Understanding the Maurice Allais Paradox

To finish the cycle of Maurice Allais for now, we let you with the Allais Paradox
Not many people understand in deep the consequences of Allais Paradox, no better source than Allais himself in the article From The New Palgrave Dictionary of Economics, Second Edition, 2008.
Since we cannot reproduce the whole article we let you the abstract, conclusion and three references for self-study.It is very important to understand the limits of the standard theory, and more important to know other approches.

Abstract

The ‘Allais paradox’ is that risk-averse persons’ choices between alternatives tend to vary according to the absolute amounts of potential gain involved in different pairs of alternatives, even though rational choice between alternatives should depend only on how the alternatives differ. But there is no paradox once we accept the non-identity of monetary and psychological values and the importance of the distribution of cardinal utility about its average value.

Conclusion

In sum, just as the St Petersburg Paradox led Daniel Bernoulli to replace the principle of maximization of the mathematical expectation of monetary values by the Bernoullian principle of maximization of cardinal utilities, the Allais Paradox leads to adding to the Bernoullian formulation a specific term characterizing the propensity to risk which takes account of the distribution as a whole of cardinal utility (Allais, 1978, pp. 4–7; 1977, pp. 548–52; 1983, pp. 35–42). Neither the St Petersburg nor the Allais Paradox involves a paradox. Both correspond to basic psychological realities: the non-identity of monetary and psychological values and the importance of the distribution of cardinal utility about its average value. For nearly forty years the supporters of the neo-Bernoullian formulation have exerted a dogmatic and intolerant, powerful and tyrannical domination over the academic world; only in very recent years has a growing reaction begun to appear. This is not the first example of the opposition of the ‘establishments’ of any kind to scientific progress, nor will it be the last (Allais, 1977, pp. 518–46; 1983, pp. 69–71, 112–14).

The Allais Paradox does not reduce to a mere counter-example of purely anectodal value based on errors of judgement as too many authors seem to think without referring to the general theory of random choice which underlies it. It is fundamentally an illustration of the need to take account not only of the mathematical expectation of cardinal utility, but also of its distribution as a whole about its average, basic elements characterizing the psychology of risk.

References
The Utility Analysis of Choises Involving Risk, Friedman and Savage, for the standard theory
Allais article with the paradox, but most importantly how to build a Decision theory involving risk
Prospect theory, inspired by Allais

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