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Utility Theory of General Lotteries

Vladimir Danilov ()

Journal of the New Economic Association, 2016, vol. 32, issue 4, 12-29

Abstract: Generalizing the notions of roulette lotteries, horse lotteries, and quantum lotteries, we introduce maximally general notion of lottery. It uses the theory of ordered vector spaces. Under appropriate conditions on preference relation between lotteries (generalizing the conditions considered by von Neumann, Savage, Aumann and Anscombe) we give a formula for the utility of lotteries. Its ingredients are a utility function of prizes and a belief functional giving probability of events. Inthe second part of paper we discuss the issue about updating of beliefs under receiving additional information. We give a formula for the updated belief (which generates Bayes rule and von Neumann-Luders projection postulate), suppose that the ordered vector space is the real part of C*-algebra.

Keywords: utility function; probability; measurement; ordered vector space; updating; C *-algebra (search for similar items in EconPapers)
JEL-codes: C44 D81 D84 (search for similar items in EconPapers)
Date: 2016
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