect. As mentioned, Elster often makes the argument that we know too little to conduct a rational search. To examine this question from another angel, I made a few investigations into search theory in economics. The literature starts with Stigler (1960). Another landmark is Rotschild (1974), and there are good surveys in Hey (1980, 1981).

 

1. Stigler

Stigler (1960) starts by noting that price dispersion is an empirical fact. This, in turn, makes it profitable to search for the lowest price before you buy a product. However searching is costly, so the question is whether there is an optimal amount of search. Stigler shows that if we assume the distribution of prices is known, then it is possible to conduct an optimal search. Assume, for instance, that we know that half of the stores charge $1 and the other half charge $2 for the same product. This implies that the expected price if we visit one store is $1.50. If we sample two stores, the probability of finding one with the lowest price is one minus the probability of sampling two stores with high prices:

Probability of finding at least one store with the minimum price = 1 - ( 1/2 * 1/2)= 0.75

Thus, the expected price if we try two stores is $1.25 [(1 * 0.75) + (2 * 0.25)]

and the gain visiting one more store (going from one to two) is $0.25. In the same way we can calculate the expected price after sampling n stores and the gain from going from n-1 to n:

 

Table 5.2 Expected price after sampling n stores

Number of stores visited (n)	Probability of finding at least one store with the lowest price	Probability of n stores with highest price	Expected price	Expected gain from increasing sample from n-1 to n
1	0.5	0.5	1.5
2	0.75	0.25	1.25	0.25
3	0.875	0.125	1.125	0.125
4	0.9375	0.0625	1.0625	0.0625
...	...	...	...	...

Based on this one might believe that the choice of an optimal amount of information is simple. The collection of information is optimal when the expected gain is equal (or as close as possible) to the expected cost of further collection. Assuming that the cost of going to one more store (or taking one more phone call or whatever it is that brings information) is known this is a simple exercise. In our case, if the cost of increasing the sample size by one is 0.11 (and constant for al n), the optimal search is n=3.

Unfortunately, things are not that simple. There are two main problems. First, the claimed optimal search rule is not optimal at all. Second, to make the example work we had to make some quite strong assumptions, such as the one about knowing the distribution of prices.

Here is an illustration of the first problem: Assume that you find the lowest price in the first store. It is then pointless to search more stores even if the "optimal rule" told you to sample three stores. One might try to avoid this problem by specifying the following rule: "Collect n price quotations, but stop searching before n if you find the lowest price." This, however, does not solve all our problems. Imagine, for instance, that you decide to collect three price quotations (which was the optimal size of sample), but you happen to draw three stores with the highest price. Should you then resign and buy the commodity at the highest price? In fact, after conducting three searches and having found three high prices, it is still optimal to conduct new searches. Stigler's "fixed sample rule" is not "credible" since it is not optimal to stop after collecting the "optimal" number of price quotations if these quotations are all high. The expected gain of collecting one more after collecting n high prices is always 0.5 which is higher than the cost of searching. This is a general problem with "fixed sample" search rules, and to be fair Stigler is aware of the problem, but "leave it to other" to specify the optimal sequential search procedure.

The second problem worth mentioning is the rather stringent assumptions needed to make the example work. Take, for instance, the assumption that the individual knows the probability distribution of prices. First, it seems strange to assume that you know the distribution but do not know anything about which stores are most likely to have the lowest price. Second, often we do not have a good idea of the true distribution so we have to ask whether it is possible to conduct a search when the distribution is unknown. The first of these is not really a problem since it is at least logically possible to know the general shape of the distribution without having specific knowledge of where to find the lowest price. I shall return to this later. The second problem has been partially answered by Rotschild (1974).

 

2. Rotschild

1.  
2. Implications

 

1. Introduction

1. What is economics?

Let me start with a very basic question: What is economics? There are many possible answers, ranging from the enjoyable ("Economics is what economists do", Jacob Viner cited in Barber 1987?, p. 88), to the frequently quoted ("Economics is the science which studies human behavior as a relationship between ends and scarce means that have alternative uses", Lionel Robbins quoted in Stigler 1984, p. 301), and finally to the very strongly held conviction expressed by Gary Becker:

"The combined assumptions of maximizing behavior, market equilibrium, and stable preferences, used relentlessly and unflinchingly, form the heart of the economic approach." (Quoted in Hirschleifer 1985, 301. Originally in Becker 1976, p. 4)

A short survey of the field, however, reveals the following two distinctions. First, there is disagreement on what questions economists should try to answer (What does the subject matter include - all behaviour or only a subset of "economic" behaviour?). Second, there is disagreement about how one should go about answering the questions (Are only rational choice explanations acceptable or are we also willing to include norm-based or psychological explanations). Cross tabulating these two distinctions, we have the following table:

 

Figure 6.1: What is economics?

		What is the subject matter?
		Some forms of behaviour	All behaviour
What is the method?	Rational choice analysis	Core economics		Imperial economics
	Focus on non-rational mechanisms (psychology, norms)	Behavioural economics		Imperial sociology

Economists in the first category work on traditional economic problems using the assumption of rational choice. Those who try to extend rational choice analysis to other areas (crime, divorce, marriage, ethnic conflict and even suicide) can be labeled imperial economists. A prime example in this tradition is the already mentioned Gary Becker. Economists focusing on the "macrofoundations of the micro" often argue that economists need to pay more attention to sociology. Finally, we have the behavioural economists who want to use psychology to explain traditional economic problems like why firms behave the way they do (Winter), consumption (Veblen), unemployment (Solow) and economic fluctuations (Keynes?).

It is not my purpose here give a comprehensive answer as to who is right and exactly where economists or different arguments should be located in the grid above. Even if this was the purpose, it may not be a very fruitful task. To ask who is right only gives meaning in those cases in which there is a conflict and we have neutral criteria to determine who is correct. Since the term "economics" - unlike, say, a cow - does not denote something that actually exists, there is no neutral criterion to judge by. And even if we could agree to some of the general criteria that should be satisfied by all good economic approaches (explanatory success, predictive success, fruitfulness, parsimony), the answer may still be indeterminate - what is fruitful in your opinion need not be fruitful in my opinion. For instance, there is no neutral weighting between explanatory scope and success. One approach may be very successful in a very restricted domain, but how is this to be compared against a less parsimonious theory that is somewhat less successful in a wider domain?

It is, however, my purpose to discuss how the arguments in the previous chapter relate to the question of behavioural economics. First of all, if I am correct to argue that there is no logical infinite regress argument in the collection of information, then it is wrong to use the infinite regress argument in support of behavioural economics. The argument is particularly important because infinite regress is presented as a logical impossibility in the theory of rational choice. Logical arguments of this type are more damaging than empirical arguments of the type "this is not how most people usually behave." Thus, it may seem that my argument in the previous chapter supports the imperial economists against the behaviouralists.

The second point reduces the force of the first conclusion. Even if the infinite regress argument about the collection of information fails, we are still left with the estimation problem. The cognitive abilities that are needed to solve this problem is - as we have seen - very large. This is a well known point which need not be elaborated (See e.g. Arrow, 1987). This, in turn, strengthens the claim that we need to examine the cognitive processes to understand economic outcomes.

Third, it is not only in the collection of information that the infinite regress argument may appear. For instance, Lipman (1991) and Smith (1987) both discuss how we should decide how to decide. Although this problem is clearly related to the problem of how to decide how much information to collect (in two senses: first: to decide how to decide we need to collect information. Second, they are structurally similar - Vassilakis (1992) tries to give a general solution to all such problems), they are conceptually distinct. Even if we assume that it has been determined that we shall decide using MEU, it may turn out that there is a problem in the collection of information. There is also a potential infinite regress problem in the formation of beliefs for given information. In sum, there may still be infinite regress problems in the theory of rational choice theory that justify an increased interest in the behavioural approach, even if the one particular infinite regress argument discussed in the previous chapter fails.

 

2. "As-if"

After arguing against the realism of the assumption of optimization, Elster follows Winter in arguing against the use of Friedman's (1953) well known "as-if" justification for studying optimizing behaviour. The argument, briefly, is that natural selection implies that those who do not optimize (or almost optimize) will be eliminate (e.g. go bankrupt). Thus, even if agents do not consciously optimize, it still makes sense to analyse their behaviour "as-if" they were optimizing.

Against this Elster and Winter argue that there is good reason to disbelieve the analogy with natural selection in biology. For instance, if there are economies of scale then a large but unfit firm could eliminate those who are "more fit." Winter makes along list of these exceptions (see Hodgeson 1988 for a discussion). Elster focuses on another aspect: the implicit assumption that the selection mechanism works faster than the changes in the environment. Once again I am in no position to give a definite answer to this criticism, but I do believe I have found some possible weaknesses in Elster's argument.

1. Are social environments really fast changing?

One possible objection is that all social environments are not fast changing. Consider the following:

There are two types of agents (P1 and P2) with different sets of characteristics (A-F):

P1: A, C, D

P2: A, B, E, F

A change in the environment may make characteristic D more functional i.e. having D is in some way beneficial in the new environment. Furthermore, there might be another structural change making B more functional and C dysfunctional. Does this mean that we are unlikely to see a clear change in the composition of P1 v. P2 in the environment?

The answer depends on the degree of the shift i.e. we need to know how much more "functional" P1 becomes as a result of having B and how much less functional it is to have characteristic C in the new environment. Hence, it is not only the speed of environmental change that matters, but also the quantity of change. As an illustration, consider the claim that the industrial revolution changed the structure of the family from extended to nuclear because a nuclear family was more functional in an industrial society. It would be incorrect to argue that his argument is invalid just because there were many other environmental changes going on at the same time (i.e. that the environment was fast changing). First, this would require the other changes to work in the opposite direction (i.e. in favour of the extended family). Second, it would require that the quantitative effect of these changes outweighed the quantitative effects of the industrial revolution. Hence, speed matters but so does quantity and direction.

 

2. Why speed might not destroy the selection mechanism: Flexibility

To argue that some environments change so fast that the social selection mechanism does not have time to "eliminate" the dysfunctional agents, overlooks the possibility that speed itself may make some individuals functional or dysfunctional. Some individuals have more of those characteristics that are functional in rapidly changing environments. For example, ability to learn quickly might lead to greater flexibility in the face of speedy environmental change. It is important to note here that they are functional precisely because the environment is changing. This implies that agents with less of these skills are less functional in fast changing environments. Thus, speed in itself does not make functional explanations invalid.

I want to emphasise once again that this is not to argue in favour of functional explanations in general, only to point out that there may be some weaknesses in Elster's arguments against the use of the "as-if" assumption based on natural selection.

 

3. "As-if" without natural selection

Even if the natural selection argument fails to justify the use of "as-if" arguments, one might still - and this may be a better interpretation of Friedman's general position - argue that it is legitimate to use unrealistic assumptions as long as they deliver useful results. For instance, Friedman's (1953) famous billiard table analogy is about how a complex mathematical model may accurately predict a pool player's shot, although the player himself does not "calculate" his shot using the same mathematical model. Thus, in addition to the literal "as-if" justification (firms that do not maximize profit go bankrupt), it is possible to defend the "as-if" using the methodological argument of instrumentalism.

There is a huge philosophical literature on instrumentalism (see, for instance, Hausmann 1998), and I only want to raise a few points that I find relevant. First, there is the obvious argument that economists do not only want to predict, we also want to explain. If the theory is build on an assumption that is both important to the result (so it is not just a simplification) and false, then the theory cannot be said to explain the phenomena in question. Second, there is a problem in terms of measuring accuracy of predictions. Friedman himself has received strong criticism for ignoring many econometric problems in his work on the money supply and inflation (e.g. spurious correlation. See Hendry). Third, there is the already mentioned problem that there is no neutral way of choosing between a theory that is moderately accurate for many phenomena vs. one that is highly accurate for only a small sub-set of phenomena (i.e. the trade-off between universalism and accuracy). These comments, of course, only scratch the surface of a large and controversial literature.

 

4. Sub-conclusion

1.  
2. Conclusion

Rational choice theory can be attacked for many reasons. However, after reviewing Elster's arguments I do not think it is a significant objection to argue that it is impossible to make a rational decision because there is an infinite regress problem in the collection of information that makes a rational decision logically impossible. As for the problems of estimation, I agree that these are significant, but they do not prove the impossibility of making a rational choice and I am uncertain about the implications that follow (i.e. Elster's recommendation of randomization and maximin). Finally, I believe some of Elster's arguments on the issue are, if not contradictory then at least "in tension" with each other.

It is difficult to say anything definite about the implications for economists. The rational choice adherents might find comfort in the fact that at least one of the arguments made against rational choice by one author is weakened. The economic behaviouralists may take refuge in the argument that empirically speaking the problem of estimation makes rational choice a very demanding assumption - even to the extent that it is not reasonable to expect people to conform to it.

Personally I leave this topic with the same schizophrenic mind I had when I started the paper. In fact, the schizophrenia is compounded by disillusionment since while writing this paper I have increasingly come to doubt the usefulness of debating the assumption of rationality. First, although I argued that there was room for scientific debate around the topic, I am less certain that the intellectual history of the past fifty years has demonstrated that the debate has led to any convergence towards a single more accepted view. Instead the same arguments keep being made (by different people) in a never-ending circle - often in a rather dogmatic and harsh style with little real communication between the antagonists. One reason for the lack of progress, could be the non-existence of neutral criteria in the trade-off between methodological principles (parsimony vs. scope vs. power vs. realistic assumption vs. good predictions). Second, one might question the importance of the debate. For instance, in the debate about economic fluctuations new models have demonstrated that near-rational behaviour has very different implications than perfectly rational behaviour. Moreover, recent research has showed that it is not necessary to assume irrationality to get a model with price-stickiness. In other words, regardless of the assumption of rationality, it seems that we can generate the results "we want" as long as we manipulate the other assumptions in the model. In short, I still have doubts about the possibility and the importance of the debate.

So, how much information should you collect? I still don't know, but I suspect the best general answer is: Very little!

 

3.  
4. References

Zeckhauser, Richard (1987): "Comments: Behavioral versus Rational Economics: What you see is what you conquer." In Robin M. Hogarth and Melvin W. Reder (eds.), Rational Choice: The contrast between economics and psychology, Chicago and London: The University of Chicago Press, 251-265.