Melberg, Hans O., The fallacy of black and white arguments

_{[Note for bibliographic reference: Melberg, Hans O. (1996), The fallacy of black
and white arguments, http://www.oocities.org/hmelberg/papers/960520.htm]

The fallacy of black and white arguments

by Hans O. Melberg

The question

How much should a person receive in compensation after being wronged (for example,
wrongfully sacked from his job)? This simple question led me to reflect on the logical
structure of arguments in general. However, before I can explain this I need to make a
conceptual clarification.

Three elements of compensation

In most systems of justice the person wronged gets at least the salary he lost since he
was fired. In addition he often get some compensation for the indirect "pain"
cause by the incident. Lastly, some systems of justice (such as the American) awards the
person a sum of money in order to deter companies from engaging in discriminatory
practices. Thus, the level of compensation is the combination if at least three sources:
the direct monetary loss, the indirect loss (psychological etc.) and the deterring motive.

Two arguments

I recently discussed the level of compensations in Norway with a friend. I argued that the
level should be increased since I (mistakenly) believed that current practice in Norway
was to consider only the direct monetary losses - not the indirect losses or the
preventive motive - when awarding a compensation. In this I was partly mistaken (since the
legal system in Norway allows the court to award compensation based on indirect losses as
well). Yet, the factual mistake is of less importance for the present argument. The
important point is the structure of the argument: That the current level of compensation
included only one - not all three elements - thus it was too low.

My friend then advanced the following argument: We should not increase the current level
because if we do we would move towards an "American" situation in which
everybody sues everyone because of the possibility of large compensations. This was the
argument which set my mind going. On the surface it seems acceptable. An increase in the
level of compensation would probably have the effect that more people tried to get
compensations. This is true, but the validity of the argument also rests on the assumption
that such an increase would be bad. To reveal this you may conduct the following though
experiment: Assume that the level of compensation is very low (For example you get $10 for
each day you were unemployed after being wrongfully sacked from a job in which you made
$100 a day). The above argument against increasing the compensation - that it would
increase the number of cases brought before the court - is still true. Nevertheless, at
this low level of compensation we do not worry too much about the increased number of
court cases. In fact, my friends argument can be used at all levels of
compensation. It is always true that an increase in the compensation would cause an
increase in the number of cases, regardless of the initial level of the compensation. Yet,
we should not conclude that an increase in compensation is always bad.

The general fallacy

The more I reflected on this, the more I became aware that I here had an example of a more
general mistake: The failure to think in terms of marginal tradeoffs. (By marginal I do
not mean unimportant, rather I use marginal in the economic/mathematical sense of the
word: a small increase or decrease of something.) The structure of the fallacy is as
follows: We have a question which can be framed in terms of "How much X should there
be" We then give an argument which shows that more of X has bad consequences in some
respect. The apparently logical conclusion is then drawn - that we should not increase X.
This is, as explained, wrong.

One more example might clarify the fallacy. Imagine you ask a person whether he thinks
state intervention in the economy should be increased or decreased. A conservative might
answer that it should be decreased because a larger state decreases personal initiative. A
left-wing person, on the other hand, might argue that state intervention should be
increased because there are market failures that need to be corrected by more state
intervention. Both these arguments are equally false since they do not consider the marginal
impact which is what the question is about. Yes, state intervention might stifle personal
initiative and it may solve market failures. However, what we are interested in is how
much state intervention will reduced personal initiative (starting from the current
level of state intervention).

Is not the above argument obvious? To some extent it is and I do not think I have
discovered anything revolutionary. However, even the obvious is sometimes overlooked and I
have encountered the fallacy on many occasions. I have even committed it myself! This
leads me to speculate that the cause of the fallacy may be psychological. It is
psychologically difficult to think in terms of marginal tradeoffs between competing
values. Somehow our brain and our emotions conspire to make us thin in black and white,
not in terms of shades of grey. This, I think, is the cause of the fallacy.

In conclusion I would emphasise that the problem is not simply a failure to take competing
values and effects into account. Even when there is only one relevant mechanism we need to
think about marginals. The correct level being that in which the marginal benefit equals
the marginal cost.

Afternote

Afternote (added 1. March, 2001): I recently found a very good example of some of what I
tried to convey in the observation above. In short, the Minister of Justice in Norway
recently proposed to reduce the number of police stations in order to "reduce
bureaucracy" and have more police on the streets. This, of course, sounds nice (to
some ...) but the logic of the argument leads to the conclusion that there should only be
one police district in the whole of Norway. Clearly what was needed was an argument about
the optimal number of stations not based on one single argument (which leads to corner
solutions), but as a trade-off between several different concerns. In the case of police
districts one could argue that centralizing the administration also could lead to more
administration because being further away from local knowledge the administrators need
more information to do their tasks. I have, of course, no knowledge about the relative
trade-offs here - the extent to which it really was efficient to centralize. My only point
is that the argument used was not one of tradeoffs and optimal size, but an argument that
"always" could be used all the way down to complete centralization.

_{[Note for bibliographic reference: Melberg, Hans O. (1996), The fallacy of black and
white arguments, http://www.oocities.org/hmelberg/papers/960520.htm]}}