Related papers: Remarks on Utility in Repeated Bets
Let $\succsim$ be a binary relation on the set of simple lotteries over a countable outcome set $Z$. We provide necessary and sufficient conditions on $\succsim$ to guarantee the existence of a set $U$ of von Neumann--Morgenstern utility…
The von Neumann-Morgenstern (VNM) utility theorem shows that under certain axioms of rationality, decision-making is reduced to maximizing the expectation of some utility function. We extend these axioms to increasingly structured…
This paper introduces a space of variable lotteries and proves a constructive version of the expected utility theorem. The word ``constructive'' is used here in two senses. First, as in constructive mathematics, the logic underlying proofs…
In this paper, we formulate a qualitative "linear" utility theory for lotteries in which uncertainty is expressed qualitatively using a Spohnian disbelief function. We argue that a rational decision maker facing an uncertain decision…
This paper presents a comprehensive formalization of the von Neumann-Morgenstern (vNM) expected utility theorem using the Lean 4 interactive theorem prover. We implement the classical axioms of preference-completeness, transitivity,…
We initiate a novel direction in randomized social choice by proposing a new definition of agent utility for randomized outcomes. Each agent has a preference over all outcomes and a {\em quantile} parameter. Given a {\em lottery} over the…
Expected Utility: Algebraic Expected Utility In this paper, we provide two axiomatizations of algebraic expected utility, which is a particular generalized expected utility, in a von Neumann-Morgenstern setting, i.e. uncertainty…
We provide and axiomatize a representation for preferences over lotteries that generalizes the expected utility model. Since the representation uses different utility functions to evaluate different lotteries, the preferences can be…
In a consideration set model, an individual maximizes utility among the considered alternatives. I relate a consideration set additive random utility model to classic discrete choice and the extended additive random utility model, in which…
The random utility model, a cornerstone in economics, is axiomatized by Falmagne (1978) and McFadden and Richter (1990) with the assumption that if a menu is observable, the choice frequencies of all alternatives are also observable.…
The main goal of this paper is to describe an axiomatic utility theory for Dempster-Shafer belief function lotteries. The axiomatic framework used is analogous to von Neumann-Morgenstern's utility theory for probabilistic lotteries as…
We study consumption dependence in the context of random utility and repeated choice. We show that, in the presence of consumption dependence, the random utility model is a misspecified model of repeated rational choice. This…
We consider randomized mechanisms with optional participation. Preferences over lotteries are modeled using skew-symmetric bilinear (SSB) utility functions, a generalization of classic von Neumann-Morgenstern utility functions. We show that…
In this note we analyze the relationship between the properties of von Neumann-Morgenstern utility functions and expected utility functions. More precisely, we investigate which of the regularity and concavity assumptions usually imposed on…
We provide sufficient conditions under which a utility function may be recovered from a finite choice experiment. Identification, as is commonly understood in decision theory, is not enough. We provide a general recoverability result that…
Quantum cognition in decision-making is a recent and rapidely growing field. In this paper we develop an expected utility theory in a context of non-classical (quantum) uncertainty. We replace the classical state space with a Hilbert space…
De Finetti's betting argument is used to justify finitely additive probabilities when only finitely many bets are considered. Under what circumstances can countably many bets be used to justify countable additivity? In this framework, one…
It is known that repeated gambling over the outcomes of independent and identically distributed (i.i.d.) random variables gives rise to alternate operational meaning of entropies in the classical case in terms of the doubling rates. We give…
We consider a generalization of the recursive utility model by adding a new component that represents utility of investment gains and losses. We also study the utility process in this generalized model with constant elasticity of…
We introduce a linear space of finitely additive measures to treat the problem of optimal expected utility from consumption under a stochastic clock and an unbounded random endowment process. In this way we establish existence and…