Allais Paradox

The independence axiom of expected utility theory offers a compelling reason for making a decision. According to this axiom, a choice between two alternatives should depend only on features in which alternatives differ but not on features in which the alternatives are equal. Any feature that is the same for both alternatives, therefore, should not influence the choice a rational person makes. For instance, when choosing between two therapies with exactly the same side effects, a rational doctor would ignore these side effects. That is, rational choice is independent of the alternatives' shared features.

This axiom seems very intuitive; if two therapies have the same side effects, it does not matter [Page 14]whether they are small or severe. Hence, rational decision makers base their choices on the distinctive rather than the shared features of the choice alternatives. In the early 1950s, however, French economist Maurice Allais proposed choice problems that challenged the independence axiom as a descriptive principle for risky choice. To illustrate this paradox, known as the Allais paradox, consider the following Allais-type choice problems presented by Adam Oliver: Which of the following would you prefer?

The majority of people selected Alternative A over B.

In the second problem, most people chose Alternative D, which constitutes a violation of the independence axiom. Table 1 shows why.

Alternatives A and B share an 89% chance of living for 12 years. Because this shared feature should not influence the choice, it can be cancelled out. Similarly, Alternatives C and D share an 89% chance of immediate death, which can be cancelled out again. Importantly, after the shared features in each problem (i.e., the bold column in Table 1) have been cancelled out, both problems become identical. A rational decision maker, thus, should choose A and C or B and D, but not A and D.