Money versus pain: experimental study of a conflict in humans.

Ten healthy human males volunteered to be subjects in an experiment in which they were to be paid to endure a painful sensation. This sensation was produced by isometric muscular contraction in the thighs. For each of six sessions the subjects received either a payment that was changed for each session (0.2, 0.5, 1.25, 3.125, 7.8125 French francs per 20 s) or a lump sum. At the beginning of a session, the subjects assumed a seated position against a wall, but without a seat, and the duration for which they could hold this position was the chief variable measured. Heart rate, blood pressure, and magnitude estimation of pain were also recorded periodically throughout each session. Pain was reported after a mean delay of 15 +/- 7 s (SE), and the magnitude estimates then increased linearly with time. The duration of maintaining the painful position increased linearly in relation to the logarithm of the increase in the amount of payment. Thus, utility of money decreased when pitted against pain.     

A simple model for the utility of gambling

A model of the utility of gambling is presented in a modified von Neumann-Morgenstern format. Axioms imply a utility function that preserves preferences between sure things and between gambles. The addition of a utility of gambling term to the expected utility of a gamble preserves preference comparisons between gambles and sure things. Aspects of the utility of gambling are noted, and comparisons are made to standard concepts of risk attitudes.The author is indebted to Joseph Sani for valuable discussions on the topic of this paper.     

Decomposition of multivariate utility functions in non-additive expected utility theory

In expected utility many results have been derived that give necessary and/or sufficient conditions for a multivariate utility function to be decomposable into lower-dimensional functions. In particular, multilinear, multiplicative and additive decompositions have been widely discussed. These utility functions can be more easily assessed in practical situations. In this paper we present a theory of decomposition in the context of nonadditive expected utility such as anticipated utility or Choquet expected utility. We show that many of the results used in conventional expected utility carry over to these more general frameworks. If preferences over lotteries depend only on the marginal probability distributions, then in expected utility the utility function is additively decomposable. We show that in anticipated utility the marginality condition implies not only that the utility function is additively decomposable but also that the distortion function is the identity function. We further demonstrate that a decision maker who is bivariate risk neutral has a utility function that is additively decomposable and a distortion function q for which q(½) = ½.     

Random error in holistic evaluations and additive decompositions of multiattribute utility — an empirical comparison

This paper details the results of an empirical investigation of the random errors associated with decomposition estimates of multiattribute utility. In a riskless setting, two groups of subjects were asked to evaluate multiattribute alternatives both holistically and with the use of an additive decomposition. For one group, the alternatives were described in terms of three attributes, and for the other in terms of five. Estimates of random error associated with the various elicitations (holistic, single-attribute utility, scaling constants, or weights) were obtained using a test-retest format. It was found for both groups that the additive decomposition had significantly smaller levels of random error than the holistic evaluation. However, the number of attributes did not seem to make a significant difference to the amount of random error associated with the decomposition estimates. The levels of error found in the various elicitations were consistent with theoretical bounds that have recently been proposed in the literature. These results show that the structure imposed on the problem through decomposition results in measurable improvement in quality of the multiattribute utility judgements, and contribute to a greater understanding of the decomposition method in decision analysis.     

Intuitions about declining marginal utility

In two studies, subjects judged the desirability of distributions of life expectancy or money. Their judgments showed declining marginal utility. That is, they were less sensitive to changes at the high end of each scale. Subjects also made utility ratings of the outcomes of individuals. And they made ratings of the distributions when these were described in terms of utility ratings rather than goods (years or dollars). The judgments of utility ratings showed equivalent declining marginal utility, even though they were based on utilities that themselves declined marginally. People extend their intuition about declining marginal utility to utility itself, as if utility had utility that declined marginally. In one experiment, a similar result was found with gambles: people are risk averse for utility as well as for money. We argue that this is an overextension of a reasonable heuristic and that this heuristic may account for one classic objection to utilitarian distributions. Copyright © 2001 John Wiley & Sons, Ltd.     

Peak-End rule versus average utility: How utility aggregation affects evaluations of experiences

The “Peak-End rule” which averages only the most extreme (Peak) and the final (End) impressions, is often a better predictor of overall evaluations of experiences than average impressions. We investigate the similarity between the evaluations of experiences based on Peak-End and average impressions. We show that the use of the Peak-End rule in cross-experience comparisons can be compatible with preferences for experiences that are better on average. Two conditions are shown to make rankings of experiences similar regardless of the aggregation rule: (i) the individual heterogeneity in the perception of stimuli, and (ii) the persistence in impressions. We describe their effects theoretically, and obtain empirical estimates using data from previous research. Higher estimates are shown to increase correlational measures of association between the Peak-End and average impressions. The high association per se is shown to be not only a theoretical possibility, but an empirical fact.     

Is Reported Happiness Five Years Ago Comparable to Present Happiness? A Cautionary Note

In the United States reported happiness five years ago is not comparable to present happiness. The improvement in happiness over the last five years obtained by differencing current reports of happiness today and happiness five years ago is not significantly related to the actual improvement in happiness over the same period. The currently reported five-year change in happiness is highly sensitive to current economic conditions, varying inversely with both the inflation and unemployment rates.Ordinarily, happiness five years ago as currently reported is less than present happiness, but the worse the current economic conditions are, the better the past looks relative to the present. If current economic conditions get bad enough, past happiness will be rated higher than present. Reports of happiness five years ago are not telling us about the utility respondents actually experienced at that time; they are telling us, instead, about respondents' current decision utility–which situation, today's or that five years ago, they would opt for if given the choice today.     

A Note on the Power of Multiattribute One‐switch Utility Functions

One‐switch utility functions model situations in which the preference between two alternatives switches only once as the outcome of one attribute of both alternatives changes from low to high. Recent research cites evidence that the sum of exponential functions (sumex) is the most convincing type for modelling one‐switch utility functions. Sumex functions allow to model exactly one preferential switch and they are convenient for estimating one‐switch utility functions. However, it is unclear so far if sumex functions are suitable to model preferential switches that are perceivable by a decision maker. This paper first analyses how different the utility of two alternatives before and after a preferential can be modelled with sumex functions given that the preferential switch is caused by a particular attribute outcome improvement. It thereafter investigates how accurately decision makers perceive such utility differences. Copyright © 2015 John Wiley & Sons, Ltd.     

Lay rationalism and inconsistency between predicted experience and decision

Decision‐makers are sometimes depicted as impulsive and overly influenced by ‘hot’, affective factors. The present research suggests that decision‐makers may be too ‘cold’ and overly focus on rationalistic attributes, such as economic values, quantitative specifications, and functions. In support of this proposition, we find a systematic inconsistency between predicted experience and decision. That is, people are more likely to favor a rationalistically‐superior option when they make a decision than when they predict experience. We discuss how this work contributes to research on predicted and decision utilities; we also discuss when decision‐makers overweight hot factors and when they overweight cold factors. Copyright © 2003 John Wiley & Sons, Ltd.     

Multiattribute signed orders

A self-reflecting signed order is a preference relation that compares relative likes and dislikes for items in a set X by jointly ordering X and a disjoint copy of X. If you would like Jones but not Smith appointed to a committee, and also think it more important to exclude Smith than include Jones, your self-reflecting signed order records this information. We review basic representational theory for signed orders, then examine them when X is multiattributed. Axioms for additive measurement of multiattribute self-reflecting signed orders are specified for several X-structures.     

Utility independence of multiattribute utility theory is equivalent to standard sequence invariance of conjoint measurement

Utility independence is a central condition in multiattribute utility theory, where attributes of outcomes are aggregated in the context of risk. The aggregation of attributes in the absence of risk is studied in conjoint measurement. In conjoint measurement, standard sequences have been widely used to empirically measure and test utility functions, and to theoretically analyze them. This paper shows that utility independence and standard sequences are closely related: utility independence is equivalent to a standard sequence invariance condition when applied to risk. This simple relation between two widely used conditions in adjacent fields of research is surprising and useful. It facilitates the testing of utility independence because standard sequences are flexible and can avoid cancelation biases that affect direct tests of utility independence. Extensions of our results to nonexpected utility models can now be provided easily. We discuss applications to the measurement of quality-adjusted life-years (QALY) in the health domain.     

The linear utility model for optimal selection

A linear utility model is introduced for optimal selection when several subpopulations of applicants are to be distinguished. Using this model, procedures are described for obtaining optimal cutting scores in subpopulations in quota-free as well as quota-restricted selection situations. The cutting scores are optimal in the sense that they maximize the overall expected utility of the selection process. The procedures are demonstrated with empirical data.     

Utility Functions: A Compromise Programming Approach to Specification and Optimization

Nowadays, utility theory and compromise programming (CP) are considered very different paradigms and methodologies to measure preferences as well as to determine decision maker's optima on an efficient frontier. In this paper, however, we show that a utility function with separate variables (presented in the form of a Taylor series around the ideal point) is reducible to a weighted sum of CP distances. This linkage between utility and compromise (based on a main assumption in which the usual utility functions hold) leads to (i) a method for specification and optimization of usual utility functions by operational technique and (ii) a reformulation of standard CP with the advantage of determining the best CP solution from a utility perspective. © 1997 John Wiley & Sons, Ltd.     

Managers' Reactions to Utility Analysis and Perceptions of What Influences Their Decisions

Recent research on providing utility analysis (UA) information has shown small positive effects on acceptance of selection tests by human resource decision-makers (Carson, Becker, & Henderson, Journal of Applied Psychology, 83 84–96 (1998). In the present study, 218 managers provided reactions to UA information. Not only do our findings replicate the positive effects of UA, we found managers also responded favorably to UA information when asked independently of the decision making process. Specifically, when asked to rank order information in terms of what they perceived to be most influential in helping them make their final decisions, those who received UA information ranked it among the highest.     

Decomposition,Interdependence and Precision in Multiattribute Utility Measurements

Traditionally, parameters of multiattribute utility models, representing a decision maker's preference judgements, are treated deterministically. This may be unrealistic, because assessment of such parameters is potentially fraught with imprecisions and errors. We thus treat such parameters as stochastic and investigate how their associated imprecision/errors are propagated in an additive multiattribute utility function in terms of the aggregate variance. Both a no information and a rank order case regarding the attribute weights are considered, assuming a uniform distribution over the feasible region of attribute weights constrained by the respective information assumption. In general, as the number of attributes increases, the variance of the aggregate utility in both cases decreases and approaches the same limit, which depends only on the variances as well as the correlations among the single-attribute utilities. However, the marginal change in aggregate utility variance decreases rather rapidly and hence decomposition as a variance reduction mechanism is generally useful but becomes relatively ineffective if the number of attributes exceed about 10. Moreover, it was found that utilities which are positively correlated increase the aggregate utility variance, hence every effort should be made to avoid positive correlations between the single-attribute utilities. We also provide guidelines for determining under what condition and to what extent a decision maker should decompose to obtain an aggregate utility variance that is smaller than that of holistic assessments. Extensions of the current model and empirical research to support some of our behavioural assumptions are discussed. © 1997 John Wiley & Sons, Ltd.     

Empirical underidentification in estimating random utility models: The role of choice sets and standardizations

A standard approach to distinguishing people’s risk preferences is to estimate a random utility model using a power utility function to characterize the preferences and a logit function to capture choice consistency. We demonstrate that with often-used choice situations, this model suffers from empirical underidentification, meaning that parameters cannot be estimated precisely. With simulations of estimation accuracy and Kullback–Leibler divergence measures we examined factors that potentially mitigate this problem. First, using a choice set that guarantees a switch in the utility order between two risky gambles in the range of plausible values leads to higher estimation accuracy than randomly created choice sets or the purpose-built choice sets common in the literature. Second, parameter estimates are regularly correlated, which contributes to empirical underidentification. Examining standardizations of the utility scale, we show that they mitigate this correlation and additionally improve the estimation accuracy for choice consistency. Yet, they can have detrimental effects on the estimation accuracy of risk preference. Finally, we also show how repeated versus distinct choice sets and an increase in observations affect estimation accuracy. Together, these results should help researchers make informed design choices to estimate parameters in the random utility model more precisely.     

不确定性风险选择的抱负水平—相对效用整合理论

本文认为不确定性风险决策备择方案的选择标准既不是规范效用理论所主张的效用最大化,也不只是研究者们基于西蒙有限理性决策理论而提出的抱负水平,而是存在于决策不同阶段上的、由启发式策略控制着的这两种标准的整合,我们称之为抱负水平－相对效用整合标准。为此,我们在研究抱负水平结构的基础上提出了负险选择的抱负水平－相对效用整合理论及其支持性研究证据,并就有关问题进行了讨论与思考。指出抱负水平－相对效用整合是风     

Providing an analytic structure for key system design choices

The design of a system, especially a system architecture, requires the balancing of multiple performance parameters with the system cost and other implementation issues. Multi-attribute utility theory provides a structured, coherent framework for conducting an analysis in which system designs are evaluated on multiple performance parameters. This paper describes the application of multi-attribute utility analysis to the design of the Worldwide Digital Signal Systems Architecture (WWDSA), a telecommunications system, by the United States' Defense Communications Agency (now called the Defense Information Systems Agency). The advantages of using multi-attribute utility theory during the system design are highlighted. In addition, we discuss several key analytical issues that led to this application being a success in the eyes of the decision makers.     

Causes of Allais common consequence paradoxes: An experimental dissection

The common consequence paradox of Allais can be decomposed into three simpler principles: transitivity, coalescing, and restricted branch independence. Different theories attribute such paradoxes to violations of restricted branch independence only, to coalescing only, or to both. This study separates tests of these two properties in order to compare these theories. Although rank-dependent utility (RDU) theories, including cumulative prospect theory (CPT), violate branch independence, the empirical pattern of violations is opposite that required by RDU theories to account for Allais paradoxes. Data also show systematic violations of coalescing, which refute RDU theories. The findings contradict both original and CPTs with or without their editing principles of combination and cancellation. Modal choices were well predicted by Birnbaum's RAM and TAX models with parameters estimated from previous data. The effects of event framing on these tests were also assessed and found to be negligible.     

Double Reference Points: the Effects of Social and Financial Reference Points on Decisions Under Risk

The existing literature is inconsistent about how social comparison affects risk attitudes. We propose a framework where the total utility is composed of the social and financial utilities. The financial utility is consistent with prospect theory (i.e., an S‐shaped utility function with a financial reference point), whereas the social utility is affected by both social and financial reference points. Therefore, social risk attitudes are determined by interaction between gains/losses in both social and financial contexts. On the basis of safety‐first principle, we propose that when experiencing financial gains, individuals tend to seek upside potential and take social risks (i.e., a convex social utility function). In contrast, when facing financial losses, people would be more risk seeking in social gains but more risk averse in social losses to maximize security (i.e., an inverse S‐shaped utility function). We also propose that the relative importance of financial and social utilities depends on the saliency of the reference points and size of stakes. Studies 1 and 2 showed that individuals were risk seeking in both social gains and losses with social reference points alone. Studies 3 and 4 demonstrated that when both financial and social reference points were salient, participants were risk averse in both social gains and losses when facing financial gains, but risk seeking in social gains and risk averse in social losses when facing financial losses. The hypotheses derived from the theoretical framework were in general supported by our experiments. Copyright © 2015 John Wiley & Sons, Ltd.