A Single-Stage Approach to Anscombe and Aumann's Expected Utility

expected utility theory;decision analysis;revealed preference

Comonotonic Book-Making with Nonadditive Probabilities

This paper shows how de Finetti's book-making principle, commonly used to justify additive subjective probabilities, can be modi-ed to agree with some nonexpected utility models.More precisely, a new foundation of the rank-dependent models is presented that is based on a comonotonic extension of the book-making principle.The extension excludes book-making only if all gambles considered induce a same rank-ordering of the states of nature through favorableness of their associated outcomes, and allows for nonadditive probabilities.Typical features of rank-dependence, hedging, ambiguity aversion, and pessimism and optimism, can be accommodated.Book-making;comonotonic;Choquet expected utility;ambiguity aversion;ordered vector space

On the Intuition of Rank-Dependent Utility

Among the most popular models for decision under risk and uncertainty are the rank-dependent models, introduced by Quiggin and Schmeidler.Central concepts in these models are rank-dependence and comonotonicity.It has been suggested in the literature that these concepts are technical tools that have no intuitive or empirical content.This paper describes such contents.As a result, rank-dependence and comonotonicity become natural concepts upon which preference conditions, empirical tests, and improvements for utility measurement can be based.Further, a new derivation of the rank-dependent models is obtained.It is not based on observable preference axioms or on empirical data, but naturally follows from the intuitive perspective assumed.We think that the popularity of the rank-dependent theories is mainly due to the natural concepts adopted in these theories.rank-dependence;comonotonicity;Choquet integral;pessimism;uncertainty aversion;prospect theory

Revealed likelihood and knightian uncertainty

expected utility theory;uncertainty;revealed preference

The Repetitions Approach to Characterize Cardinal Utility

Building on previous work of A. Camacho, we give necessary and sufficient conditions for the existence of a cardinal utility function to represent, through summation, a preference relation on sequences of alternatives

Clarification of some mathematical misunderstandings about Savage's foundations of statistics, 1954

This note discusses some mathematical misunderstandings about Savage (1954). It is shown that in his model the probability measure cannot be countably additive, that the set of events must be a σ-algebra and not just an algebra, that Savage did not characterize all atomless finitely additive probability measures, and that the state space in his model, while infinite, does not have to be uncountable

A Graph-Theoretic Approach to Revealed Preference

One of the issues in the impossibility theorem of Arrow is the difference between choice behaviour, as considered by Arrow in most of the illustrations for the conditions in his theorem, and binary relations as dealt with in Arrow's theorem. The relations between choice behaviour and binary relations are studied in revealed preference theory, a theory which originates from consumer demand theory. This paper presents a graph-theoretic approach to revealed preference theory. This is done by considering alternatives as vertices, and choice situations as arcs. By means of this method alternative proofs are obtained for some known results. In particular it is shown that many results from literature can be derived from what may be the main result from revealed preference theory, a theorem of Richter (1966). Next a duality approach is sketched, where vertices and arcs are interchanged as done in dual graph theory. Finally some results are given for non-transitive binary relations. For these there is an increasing interest because of Arrow's theorem

Additive representations on rank-ordered sets. I. The algebraic approach

This paper considers additive conjoint measurement on subsets of Cartesian products containing “rank-ordered‘ n-tuples. Contrary to what has often been thought, additive conjoint measurement on subsets of Cartesian products has characteristics different from additive conjoint measurement on full Cartesian products

Choquet Integrals With Respect to Non-Monotonic Set Functions

This paper introduces the signed Choquet integral, i.e., a nonmonotonic generalization of the Choquet integral. Applications to welfare theory, multi-period optimization, and asset pricing are described.Choquet integral;comonotonicity;arbitrage;time preference