In identical experiments, an Allais paradox occurs when the addition of an independent event influences choice behavior. Consider the choices in the following table (Kahneman and Tversky 1979).
lottery
1 to 33
34
35 to 100
preference
0
18%
82%
0
0
83%
0
17%
In Experiment 1, a choice of and was given, and most participants picked . In Experiment 2, a choice of and was given, and most participants picked .
This observed pattern violates the independence axiom, since in both experiments, the payoff is identical if a ball is picked, while if the event is disregarded, the two experiments are identical.
To see it another way, consider the event to be a black box that is always received if the
random ball value is .
Knowing or not knowing the contents of the black box should not influence behavior.
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