Generalized similarity judgments: An alternative explanation for choice anomalies

Rubinstein's (1988) procedure for choosing between risky prospects, based, in part, upon similarities between prizes and probabilities across lotteries, is modified and extended to apply to a more general class of binary choices. This modified procedure is shown to imply behaviors following from Loomes and Sugden's (1982) Regret Theory, although under more general conditions, and provides an alternative explanation for much of the data which led to the specification of Prospect Theory's value and decision weighing functions. The procedure also explains observed violations of stochastic dominance, transitivity, and invariance not accounted for in available alternatives to expected utility.     

Invariant multiattribute utility functions

We present a method to characterize the preferences of a decision maker in decisions with multiple attributes. The approach modifies the outcomes of a multivariate lottery with a multivariate transformation and observes the change in the decision maker’s certain equivalent. If the certain equivalent follows this multivariate transformation, we refer to this situation as multiattribute transformation invariance, and we derive the functional form of the utility function. We then show that any additive or multiplicative utility function that is formed of continuous and strictly monotonic utility functions of the individual attributes must satisfy transformation invariance with a multivariate transformation. This result provides a new interpretation for multiattribute utility functions with mutual utility independence as well as a necessary and sufficient condition that must be satisfied when assuming these widely used functional forms. We work through several examples to illustrate the approach.     

Comparative statics for rank-dependent expected utility theory

Recently, a number of generalizations of the expected utility (EU) model have been proposed. In order to make such generalizations useful, it is necessary that they should yield sharp comparative static results, like those obtained using EU theory. In this article, rank dependent expected utility (RDEU) theory, a generalization of EU theory based on the concept of probability weighting, is examined. A number of methods of extending results from EU to RDEU are considered. It is shown that a major class of comparative static results can be extended to the RDEU model, but not to the case of general smooth preferences. This is because RDEU maintains the separation between probabilities and utilities that is abandoned in the general case.     

Expected utility from additive utility on semigroups

In the present paper we study the framework of additive utility theory, obtaining new results derived from a concurrence of algebraic and topological techniques. Such techniques lean on the concept of a connected topological totally ordered semigroup. We achieve a general result concerning the existence of continuous and additive utility functions on completely preordered sets endowed with a binary operation ``+', not necessarily being commutative or associative. In the final part of the paper we get some applications to expected utility theory, and a representation theorem for a class of complete preorders on a quite general family of real mixture spaces.     

Ranked Additive Utility Representations of Gambles: Old and New Axiomatizations

A number of classical as well as quite new utility representations for gains are explored with the aim of understanding the behavioral conditions that are necessary and sufficient for various subfamilies of successively stronger representations to hold. Among the utility representations are: ranked additive, weighted, rank-dependent (which includes cumulative prospect theory as a special case), gains decomposition, subjective expected, and independent increments*, where * denotes something new in this article. Among the key behavioral conditions are: idempotence, general event commutativity*, coalescing, gains decomposition, and component summing*. The structure of relations is sufficiently simple that certain key experiments are able to exclude entire classes of representations. For example, the class of rank-dependent utility models is very likely excluded because of empirical results about the failure of coalescing. Figures 1–3 summarize some of the primary results.JEL Classification  D46, D81     

Is “Generic Utility Theory” a Suitable Theory of Choice Behavior for Gambles with Mixed Gains and Losses?

Miyamoto's (1988, 1992) generic utility theory (GUT) subsumes a broad class of bilinear utility models. 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.     

Compatibility of multiple goal programming and the maximize expected utility criterion

Assuming a decision maker accepts the basic axioms of von Neumann-Morgenstern utility theory and is therefore an expected utility maximizer, this paper argues that the domain of the decision variables in a multiobjective program should be altered in order to guarantee that it will be compatible with the maximize expected utility critierion. Stochastic dominance is employed to approximate this new domain, and for a certain class of decision problems it is shown that this approximation is very good.     

Measuring the Utility of Losses by Means of the Tradeoff Method

This paper investigates the shape of the utility function for losses. From a rational point of view it can be argued that utility should be concave. Empirically, measurements of the utility for losses show mixed results but most evidence supports convex rather than concave utilities. However, these measurements use methods that are either biased by the certainty effect or require complex parametrical estimations. This paper re-examines utility for losses, avoiding the mentioned pitfalls by using the tradeoff method. We find that utility for losses is convex. This is contrary to common assumption in the economics literature. Also, we investigate properties of the tradeoff method showing a new violation of procedure invariance. Our findings demonstrate that diminishing sensitivity is an important phenomenon for utility elicitation.     

A Process Approach to the Utility for Gambling

This paper argues that any specific utility or disutility for gambling must be excluded from expected utility because such a theory is consequential while a pleasure or displeasure for gambling is a matter of process, not of consequences. A (dis)utility for gambling is modeled as a process utility which monotonically combines with expected utility restricted to consequences. This allows for a process (dis)utility for gambling to be revealed. As an illustration, the model shows how empirical observations in the Allais paradox can reveal a process disutility of gambling. A more general model of rational behavior combining processes and consequences is then proposed and discussed.     

Interpersonal comparisons of utility for 2 of 3 types of people

This article argues that there is a natural solution to carry out interpersonal comparisons of utility when the theory of gambles is supplemented with a group operation of joint receipts. If so, three types of people can exist, and the two types having multiplicative representations of joint receipt have, in contrast to most utility theories, absolute scales of utility. This makes possible, at least in principle, meaningful interpersonal comparisons of utility with desirable properties, thus resolving a long standing philosophical problem and having potentially important implications in economics. Two behavioral criteria are given for the three classes of people. At this point the relative class sizes are unknown.     

Meta-Analysis as a Research Synthesis Methodology: Cause for Concern

ABSTRACT

The use of meta-analysis is growing in popularity. It is based on the fundamental notion of the effect size, and a critical assumption is that effect sizes based on different measures are directly comparable. In this article it is argued that the direct comparability of effect sizes across measures implies the invariance of the effect sizes across these measures. A model of standardized mean difference (SMD) effect size invariance is developed, based on multifacet generalizability theory, which shows that SMD effect size invariance requires certain validity invariance conditions to hold. One implication of these findings is that the direct comparability of SMD effect sizes based on different measurement procedures is an empirical matter requiring testing prior to conducting a meta-analysis. Findings are also discussed suggesting that violations of one of these conditions—universe score validity invariance—can bring about substantial differences across SMD effect sizes as a function of measurement procedure. These findings suggest the need for a more refined use of meta-analysis since meta-analytic results may be adversely impacted by the lack of direct comparability of effect sizes based on different measures.     

Ambiguity framed

In his exposition of subjective expected utility theory, Savage (1954) proposed that the Allais paradox could be reduced if it were recast into a format which made the appeal of the independence axiom of expected utility theory more transparent. Recent studies consistently find support for this prediction. We consider a salience-based choice model which explains this frame-dependence of the Allais paradox. We then derive the novel prediction that the presentation format responsible for reductions in Allais-style violations of expected utility theory will also reduce Ellsberg-style violations of subjective expected utility theory. This format makes the appeal of Savage’s “sure thing principle” more transparent. We design an experiment to test this prediction and find strong support for such frame-dependence of ambiguity aversion in Ellsberg-style choices. In particular, we observe markedly less ambiguity-averse behavior in Savage’s matrix format than in a more standard “prospect” format. This finding poses a new challenge for the leading models of ambiguity aversion.     

Moment characterization of higher-order risk preferences

This article presents a characterization of higher-order risk preferences such as prudence or temperance in terms of statistical moments. Our results, which are generalizations of Roger (Theory Decis, 70(1):27–44, 2011) and Ekern (Econ Lett, 6(4), 329–333, 1980), give a better understanding of how higher-order risk preferences relate to skewness preference and kurtosis aversion. While they are not based on expected utility theory, an implication within that theory is that all commonly used utility functions exhibit skewness preference and kurtosis aversion.     

A note on deriving rank-dependent utility using additive joint receipts

Luce and Fishburn (1991) derived a general rank-dependent utility model using an operation ⊕ of joint receipt. Their argument rested on an empirically supported property (now) calledsegregation and on the assumption that utility is additive over ⊕. This note generalizes that conclusion to the case where utility need not be additive over ⊕, but rather is of a more general form, which they derived but did not use in their article. Tversky and Kahneman (1992), conjecturing that the joint receipt of two sums of money is simply their sum, criticized that original model because ⊕=+ together with additive utility implies the unacceptable conclusion that the utility of money is proportional to money. In the present generalized theory, if ⊕=+, utility is a negative exponential function of money rather than proportional. Similar results hold for losses. The case of mixed gains and losses is less well understood.     

A theory of subjective expected utility with vague preferences

This paper shows how notions of vagueness in preferences and judgments of personal probabilities can be accommodated within an axiomatization of subjective expected utility by the use of extraneous scaling probabilities and gambles on consequences. The representational form obtained says that the subjective expected utility of one act exceeds the subjective expected utility of a second act whenever the first is preferred to the second. The paper also explores the possibility of obtaining this representational form under Savage's formulation, which does not use extraneous probabilities, and discusses difficulties encountered in this approach.     

A multiattribute decision time theory

In this study, we analyze choice in the presence of some conflict that affects the decision time (response time), a subject that has been documented in the literature. We axiomatize a multiattribute decision time (MDT) representation, which is a dynamic extension of the classic multiattribute expected utility theory that allows potentially incomplete preferences. Under this framework, one alternative is preferred to another in a certain period if and only if the weighted sum of the attribute-dependent expected utility induced by the former alternative is larger than that induced by the latter for all attribute weights in a closed and convex set. MDT uniquely determines the decision time as the earliest period at which the ranking between alternatives becomes decisive. The comparative statics result indicates that the decision time provides useful information to locate indifference curves in a specific setting. MDT also explains various empirical findings in economics and other relevant fields.     

Individual vs. couple behavior: an experimental investigation of risk preferences

In this article, we elicit both individuals’ and couples’ preferences assuming prospect theory (PT) as a general theoretical framework for decision under risk. Our experimental method, based on certainty equivalents, allows to infer measurements of utility and probability weighting at the individual level and at the couple level. Our main results are twofold. First, risk attitude for couples is compatible with PT and incorporates deviations from expected utility similar to those found in individual decision making. Second, couples’ attitudes towards risk are found to be consistent with a mix of individual attitudes, women being more influent on couples’ preferences at low probability levels.     

Reconciliation with the Utility of Chance by Elaborated Outcomes Destroys the Axiomatic Basis of Expected Utility Theory

Expected utility theory does not directly deal with the utility of chance. It has been suggested in the literature (Samuelson, 1952, Markowitz, 1959) that this can be remedied by an approach which explicitly models the emotional consequences which give rise to the utility of chance. We refer to this as the elaborated outcomes approach. It is argued that the elaborated outcomes approach destroys the possibility of deriving a representation theorem based on the usual axioms of expected utility theory. This is shown with the help of an example due to Markowitz. It turns out that the space of conceivable lotteries over elaborated outcomes is too narrow to permit the application of the axioms. Moreover it is shown that a representation theorem does not hold for the example.     

Empirical rules of thumb for choice under uncertainty

A substantial body of empirical evidence shows that individuals overweight extreme events and act in conflict with the expected utility theory. These findings were the primary motivation behind the development of a rank-dependent utility theory for choice under uncertainty. The purpose of this paper is to demonstrate that some simple empirical rules of thumb for choice under uncertainty are consistent with the rank-dependent utility theory.     

Dishonest Academic Conduct: From the Perspective of the Utility Function

Dishonest academic conduct has aroused extensive attention in academic circles. To explore how scholars make decisions according to the principle of maximal utility, the author has constructed the general utility function based on the expected utility theory. The concrete utility functions of different types of scholars were deduced. They are as follows: risk neutral, risk averse, and risk preference. Following this, the assignment method was adopted to analyze and compare the scholars’ utilities of academic conduct. It was concluded that changing the values of risk costs, internal condemnation costs, academic benefits, and the subjective estimation of penalties following dishonest academic conduct can lead to changes in the utility of academic dishonesty. The results of the current study suggest that within scientific research, measures to prevent and govern dishonest academic conduct should be formulated according to the various effects of the above four variables.