Binary Choice Probabilities on Mixture Sets - Matthew Ryan (Auckland University of Technology (AUT), Faculty of Business, Economics and Law, 2015)
Experimental evidence suggests that choice behaviour has a stochastic element. Much of this evidence is based on studying choices between lotteries \~nchoice under risk. Binary choice probabilities admit a strong utility representation (SUR) if there is a utility function such that the probability of choosing option A over option B is a strictly increasing function of the utility dierence between A and B. Debreu (1958) obtained a simple set of su cient conditions on binary choice probabilities for the existence of a SUR. More recently, Dagsvik (2008) considered binary choices between lotteries and provided axiomatic foundations for a SUR in which the underlying utility function is linear (i.e., conforms to expected utility). Our paper strengthens and generalises Dagsvikís result. We show that one of Dagsvikís axioms can be weakened, and we extend his analysis to encompass choices between uncertain prospects, as well as various non-linear speciÖcations of utility.
Keywords: 330; Strong utility representation; Choice probabilities