Allais paradox


Instructions

Please choose between: A: A chance of winning 4000 Euro with probability 0.2 (expected value 800 Euro)
B: A chance of winning 3000 Euro with probability 0.25 (expected value 750 Euro)

Please choose between:

C: A chance of winning 4000 Euro with probability 0.8 (expected value 3200 Euro)
D: A chance of winning 3000 Euro with certainty.

Evaluations Number of players: 25
Frequency of different decisions:
Comments In large scale experiments, most players (about 70%) choose 4000 Euro with probability 0.2 (A) rather than 3000 Euro with probability 0.25 (B). And indeed, the expected value 4000 Euro with probability 0.2 (800 Euro) is larger than of 3000 Euro with probability 0.25 (750 Euro). In the second decision, most choose 3000 Euro with certainty (D). This is paradox. First of all, the expected value of C, 4000 Euro with probability 0.8 (3200 Euro), is larger than that of D, 3000 Euro with certainty (3000 Euro). More puzzling still, the values in the first decision are obtained from those in the second decision simply by reducing the odds by the factor 4. It is as if we first tossed two coins and do the second decision only if both show heads.

Addendum (November 10, 2003)

The irrational switching behavior of the majority of participants can be illustrated in an even more striking way by showing the percentage of participants that chose A in the first round and C in the second, those that chose first A then D, B then C and finally B followed by D.

Evaluations Number of players: 25
Frequency of different pairs of decisions:
Comments As expected, the majority of people (44%) choose first A and then D. 20% make the rational choice of A followed by C. Somewhat surprising is the considerable percentage that is extremely risk averse and chooses B and then D. Only a single individual chose first B and the C - might be simply a miscalculation.


Written by Christoph Hauert