Combining additive representations on subsets into an overall representation

Many traditional conjoint representations of binary preferences are additively decomposable, or additive for short. An important generalization arises under rank-dependence, when additivity is restricted to cones with a fixed ranking of components from best to worst (comonotonicity), leading to configural weighting, rank-dependent utility, and rank- and sign-dependent utility (prospect theory). This paper provides a general result showing how additive representations on an arbitrary collection of comonotonic cones can be combined into one overall representation that applies to the union of all cones considered. The result is applied to a new paradigm for decision under uncertainty developed by Duncan Luce and others, which allows for violations of basic rationality properties such as the coalescing of events and other framing conditions. Through our result, a complete preference foundation of a number of new models by Luce and others can be obtained. We also show how additive representations on different full product sets can be combined into a representation on the union of these different product sets.     

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.     

厌而避额外之“利”；喜而趋额外之“害”

趋利避害是生物的本能。《管子·禁藏》云：夫凡人之情, 见利莫能勿就, 见害莫能勿避。“两利相权取其重, 两害相权取其轻”是规范性决策理论的一基本原则。本研究以金钱作为奖赏或惩罚刺激, 检验人们能否理性地遵循“价值最大化”原则。在实验中, 主试以检查硬币生产年代的数目为由, 让被试逐枚地感受两个金钱序列：10元硬币序列(由20枚五角硬币组成)和10.3元硬币序列(由20枚五角硬币和3枚一角硬币组成),随后评定获得(或损失)各金钱序列的高兴(或不高兴)程度, 并从中选择一金钱序列(与硬币等值的金钱)作为其奖赏(或惩罚)。实验为2 (3枚一角硬币在序列首vs. 3枚一角硬币在序列尾)´2(先检查10元硬币序列vs. 先检查10.3元硬币序列)´2(损失vs. 获得)三因素设计, 每种条件随机分配15名商学院学生被试。结果表明, 被试倾向选择获益少(10元)和损失多(-10.3元)的金钱序列; 且获益大(10.3元)时高兴程度小, 损失小(-10元)时不高兴程度大。这一结果意味着：“聊”并不胜于“无”,反而是“无”胜于“聊”。其中, 伴随着违背价值最大化原则所产生的情感亦有悖逻辑。负性情感的引发一般有其“逻辑正确”的原因(如, 无惠而不乐); 而引发本研究负性情感的原因实属“逻辑错误”(如, 惠多而不乐)。这种不曾被定义而类似于“冤”的情感不仅见于个人,也见于民族、国家间的持续交往, 值得进一步研究。     

On the equivalence between elimination-by-aspects and generalised extreme value models of choice behaviour

Elimination-by-aspects and generalised extreme value offer competing paradigms for the representation of a common behaviour, that of individual discrete choice. Observing certain consistencies in their mathematical structure, several eminent authors have commented on the degree of equivalence between the two paradigms. Most contributions to this debate have, however, been less than definitive. More fundamentally, the contributions lack consensus. We advance the debate by establishing formal mathematical conditions under which three-alternative tree models from the two paradigms are exactly equivalent. We then extend our analysis to consider more general models, showing that equivalence can be established for general tree models, but not for cross-nested models.     

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.     

行为决策理论之父：纪念Edwards教授2周年忌辰

著名心理学家W ard Edwards对行为决策的学科形成与理论发展作出了巨大贡献。文章简要介绍了Edwards的生平,以主观期望效用模型和贝叶斯决策为核心回顾了Edwards的决策理论、主要成就及其对行为决策研究的学术贡献。文章并从行为决策领域的研究、科普、应用及人才培养等方面总结了中国行为决策研究的发展历程,以及Edwards的学术思想对中国行为决策研究的主要影响。文章展望了行为决策研究的前景,并呼吁更多的中国心理学工作者投身于行为决策研究。     

Distortion of probability and outcome information in risky decisions

Substantial evidence indicates that information is distorted during decision making, but very few studies have assessed the distortion of probability and outcome information in risky decisions. In two studies involving six binary decisions (e.g., banning blood donations from people who have visited England, because of “mad cow disease”), student and nonstudent participants distorted their evaluations of probability and outcome information in the direction of their preferred decision alternative and used these biased evaluations to update their preferences. Participants also evaluated the utilities of possible outcomes more positively when the outcomes could follow only from the preferred alternative and more negatively when they could follow only from the competing alternative. Such circular reasoning is antithetical to the normative consequentialist principles underlying decision analysis. Presenting numerical information as precise values or as ranges of values did not significantly affect information distortion, apparently because the manipulation did not affect perceived ambiguity as intended.     

Better safe than sorry: Precautionary reasoning and implied dominance in risky decisions

In four studies, student and nonstudent participants evaluated the possible outcomes of binary decisions involving health, safety, and environmental risks (e.g., whether to issue a dam‐failure evacuation order). Many participants indicated that false positives (e.g., evacuation, but no dam failure) were better than true negatives (e.g., no evacuation and no dam failure), thereby implying that the more protective action dominated the less protective action. A common rationale for this response pattern was the precautionary maxim “better safe than sorry.” Participants apparently evaluated outcomes partly on the basis of the decisions that might lead to them, in conflict with consequentialist decision models. Consistent with this explanation, the prevalence of implied dominance decreased substantially when the emphasis on decisions was reduced. These results demonstrate that an initial preference for a decision alternative can alter the evaluation of possible consequences of both the preferred alternative and a competing alternative, suggesting positive feedback loops that reinforce the initial preference. The rationality of considering the decision itself as an attribute of possible outcomes is discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

Projective expected utility

Motivated by several classic decision-theoretic paradoxes, and by analogies with the paradoxes which in physics motivated the development of quantum mechanics, we introduce a projective generalization of expected utility along the lines of the quantum-mechanical generalization of probability theory. The resulting decision theory accommodates the dominant paradoxes, while retaining significant simplicity and tractability. In particular, every finite game within this larger class of preferences still has an equilibrium.     

Life satisfaction,ethical reflection,and the science of happiness

Life satisfaction is widely considered to be a central aspect of human welfare. Many have identified happiness with it, and some maintain that well-being consists largely or wholly in being satisfied with one’s life. Empirical research on well-being relies heavily on life satisfaction studies. The paper contends that life satisfaction attitudes are less important, and matter for different reasons, than is widely believed.] For such attitudes are appropriately governed by ethical norms and are perspectival in ways that make the relationship between life satisfaction and welfare far more convoluted than we tend to expect. And the common identification of life satisfaction with happiness, as well as widespread views about the centrality of life satisfaction for well-being, are problematical at best. The argument also reveals an unexpected way in which philosophical ethics can inform scientific psychology: specifically, ethical reflection can help explain empirical results insofar as they depend on people’s values.