Postlewaite ea’s Rationality, Uncertainty

Andrew Postlewaite and David Schmeidler,  “Rationality and Uncertainty,” Rivista Internazionale di Scienze Sociali, Special Issue on “The Whole  Breadth of Reason”. To appear, 2013.

Abstract

Experimental psychologists and economists … find non-negligible differences between the observed behavior of participants and the theoretically implied behavior. … We comment on the question whether rationality, implies these theoretical behaviors and whether the non-negligible differences as above imply that participants in experiments are irrational. We also comment on the relation between rationality and consistency, in particular in situations of uncertainty.

Rationality and Uncertainty

One possible explanation for observed differences between theory and practice is ‘denial’:

The actors behave differently than the agents because the actual task they face is not what the experimenter claims it to be, their goals are not those assigned by the experimenter, external validity does not hold, etc…

A challenge for the theoretically implied behaviour is where an event, E, may happen or not and one has a choice between three actions, ‘T’, ‘M’ and ‘B’, whose returns are 19 utiles on E, 19 utiles on ‘not E’ and 9 utiles whatever, respectively. Choosing the last option, B, contradicts the theory, yet seems very sensible if you have no idea about the ‘probability’ of E. E.g.:

[If the utiles] represent a non negligible share of savings toward pension, choosing T or M may appear too hazardous.

As an alternative to ‘denial’ the authors note:

Gilboa, Maccheroni, Marinacci, and Schmeidler (2010) call an action objectively rational if the decision maker can convince others that the chosen actions best for attaining his goals. They call it subjectively rational if others can not convince the decision maker of the opposite. …

… The chosen action may be consistent with some beliefs (implicit or explicit) that are not justified by data. We conjecture that the majority of the decision makers will regret their choice if confronted with analysis showing the data they had access to contradicts these beliefs.

See Also

Itzhak Gilboa, Fabio Maccheroni, Massimo Marinacci and David Schmeidler,   Objective and Subjective Rationality in a Multiple Prior Model ,  Econometrica, Vol 78, 755 – 70, (2010). This is referred to above. It supplies a conventionally objective extension to theories such as that below.

Von Neumann and Morgenstern. This may be one of the classical sources to which the authors implicitly refer. But this theory only applies to complete preferences, which imply definite probability judgements. A definite judgement about the probability of E will yield a definite judgement about which of T, M, B is best. But that is not our situation, and so the theory does not rule out a preference for B.

Comments

This paper is psychological, in the sense that reasonableness (as an alternative to conventional rationality) is judged by individual perceptions of ‘analysis’, ‘contradictions’ and ‘beliefs’. It leaves open the question of the logicality of conventional rationality.

The common (Benthamite) rationale for utility maximization is that in the long-run, attempting to maximize immediate utility  over a series of decisions will maximize overall utility, with very little uncertainty (the law of large numbers). But if one is faced with a choice of pension annuities that have differing indexations and guarantees, one is in a very different situation. If a pension is intended to provide ‘security’, then option B seems most reasonable. The authors put this forward ‘subjectively’. According to Ellsberg this type of choice may not be objectively rational, since some people would stick to the conventional concept of utility maximization, even when there is no logical theory whose axioms seem to apply. This leaves open the question as to whether there might not be some logical sense in which option B was best.

To be more definite, suppose that the goal is to have an adequate income under all conceived eventualities, and that B provides for this whereas T and M do not. Or that B guarantees you your taxi-fare home, whereas with T and M you may have a long, cold, wet walk home. Is it reasonable to deny the objective rationality of B just because some people do not get it?

Perhaps an  option should be considered objectively irrational if it can be shown on the basis of the available data that it actually contradicts a reference set of beliefs (e.g., those espoused). An option might be considered rational if it can be shown that it is nor irrational. In applications there would normally be some ambiguity about given data and beliefs, so that one could not say that an option was definitely rational or irrational, only when taken in combination with other beliefs. Thus the taking of an option by a supposedly rational actor might be taken to imply certain beliefs. Thus someone who chose option T might be supposed to believe that E was highly probable, or to be irrational.

Dave Marsay

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