### Abstract

In the world of subjective probability, there is no a priori reason why probabilities interpreted as a willingness-to-bet should necessarily lie in the interval [0,1]. We weaken the Monotonicity axiom in classical subjective expected utility (Anscombe and Aumann, 1963) to obtain a representation of preferences in terms of an affine utility function and a signed (subjective) probability measure on states. We decompose this probability measure into a non-negative probability measure (“probability”) and an additive set function on states which sums to zero (“valence”). States with positive (resp. negative) valence are attractive (resp. aversive) for the decision maker. We show how our decision theory can resolve several paradoxes in decision theory, including “hedging aversion” (Morewedge et al., 2018), the conjunction effect (Tversky and Kahneman, 1982, 1983), the co-existence of insurance and betting (Friedman and Savage, 1948), and the choice of dominated strategies in strategyproof mechanisms (Hassidim et al., 2016). We extend our theory to allow for a non-additive willingness-to-bet, which also relaxes our earlier constraints on how valence can behave.

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###### Assistant Professor of Economics

Greetings! I hold concurrent appointments as an Assistant Professor at Collegio Carlo Alberto and within the Department of Economics, Social Studies, Applied Mathematics and Statistics (ESOMAS) at the University of Turin. My academic focus is centered on economic theory, with a particular emphasis on decision theory.