Preference Reversal and the Symmetric Choquet Integral

Abstract

We regard decisions over uncertain or risky prospects X (or. in another terminology, acts). It is a well established empirical fact (cf. Kahneman and Tver sky) that a majority of decision takers behaves risk or uncertainty averse if the prospects offer gains but the same persons are attracted by risk or uncertainty if they have to decide over losses. A real functional Y represents these preferences if it has the following properties: (1) $$\Gamma \left( {X + Y} \right) \geqslant \Gamma X + \Gamma Y\quad for\;X.Y \geqslant 0$$ , (2) $$\Gamma \left( { - X} \right) = - \Gamma X\quad for\;X \geqslant 0$$ .

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