Why be consistent?

23 Sep, 2014 at 08:16 | Posted in Economics | 1 Comment

consistentAxioms of ‘internal consistency’ of choice, such as the weak and the strong axioms of revealed preference … are often used in decision theory, micro-economics, game theory, social choice theory, and in related disciplines …

Paul Samuelson’s (1938) justly famous foundational contribution to revealed preference theory … can be interpreted in several different ways. One interpretation that has received much attention in the subsequent literature (and has had a profound impact on the direction of economic research) is the program of developing a theory of behavior “freed from any vestigial traces of the utility concept” (Samuelson (1938, p. 71)). While this was not in line with John Hicks’s earlier works, particularly his Value and Capital (Hicks (1939)), which began with the priority of the concept of preference or utility, Hicks too became persuaded by the alleged superiority of the new approach …

This paper argues against this influential approach to choice and behavior, and indicates the inescapable need to go beyond the internal features of a choice function to understand its cogency and consistency …

At the foundational level, the basic difficulty arises from the implicit presumption underlying that approach that acts of choice are, on their own, like statements which can contradict, or be consistent with, each other. That diagnosis is deeply problematic …

Can a set of choices really be seen as consistent or inconsistent on purely internal grounds, without bringing in something external to choice, such as the underlying objectives or values that are pursued or acknowledged by choice? …

The presumption of inconsistency may be easily disputed, depending on the context, if we know a bit more about what the person is trying to do. Suppose the person faces a choice at a dinner table between having the last remaining apple in the fruit basket (y) and having nothing instead (x), forgoing the nice-looking apple. She decides to behave decently and picks nothing (x), rather than the one apple (y). If, instead, the basket had contained two apples, and she had encountered the choice between having nothing (x), having one nice apple (y) and having another nice one (z), she could reasonably enough choose one (y), without violating any rule of good behavior. The presence of another apple (z) makes one of the two apples decently choosable, but this combination of choices would violate the standard consistency conditions, including Property a, even though there is nothing particularly “inconsistent” in this pair of choices (given her values and scruples) … We cannot determine whether the person is failing in any way without knowing what he is trying to do, that is, without knowing something external to the choice itself.

Amartya Sen

1 Comment

  1. “Can a set of choices really be seen as consistent or inconsistent on purely internal grounds, without bringing in something external to choice, such as the underlying objectives or values that are pursued or acknowledged by choice? …”

    Yes. You can look at an effect (event) and condition consistency on that instead of the cause, which can be part of an infinite regression of causes anyway.

    For example, if a series of choices C(i) of individual I(i) produce the same effect, then the set of choices can be called consistent in a counter-factual sense. Example:

    Choice 1: The person does not choose the last apple

    Choice 2: The person chooses one of the two remaining apples

    Effect: Only one apple remains on the table in both cases, Therefore the choices are consistent without any reference to externals when conditioned on the number of apples remaining on the table, i.e. on the effect.

    The debate of background independent vs purely relational theories is metaphysical.

    To settle this I propose the following Theorem:

    For any set of choices C(i) in a space S, there exists at least one common internal effect of these choices with respect to which they are all consistent.

    Proof:

    Left as an exercise to the readers. Hint: if there is not one, invent one.


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