What does Paradox 2
M. Allais demonstrated violation of decision-makers against the axiom of independence and thus against the Bernoulli principle (expected utility theory).
To clarify, two electoral situations are considered: In electoral situation A, the decision maker has between the sure win 3000 (A1) and a lottery (A2), where there is a probability of 80% that he will win 4000 (with an opposite probability of 20% he will win nothing). In election situation B, the decision maker has to choose between a lottery (A3), in which there is a 25% probability of winning 3000 (with the opposite probability of 75% he will not win anything), and a lottery (A.4), where there is a 20% probability of winning 4000 (with an opposite probability of 80% he will not win anything).
If the decision maker is rational in the sense of the Bernoulli Principle, he will either be A.1 and A3 or A2 and A4 prefer but not A1 and A4 or A2 and A3. Real decision-makers, however, often draw A.1 and A4 in front. This means a violation of the axiom of independence.
The Allais paradox was explained by the security effect (D. Kahneman and A. Tversky, Prospect Theory - An Analysis of Decision under Risk, Econometrica 47 (1979), pp. 263-292). According to this effect, certain results are overweighted compared to probable results, i.e. the evaluation of a certain result exceeds the evaluation of an equally high, non-certain result more than the difference in the probability of occurrence implies. In the example, the profit of 3000 on the transition from A3 on A1 Sure, the profit of 4000 remains with the transition from A4 on A2 unsure what A1 relative to A2 more attractive, although the probability of winning quadruples each time (from 25% to 100% when moving from A3 on A1 and from 20% to 80% when transitioning from A4 on A2).
See also prospect theory.
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