Koopmans’ constant discounting for intertemporal choice: A simplification and a generalization

Koopmans provided a well-known preference axiomatization for discounted utility, the most widely used model for maximizing intertemporal choice. There were, however, some technical problems in his analysis. For example, there was an unforeseen implication of bounded utility. Some partial solutions have been advanced in various fields in the literature. The technical problems in Koopmans’ analysis obscure the appeal of his intuitive axioms. This paper completely resolves Koopmans’ technical problems. In particular, it obtains complete flexibility concerning the utility functions that can be used. This paper, thus, provides a clean and complete preference axiomatization of discounted utility, clarifying the appeal of Koopmans’ intuitive axioms.     

A solution to a problem raised in Luce and Marley (2005)

Luce and Marley [2005. Ranked additive utility representations of gambles: Old and new axiomatizations. Journal of Risk and Uncertainty, 30, 21-62] examined various relations between mathematical forms for the utility of joint receipt ⊕ of gambles and for the utility of uncertain gambles. Their assumptions lead to a bisymmetry functional equation which, when the gambles are ranked, is defined on a restricted domain. Maksa [1999. Solution of generalized bisymmetry type equations without surjectivity. Aequationes Mathematicae, 57, 50-74] solved the general case and Kocsis [2007. A bisymmetry equation on restricted domain. Aequationes Mathematicae, 73, 280-284] presents the solution for the ranked case. The latter solution allows us to solve open problem 5 in Luce and Marley (2005) by showing that the assumptions of their Theorem 19 for an order-preserving ranked additive utility (RAU) representation U imply that U is a ranked weighted utility (RWU) representation that is additive over ⊕.     

Balance in Life and Declining Marginal Utility of Diverse Resources

Declining marginal utility (DMU) describes the reduced value that additional units of money or consumer goods have in comparison to units acquired earlier. We extend this idea to social resources and activities such as socializing time, free time, and number of children, suggesting that most resources will show DMU as the person experiences more of them. In Study 1, participants reported how many years of adult life they would sacrifice to have increasingly more of each resource or activity. Income showed declining marginal utility, but other goods showed an ideal-level pattern in which they were valued less after an optimal amount. In Phase 2 of Study 1, we assessed the mix of activities people most prefer. Participants rated the desirability of various combinations of time spent in different activities. Spending all of one’s free time in a pleasant activity was not as desirable as spending some of the time in other desirable, but less enjoyable, activities. In Study 2, we used a representative sample of the world to assess people’s affect balance (positive minus negative moods) on the previous day, along with how much time they spent in activities such as socializing with family and friends. The most popular activity was socializing with family and friends, but even here there was DMU for more hours of this behavior. We also analyzed several forms of well-being in reference to household income. Income showed a clear DMU pattern using daily moods as the outcome, as well as for life evaluations and satisfaction with standard of living. The results of the two studies explain why people do not pursue happiness by spending all of their time in the most pleasant activities, such as socializing, but instead choose a mixture of activities. A desire for balance in human activities and resources has important implications for the structure of the workplace, leisure time, work hours, and other important domains of life.     

Social value orientations and the strategic use of fairness in ultimatum bargaining

One of the main issues in research on ultimatum bargaining is whether bargainers are motivated by self-interest or by a concern for fairness. It is difficult to distinguish between both motivations, because it may be in the own interest to make fair offers. In the current paper on ultimatum bargaining, it is investigated whether bargainers are truly motivated to be fair, or whether they merely strategically use fairness as a means to increase their own outcomes. The results of two experimental studies indicate that social value orientations play an important role: strategic use of fairness is mainly displayed by proselfs.     

Deterrence, Compellence, and Prospect Theory

Deterrence and compellence couple demands for inaction and action, respectively, to a threat of sanctions. Conventional wisdom holds that deterrence requires less coercive effort than compellence, yet expected utility theory contradicts this claim. Only if exogenous factors affect these situations in a systematic and asymmetrical manner will the claim hold within expected utility theory. Prospect theory provides a systematic and endogenous account for this claim. Experimental findings suggest the degree of effort required to obtain compliance in comparable deterrence and compellence situations. Deterrence is "easier" than compellence, but this relationship is variable. Deterrence requires less effort than expected, and the relative effort it requires decreases substantially as the stakes demanded and costs threatened grow. Compellence requires more effort than expected, and the relative effort it requires decreases slightly as the stakes demanded and costs threatened grow.     

“时间流”:概念、维度及影响因素初探

"时间流"(timeflow)是指从行为体验的角度来定义时间,即个体在当前某项活动中所感知到行为体验的时间过程,塑造"时间流"的维度包括:外部场景的塑造、自身肢体动作的配合、活动规则的初步感知、目标情感的逐渐融入、文化喻义的深入联想。影响个体"时间流"的主要因素包括感知和情绪,"时间流"也会影响消费体验和幸福体验。未来应关注时间"双扭结"价值函数如何影响人们的行为决策及验证"时间流"五个维度之间的耦合关系。     

拖延的决策模型

拖延是指尽管预见到该行为会带来不利后果,人们仍自愿推迟开始或完成某一计划好的行为。先前的研究对拖延的类型、影响因素、成因以及干预等方面进行了广泛的探讨,然而拖延的决策过程——"现在做还是以后做?"认知机制还非常不清楚。因此,本文提出拖延决策模型试图从三方面阐明"现在做还是以后做?"的决策机制:首先,拖延动机和不拖延动机的斗争是决定是否拖延的根本;其次,拖延动机的斗争可以进一步简化为任务负性过程和任务正性结果的权衡;最后,主动推迟任务使负性过程发生延迟折扣是拖延的核心目的。拖延决策模型不仅有助于探明拖延的核心认知机制,也能够帮助预测拖延行为的发生及解释各种影响因素的作用机制,因此未来的研究可以借此整合一个从拖延的核心发生机制到各种影响因素的理论系统。     

基于体验效用的幸福及其测量

体验幸福是指基于体验效用的时刻评价方式获得的多重情感体验的整合结果。体验幸福的概念主要源于Kahneman等人对体验效应的重新发现与诠释。基于时刻评价的体验效用以及时刻效用的测量假设是测量体验幸福的理论依据。体验幸福的测量方法主要有体验取样法与日重现法。基于这两种方法的国民幸福账户与国民时间账户更加直接地分析了人们如何在各种日常活动中分配时间和进行情感体验。同时, 体验幸福的概念及其测量为公共政策的评价与制定提供了更加真实具体的、可供参考的科学依据。     

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.     

Thurstonian-Based Analyses: Past, Present, and Future Utilities

Current psychometric models of choice behavior are strongly influenced by Thurstone’s (1927, 1931) experimental and statistical work on measuring and scaling preferences. Aided by advances in computational techniques, choice models can now accommodate a wide range of different data types and sources of preference variability among respondents induced by such diverse factors as person-specific choice sets or different functional forms for the underlying utility representations. At the same time, these models are increasingly challenged by behavioral work demonstrating the prevalence of choice behavior that is not consistent with the underlying assumptions of these models. I discuss new modeling avenues that can account for such seemingly inconsistent choice behavior and conclude by emphasizing the interdisciplinary frontiers in the study of choice behavior and the resulting challenges for psychometricians. The author would like to thank R. Darrell Bock whose work inspired many of the ideas presented here. The paper benefitted from helpful comments by Albert Maydeu-Olivares and Rung-Ching Tsai. The reported research was supported in parts by the Social Sciences and Humanities Research Council of Canada.