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.     

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.     

A simple trade-off condition for additive multiattribute utility

We show that only two simple trade-off judgments are sufficient to determine whether the multiplicative multiattribute model assumes its additive form, regardless of the number of attributes in the model. This additivity condition offers a useful alternative to the test based on multiattribute lotteries commonly presented in textbooks. It can make the determination of additivity easier and more reliable. © 1997 John Wiley & Sons, Ltd.     

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.     

Functional measurement approach to self-estimation in multiattribute evaluation

Multiattribute analysis depends on measurement of values and weights. Unless these measures reflect the decision maker's true values and weights, the multiattribute formula may put a less-preferred alternative in first place. To avoid such disordinality requires stringent measurement conditions: First, the values and weights must be on linear (equal interval) or ratio (known zero) scales. Second, these scales must satisfy a condition of common unit across disparate attribute dimensions. Most methods of range adjustment beg both of these measurement questions. Functional measurement theory can solve both problems and so can be useful in multiattribute analysis. Past work has established the operation of a general cognitive algebra as an empirical reality. The averaging model, in particular, makes possible the definition and estimation of weights and values as distinct psychological parameters. It can also solve the problem of common unit. Cognitive algebra thus provides a grounded theoretical foundation on which to develop self-estimation methodology, in which decision makers provide direct estimates of their values and weights. The logic is straightforward. Functional measurement can analyze global judgments to obtain validated psychological scales. These scales may then be used as validational criteria for the self-estimates. Procedures to eliminate biases in the self-estimates can thus be tested and refined in well-learned multiattribute tasks, such as judgments of meals, in which global judgments are trustworthy. Once developed, such self-estimation procedures may be used with some confidence for general multiattribute analysis. A number of studies from 20-odd years of work on the theory of information integration are summarized to show good, although not unmixed promise for self-estimation.     

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.     

Random noun generation in younger and older adults

We examined age-related changes of executive functions by means of random noun generation. Consistent with previous observations on random letter generation, older participants produced more prepotent responses than younger ones. In the case of random noun generation, prepotent responses are nouns of the same category as the preceding noun. In contrast to previous observations, older participants exhibited stronger repetition avoidance and a stronger tendency toward local evenness—that is, toward equal frequencies of the alternative responses even in short subsequences. These data suggest that at higher adult age inhibition of prepotent responses is impaired. In addition, strategic attentional processes of response selection are strengthened, in particular the application of a heuristic for randomness. In this sense response selection is more controlled in older than in younger adults.     

The roles of retribution and utility in determining punishment

Three studies examined the motives underlying people’s desire to punish. In previous research, participants have read hypothetical criminal scenarios and assigned “fair” sentences to the perpetrators. Systematic manipulations within these scenarios revealed high sensitivity to factors associated with motives of retribution, but low sensitivity to utilitarian motives. This research identifies the types of information that people seek when punishing criminals, and explores how different types of information affect punishments and confidence ratings. Study 1 demonstrated that retribution information is more relevant to punishment than either deterrence or incapacitation information. Study 2 traced the information that people actually seek when punishing others and found a consistent preference for retribution information. Finally, Study 3 confirmed that retribution information increases participant confidence in assigned punishments. The results thus provide converging evidence that people punish primarily on the basis of retribution.     

Why additive utility models fail as descriptions of choice behavior

This experiment sought to determine whether previously found metric violations of additive expectancy-value models C.F. J. C. Shanteau, Journal of Experimental Psychology, 1974, 103, 680–691; J. G. Lynch and J. L. Cohen, Journal of Personality and Social Psychology, 1978, 36, 1138–1151) were attributable to the inappropriateness of these models or to nonlinearities in the relationship between numerical ratings and underlying psychological impressions. Undergraduate participants performed two tasks employing the same experimental stimuli. In the first task, they rated the subjective values of hypothetical bets, judged separately and in combination. In the second task, they made pairwise comparisons of the same bets in terms of preference. The use of the same experimental stimuli in both tasks allowed a test of alternative models of utility judgment through application of the criterion of scale convergence (M. H. Birnbaum & C. T. Veit, Perception and Psychophysics, 1974, 15, 7–15). Results suggested that the additive expectancy-value model of judgments of the utilities of combinations of outcomes should be replaced by a weighted averaging rule in which the weight given to the value of each outcome in the averaging process is greater when this value is negative and extreme than when it is neutral.     

Processing time predictions of current models of perception in the classic additive factors paradigm

This article explores the consequences for factorial additivity in a Sternberg [(1969). The discovery of processing stages: Extensions of donders method In: W.G. Koster (Ed.), Attention and performance II, Acta Psychologica, 30, 276-315] additive-factors paradigm of the assumptions adopted by models of perception that relate the representation of a stimulus to decision time. Three example models, signal detection theory with the latency-distance hypothesis, stochastic general recognition theory, and a random walk model of exemplar classification, are interrogated to determine what type of interaction they predict factors will yield in a hypothetical factorial (choice) reaction time experiment in which the ‘empirical’ factors’ effects are manifest as parameter changes. All frameworks make the critical assumption that decision time depends on the perceptual representation of the stimulus as well as the architecture. As a consequence, nonadditivity of factors thought to affect different “stages” in the classical approach emerges within the current modeling approach. The nature of this influence is revealed through analytic investigations and simulation. Earlier empirical findings of failures of selective influence that have defied adequate explanation are reinterpreted in light of the present findings.     

Probabilistic choice (models) as a result of balancing multiple goals

We conceptualize probabilistic choice as the result of the simultaneous pursuit of multiple goals in a vector optimization representation, which is reduced to a scalar optimization that implies goal balancing. The majority of prior theoretical and empirical work on such probabilistic choice is based on random utility models, the most basic of which assume that each choice option has a valuation that has a deterministic (systematic) component plus a random component determined by some specified distribution. An alternate approach to probabilistic choice has considered maximization of one quantity (e.g., utility), subject to constraints on one or more other quantities (e.g., cost). The multiple goal perspective integrates the results regarding the well-studied multinomial logit model of probabilistic choice that has been derived from each of the above approaches; extends the results to other models in the generalized extreme value (GEV) class; and relates them to recent axiomatic work on the utility of gambling.     

Judgment of line orientation depends on gender, education, and type of error

Visuospatial tasks are particularly proficient at eliciting gender differences during neuropsychological performance. Here we tested the hypothesis that gender and education are related to different types of visuospatial errors on a task of line orientation that allowed the independent scoring of correct responses ("hits", or H) and one type of incorrect responses ("commission errors", or CE). We studied 343 volunteers of roughly comparable ages and with different levels of education. Education and gender were significantly associated with H scores, which were higher in men and in the groups with higher education. In contrast, the differences between men and women on CE depended on education. We concluded that (I) the ability to find the correct responses differs from the ability to avoid the wrong responses amidst an array of possible alternatives, and that (II) education interacts with gender to promote a stable performance on CE earlier in men than in women.     

Introversion,inhibition, and displayed anxiety: The role of error reactivity processes

Three studies involving 176 undergraduates examined the personality-related correlates of tendencies to slow down following errors in choice reaction time tasks. Such tendencies were hypothesized to tap individual differences in threat reactivity processes and therefore be relevant to the prediction of phobic-like fear (Study 1) and displayed anxiety as rated by informants (Studies 2 and 3). However, on the basis of the idea that high levels of extraversion may suppress threat reactivity processes, it was hypothesized that extraversion and post-error slowing tendencies would interact in predicting the dependent measures. The studies supported the latter interactive hypothesis in that post-error slowing tendencies were predictive of displayed anxiety at low, but not high, levels of extraversion. The discussion focuses on the respective roles of error-reactivity processes and extraversion in predicting behavioral inhibition and displayed anxiety.     

Estimation of indifference curves in the Marschak-Machina triangle a direct test of the “fanning out” hypothesis

The ongoing debate on the correct modelling of economic behaviour under risk makes heavy expositional use of the 'Marschak-Machina Triangle'. This has also been used when constructing tests of the various competing theories. In this paper, we adopt a more direct approach - by estimating subjects' indifference maps in the Triangle. Employing an interview technique, we find that most subjects have maps which are nearly consistent with those implied by Subjective Expected Utility theory.     

Factors influencing the use of internal summary evaluations versus external information in choice

Decision makers cope with more demanding tasks by shifting their cognitive strategies, balancing effort expenditure against the desire to produce an accurate response. In choice tasks, one method for reducing effort while simultaneously maintaining accuracy is to shift from a reliance on information obtained from the external environment to that retrieved from memory, particularly summary evaluations (i.e. relatively stable evaluative reactions to the overall attractiveness of individual alternatives) acquired from previous decision-making experience. We examined four factors that should all encourage decision makers to rely to some extent on internal summary evaluations rather than external information search: (1) increased external search costs, (2) greater time pressure, (3) increased incentives to make an accurate choice, and (4) increased levels of prior experience with the choice context. Sixty experimental subjects chose their preferred alternative from a set of women's magazines. Decision processes were inferred from verbal protocols, computer-generated search records, and decision times. Only increased external search costs led to a greater reliance on summary evaluations. Although increased time pressure, increased incentives, and increased experience with the context did lead to changes in search and evaluation processes, contrary to initial expectations decision makers did not shift to a greater reliance on summary evaluations. These results suggest that while decision makers do sometimes use summary evaluations as a substitute for external search, this is only one of several mechanisms available for effort reduction. Understanding when and where decision makers rely upon summary evaluations probably requires a broader conceptualization of knowledge structures, particularly a consideration of the knowledge that decision makers possess about different choice strategies and their effectiveness.     

归纳认知过程中的价值因素

现代归纳逻辑产生之初,一些逻辑学家依照逻辑学求真的传统研究归纳推理前提的真对结论真的支持程度。随着研究的深入,价值因素进入归纳逻辑的视野,逻辑学家发现,在人的归纳认知过程中渗透着价值因素。