Emergent Properties of Choice :: Allais Paradox Essays

Emergent Properties of Choice ABSTRACT: Allais' paradox provides a convenient way to demonstrate that the distribution of alternatives we face in a situation of choice may give rise to new factors. These emergent factors may need to influence a one time choice of rational decision-makers, although they should not be taken into account in long reiterative games. I start from a brief presentation of Allais' paradox; yet, I am not primarily concerned with the question how to solve it. The paradox provides a convenient way to demonstrate that distribution of alternatives we face in a situation of choice may give rise to new factors. These emergent properties may need to influence a one time choice of rational decision-makers, although they should not be taken into account in long reiterative games. Let me introduce to you decisiotheoretic emergentism. According to the independence axiom an outcome of the choice shall be neutral if a constant value is added to each alternative. But if we consider the table of preferences presented by Allais this presumption seems intuitively questionable. Y=1 B=10 R=89 g1 M M M g2 0 5M M g3 M M 0 g4 0 5M 0 In the choice between g1 and g2 (where M stands for one million crowns), most people choose g1 over g2, although g2 gives higher expected value. Yet, if we choose between g3 and g4, almost everybody prefers g4 over g3. But the problem may be seen as two identical alternatives g1=g3 and g2=g4 just in the choice between g1 and g2 in column R an outcome of one million crowns has been added to each alternative whereas in the second case the constant added equals zero. These results contradict with the independence axiom. The first solution is to go Savage's way and, after reconsideration, to change one's mind in the g1/g2 choice. But strong intuitiveness of the Allais paradox makes this solution less than attractive. It might seem better to search for some troublesome decisio-theoretic axioms easy to replace. This is the way decision theorists usually go. But they have a problem in finding axioms to be eliminated.