Utility of gambling II: risk, paradoxes, and data

Theory and Decision, 2009

The present theory leads to a set of subjective weights such that the utility of an uncertain alternative (gamble) is partitioned into three terms involving those weights -a conventional subjectively weighted utility function over pure consequences, a subjectively weighted value function over events, and a subjectively weighted function of the subjective weights. Under several assumptions, this becomes one of several standard utility representations, plus a weighted value function over events, plus an entropy term of the weights. In the finitely additive case, the latter is the Shannon entropy; in all other cases it is entropy of degree not 1. The primary mathematical tool is the theory of inset entropy.

Economic Theory, 2008

Behavioral axioms about preference orderings among gambles and their joint receipt lead to numerical representations consisting of a subjective utility term plus a term depending upon the events and the subjective weights. The results here are for uncertain alternatives, in much the same sense as Savage's usage. Several open problems are described. Results for the risky case are in a second article.

Studies in Choice and Welfare, 2009

Journal of Mathematical Psychology, 1987

's ((1979) Prospect theory: An analysis of decision under risk, Econometrica, 47, 263-291) prospect theory postulates that the subjective value of a gamble is determined by different combination rules depending on the outcomes of the gamble. The theory distinguishes regular from irregular gambles, and in addition, distinguishes two different kinds of irregular gambles. The representations of value for these classes of gambles are formally analogous, but they differ in the way that gamble probabilities are integrated with the worth of gamble outcomes. The present work identifies properties of preference, restricted betweenness and equivalence under interchange, that play a central role in justifying the use of different combination rules for different classes of gambles in prospect theory. 'i" 1987 Academic Press, Inc.

Aequationes mathematicae, 2008

J. R. Meginniss modified expected utility to accommodate a concept of the utility of gambling that led to a representation composed of a utility expectation term plus an entropy of degree κ term. He imposed several apparently strong assumptions. One of these is that a number of unknown generating functions are identical. A second is that he assumed he was working with given probabilities. Here we follow his general framework but weaken considerably those assumptions. Our problem is reduced to solving some functional equations induced by gamble decomposition. From the solutions, we obtain the representation of the utility function. Further axiomatic restrictions are imposed that lead ultimately to Meginniss' earlier result. . 94A17, 91B16, 39B22.

2000

Ž. Ž. Miyamoto's 1988, 1992 generic utility theory GUT subsumes a broad class of bilinear utility models. Ž. Chechile and Cooke 1997 tested the GUT class of models and found model failure due to the systematic variation of a parameter that should be a positive constant across a range of contexts. In the current study, an improved experimental design is employed to evaluate utility theory. The current study provides further evidence against the GUT class of models for mixed gambles. Moreover, evidence is also provided to demonstrate individual behavior that is incompatible with a coherent bilinear utility theory of choice behavior in the context of mixed gambles with gains and losses.

Journal of Experimental Psychology: Learning, Memory, and Cognition, 1987

This article is concerned with a recent debate on the generality of utility theory. It has been argued by Lopes (198 i) that decisions regarding preferences between gambles are different for unique and repeated gambles. The present article provides empirical support for the need to distinguish between these two. It is proposed that violations of utility theory obtained under unique conditions (e.g., Kahneman & Tversky, 1979), cannot necessarily be generalized to repeated conditions. We would like to thank Baruch Fischhoff, Sarah Lichtenstein, Charles Lewis, and Charles Vlek for many valuable comments on previous drafts of this article.

Economica, 2009

One feature of experimental work is the heterogeneity in risk attitudes and probability distortion displayed by agents. We outline a more general non-expected utility model, which nests the models of Markowitz, and Kahneman and Tversky. The model can generate the standard favourite-longshot bias or a reverse favourite-longshot bias as a result of optimal behaviour. We also provide new empirical evidence on the relationship between Tote and bookmaker returns and confirm that the relationship is not as originally conjectured by Gabriel and Marsden. We outline how our new model can provide an explanation of the relationship that is observed.

Organizational Behavior and Human Decision Processes, 2004

Four studies with 3440 participants investigated four new paradoxes that refute rank-dependent utility and cumulative prospect theories of risky decision making. All four paradoxes can be interpreted as violations of coalescing, the assumption that branches leading to the same consequence can be combined by adding their probabilities. These studies explored if there is some format in which coalescing and cumulative prospect theory would be satisfied. Three variables were manipulated: probability format, branch splitting, and event-framing. Probability was displayed via text, pie charts, natural frequencies, and lists of equally likely consequences. Probability format and event framing had minimal effects, but branch splitting had large effects. In all 12 conditions of format and framing, splitting created majority violations of stochastic dominance and a second round of splitting reversed preferences, restoring majority satisfaction of stochastic dominance. Two cumulative independence properties were violated in 47 of 48 new tests. BirnbaumÕs TAX model, in which the relative weight of each probability-consequence branch depends on probability and rank of its consequence, correctly predicted the main trends. In this model, splitting the branch with the lowest consequence can make a gamble worse, and splitting the branch with the highest consequence can make a gamble better.

Insurance: Mathematics and Economics, 1993

Choice is viewed as a derived, not a primitive, concept. Individual gambles are assigned subjective certainty equivalents (CE1); the choice set X has an associated reference level [RL(X)] based on the CEls of its members; the outcomes of each gamble are recoded as deviations from the RL(X); and new CEes are constructed. The gamble having the largest CE2 is chosen. The CEs are described by the rank-and sign-dependent theory of Luce (1992b). The concept of RL is studied axiomatically. The model predicts many behavioral anomalies and is tested with data sets of .