The Allais paradox demonstrates that individuals rarely make rational decisions consistently when required to do so immediately.
The independence axiom of expected utility theory, which requires that the preferences of an individual should not change when altering two lotteries by equal proportions, was proven to be violated by the paradox.
Allais further asserted that it was reasonable to choose 1A alone or 2B alone, as the expected average outcomes (in millions) are 1.00 for 1A gamble, 1.39 for 1B, 0.11 for 2A and 0.50 for 2B.
The point of these models was to allow a wider range of behavior than was consistent with expected utility theory.
Michael Birnbaum performed experimental dissections of the paradox and showed that the results violated the theories of Quiggin, Kahneman, Tversky, and others, but could be explained by his configural weight theory that violates the property of coalescing.
However, this 1% chance of getting nothing also carries with it a great sense of disappointment if you were to pick that gamble and lose, knowing you could have won with 100% certainty if you had chosen 1A.
We don't act irrationally when choosing 1A and 2B; rather expected utility theory is not robust enough to capture such "bounded rationality" choices that in this case arise because of complementarities.
The most common explanation of the Allais paradox is that individuals prefer certainty over a risky outcome even if this defies the expected utility axiom.
Running two additional lotteries allowed the two effects to be distinguished and hence, their statistical significance to be tested.
Participants who chose (1A,2B,3A) deviated from the rational lottery choice to avoid the risk of winning nothing (aversion to zero).
The certainty effect was found to be statistically insignificant and not the intuitive explanation individuals deviating from the expected utility theory.
The Allais Paradox was first introduced in 1952, where Maurice Allais presented various choice sets to an audience of economists at Colloques Internationaux du Centre National de la Recherche Scientifique, an economics conference in Paris.
[8] Similar to the choice sets above, the audience provided decisions that were inconsistent with expected utility theory.
Despite this result, the audience was not convinced of the validity of Allais's finding and dismissed the paradox as a simple irregularity.
Critiquing expected utility theory and postulating that individuals perceive the prospect of a loss differently to that of a gain, Kahneman and Tversky's research credited the Allais paradox as the “best known counterexample to expected utility theory”.
[11] The Allais Paradox was again presented in Tversky and Kahneman's Thinking, Fast and Slow (2011), a New York Times Best Seller.
[12] Finally, Allais's prominence was further promoted when he received the Nobel Prize in Economic Sciences in 1988 for "his pioneering contributions to the theory of markets and efficient utilization of resources", thus bolstering the recognition of the paradox.
[14] The mismatch between human behaviour and classical economics that is highlighted by the Allais paradox indicates the need for a remodelled expected utility function to account for the violation of the independence axiom.
[15] The findings of this experiment suggested that the switching of preferences apparent in the Allais paradox are due to the state of the individual, which include bankruptcy and wealth.
[15] List & Haigh (2005) tests the appearance of the Allais paradox in the behaviours of professional traders through an experiment and compares the results with those of university students.
[16] By providing two lotteries similar to those used to prove the Allais paradox, the researchers concluded that those who were professional traders less frequently make choices that are inconsistent with expected utility, as opposed to students.