Classical Expected Utility Theory and Its Paradoxes

G. Charles-Cadogan

Louis Marinoff

V. I. Danilov, Ariane Lambert‐Mogiliansky, Vassili Vergopoulos

Giuseppe M. Ferro, Tatyana Kovalenko, Didier Sornette

Pierfrancesco La Mura

Motivated by classical decision-theoretic paradoxes (Allais 1953, Ellsberg 1961), we introduce a projective generalization of expected utility along the lines of the quantum-mechanical generalization of probability theory. The resulting decision theory accommodates the paradoxes, while retaining significant simplicity and tractability. In particular, every finite game within this larger class of preferences still has an equilibrium.

Diederik Aerts, Sandro Sozzo, Jocelyn Tapia

The Ellsberg and Machina paradoxes reveal that expected utility theory is problematical when real subjects take decisions under uncertainty. Suitable generalizations of expected utility exist which attempt to solve the Ellsberg paradox, but none of them provides a satisfactory solution of the Machina paradox. In this paper we elaborate a quantum model in Hilbert space describing the Ellsberg situation and also the Machina situation, and show that we can model the specific aspect of the Machina situation that is unable to be modeled within the existing generalizations of expected utility.