Min- and Max-induced rankings: an experimental study

The current paper is the first to report an experimental study of “Min- and Max-induced rankings” (MMIR), i.e., a family of set rankings that require preferences over sets to be induced from comparison of the best and/or worst elements within those sets. These MMIR do not perform well in predicting preferences over simple sets of monetary outcomes. In this paper, we investigate the axiomatic underpinnings of these models by means of pairwise choice experiments. From this investigation, some important conclusions can be drawn: Axioms that prevent rankings to be based on total-goodness, as well as monotonicity conditions (ensuring that replacing a set element with a better one results in a better set) cannot be refuted. Axioms that rule out any utilization of the relative difference in the values of the outcomes and axioms that prevent rankings to be based on average-goodness are all systematically violated. The Uniform Expected Utility (UEU) criterion seems to meet the apparent shortcomings of the MMIR. Some frequently occurring preference patterns, however, suggest that a significant portion of the participants uses neither a Min- or Max-induced ranking, nor UEU, but some other unspecified decision rule, possibly characterized by the tendency to prefer a diversification of uncertainty.     

A further exploration of the uncertainty effect

Individual valuation of a binary lottery at values less than the lottery’s worst outcome has been designated as the “uncertainty effect”. Our paper aims to explore the boundary conditions of the uncertainty effect by investigating a plausible underlying process and proposing two possible methods. First, we examine how providing an exogenous evaluation opportunity prior to judging the value of the lottery affects individuals’ judgments, and find that first valuing the worst outcome and then the lottery eliminates the uncertainty effect. Second, we explore whether introducing additional cognitive load dampens how far decision makers correct their initial evaluations, and find that additional cognitive load is able to eliminate the uncertainty effect.     

Competence effects for choices involving gains and losses

We investigate how choices for uncertain gain and loss prospects are affected by the decision maker’s perceived level of knowledge about the underlying domain of uncertainty. Specifically, we test whether Heath and Tversky’s (J Risk Uncertain 4:5–28, 1991) competence hypothesis extends from gains to losses. We predict that the commonly-observed preference for high knowledge over low knowledge prospects for gains reverses for losses. We employ an empirical setup in which participants make hypothetical choices between gain or loss prospects in which the outcome depends on whether a high or low knowledge event occurs. We infer decision weighting functions for high and low knowledge events from choices using a representative agent preference model. For gains, we replicate the results of Kilka and Weber (Manage Sci 47:1712–1726, 2001), finding that decision makers are more attracted to choices that they feel more knowledgeable about. However, for losses, we find limited support for our extension of the competence effect.     

Context dependence and consistency in dynamic choice under uncertainty: the case of anticipated regret

We examine if and to what extent choice dispositions can allow dependence on contexts and maintain consistency over time, in a dynamic environment under uncertainty. We focus on one of the context dependence properties, opportunity dependence because of being affected by anticipated regret, where the consequentialist choice framework is maintained. There are two sources of potential inconsistency: one is arrival of information, and the other is changing opportunities. First, we go over the general method of resolution of potential inconsistency, by taking any kinds of inconsistency as given constraints. Second, we characterize a class of choice dispositions that are consistent to information arrival, but may be inconsistent to changing opportunities. Finally, we consider the overall requirement of dynamic consistency and show that it necessarily implies each of consistency to information arrival and independence of choice opportunities. The last result states that the two kinds of potential inconsistency cannot “compensate” each other to recover dynamic consistency overall.     

Social Workers Talking to Clients: A Comment

Summary I read Baldock and Prior's article with interest in view ofthe shortage of studies examining day-to-day practice in socialwork, but the authors' analysis leaves me reflecting uneasilyupon the state of uncertainty into which social work has fallen.The authors conclude by describing as ‘skilled’,practices which they say resulted in confusion for clients andwhich only apparently reflected social work principles. We arenot told whether the authors checked their analysis with workersor clients and it is possible that the clients were not as confusedas we are led to believe, given their long term contact withthe workers. If, however, the picture is an accurate one, shouldit really be described as representing skilled social work?Baldock and Prior do so but neglect to examine the ends towardswhich interviewing skill should be directed in social work.The result is a strangely ambiguous statement about practice,particularly in the light of research findings on effectivenessand client satisfaction, and one which offers little scope forcomplacency.     

Cognition and uncertainty

In the first part, we try to give a representation of the process by which man endeavours to grasp uncertainty. We propose a backward exploration which we will modelize through an influence diagram and then we can draw a few conclusions from that representation for the axiomatics of Decision.In the second part, we deal with the processing of the information formatted in such a way, regarding both its temporal complexity and its elective complexity.The first part as the second one dealing with representation and the consequences for information processing of uncertainty cognition lead to a severe criticism of the expected utility hypothesis.To conclude, we suggest a few remarks on expert systems of decision aid under uncertainty.     

Choice uncertainty and the endowment effect

Journal of Risk and Uncertainty - We experimentally test for the role of choice uncertainty in generating “endowment effects” - the robust empirical finding that endowing participants...     

Uncertainty aversion and aversion to increasing uncertainty

According to the original Ellsberg (1961) examples there is uncertainty version if the decision maker prefers to bet on an urn of known composition rather than on an urn of unknown composition. According to another definition (Schmeidler, 1989), there is uncertainty aversion if any convex combination of two acts is preferred to the least favorable of these acts. We show that these two definitions differ: while the first one truly refers to uncertainty aversion, the second one refers to aversion to increasing uncertainty. Besides, with reference to Choquet Expected Utility theory, uncertainty aversion means that there exists the core of a capacity, while aversion to increasing uncertainty means that the capacity is convex. Consequently, aversion to increasing uncertainty implies uncertainty aversion, but the opposite does not hold. We also show that a completely analogous situation holds for the case of risk and we define a set of risk and uncertainty premiums according to the previous analysis.     

Deterrence, expected cost, uncertainty and voting: Experimental evidence

We conduct laboratory experiments to investigate the effects of deterrence mechanisms under controlled conditions. The effect of the expected cost of punishment of an individual’s decision to engage in a proscribed activity and the effect of uncertainty on an individual’s decision to commit a violation are very difficult to isolate in field data. We use a roadway speeding framing and find that (a) individuals respond considerably to increases in the expected cost of speeding, (b) uncertainty about the enforcement regime yields a significant reduction in violations committed, and (c) people are much more likely to speed when the punishment regime for which they voted is implemented. Our results have important implications for a behavioral theory of deterrence under uncertainty.     

The Effects of Beliefs Versus Risk Attitude on Bargaining Outcomes

In bargaining environments with uncertain disagreement or “impasse” outcomes (e.g., litigation or labor strike outcomes), there is an identification problem that confounds data interpretation. Specifically, the minimally acceptable settlement value from a risk-averse (risk-loving) but unbiased-belief bargainer is empirically indistinguishable from what one could get with risk-neutrality and pessimistically (optimistically) biased beliefs. This article reports results from a controlled bargaining experiment where data on both risk attitude and beliefs under uncertainty are generated in order to assess their relative importance in bargaining experiment outcomes. The average lab subject is risk-averse, yet optimistic with respect to uncertainty, which is consistent with existing studies that examine each in isolation. I also find that the effects of optimism dominate those of risk-aversion. Optimistic bargainers are significantly more likely to dispute and have aggressive final bargaining positions. Dispute rates are not statistically affected by risk attitude, but there is some evidence that risk aversion leads to a weakened bargaining position. Though additional research is needed to understand the limits of extending these results, a key implication follows. In uncertainty environments where optimism dominates, increased settlement rates are more likely achieved by minimizing impasse uncertainty (to limit the potential for optimism) rather than maximizing uncertainty (to weaken the reservation point of risk-averse bargainers), as has been argued in the dispute resolution literature.      

A possibilistic hierarchical model for behaviour under uncertainty

Hierarchical models are commonly used for modelling uncertainty. They arise whenever there is a `correct' or `ideal' uncertainty model but the modeller is uncertain about what it is. Hierarchical models which involve probability distributions are widely used in Bayesian inference. Alternative models which involve possibility distributions have been proposed by several authors, but these models do not have a clear operational meaning. This paper describes a new hierarchical model which is mathematically equivalent to some of the earlier, possibilistic models and also has a simple behavioural interpretation, in terms of betting rates concerning whether or not a decision maker will agree to buy or sell a risky investment for a specified price. We give a representation theorem which shows that any consistent model of this kind can be interpreted as a model for uncertainty about the behaviour of a Bayesian decision maker. We describe how the model can be used to generate buying and selling prices and to make decisions.     

Portfolio Inertia and Epsilon-Contaminations

This article analyzes investors’ portfolio selection problems in a two-period dynamic model of Knightian uncertainty. We account for the existence of portfolio inertia in this two-period framework. Furthermore, by incorporating investors’ updating behavior, we analyze how observing new information in the first period will affect investors’ behavior. By this analysis, we show that observing new information in the first period will expand portfolio inertia in the second period compared with the case in which observing new information has not been gained in the first period if the degree of Knightian uncertainty is sufficiently large.     

Ranking sets additively in decisional contexts: an axiomatic characterization

Ranking finite subsets of a given set X of elements is the formal object of analysis in this article. This problem has found a wide range of economic interpretations in the literature. The focus of the article is on the family of rankings that are additively representable. Existing characterizations are too complex and hard to grasp in decisional contexts. Furthermore, Fishburn (1996), Journal of Mathematical Psychology 40, 64–77 showed that the number of sufficient and necessary conditions that are needed to characterize such a family has no upper bound as the cardinality of X increases. In turn, this article proposes a way to overcome these difficulties and allows for the characterization of a meaningful (sub)family of additively representable rankings of sets by means of a few simple axioms. Pattanaik and Xu’s (1990), Recherches Economiques de Louvain 56, 383–390) characterization of the cardinality-based rule will be derived from our main result, and other new rules that stem from our general proposal are discussed and characterized in even simpler terms. In particular, we analyze restricted-cardinality based rules, where the set of “focal” elements is not given ex-ante; but brought out by the axioms.      

Dopamine and risk choices in different domains: Findings among serious tournament bridge players

We explore how risk-taking in the card game contract bridge, and in a financial gamble, correlate with variation in the dopamine receptor D4 gene (DRD4) among serious tournament bridge players. In bridge risk-taking, we find significant interactions between genetic predisposition and skill. Among men with the 7-repeat allele of DRD4, namely 7R + men, those with more bridge skill take more good risks and fewer bad risks, while the opposite is found for less-expert 7R + men. Conversely, skill does not predict risk-taking among men without the 7R + allele. Consistent with some prior studies, we also find that 7R + men take more risk in the financial gamble. We find no relationship between 7R + and either risk measure among our female subjects. Our results suggest that the dopamine system plays an important role in individual differences in risk-taking among men, and is the first to distinguish between advantageous and disadvantageous risk-taking.     

Preference for gradual resolution of uncertainty

Analyses of preference for the timing of uncertainty resolution usually assumes all uncertainty to resolve in one point in time. More realistically, uncertainty should be modelled to resolve gradually over time. Kreps and Porteus (1978) have introduced an axiomatically based model of time preference which can explain preferences for gradual uncertainty resolution. This paper presents an experimental test of the Kreps-Porteus model. We derive implications of the model relating preferences for gradual and one-time resolving lotteries. Our data do not support the Kreps-Porteus model but show that some of the behaviour observed may be explained by similarity heuristics.     

Recursive expected utility and the separation of attitudes towards risk and ambiguity: an experimental study

We use the multiple price list method and a recursive expected utility theory of smooth ambiguity to separate out attitude towards risk from that towards ambiguity. Based on this separation, we investigate if there are differences in agent behaviour under uncertainty over gain amounts vis-a-vis uncertainty over loss amounts. On an aggregate level, we find that (i) subjects are risk averse over gains and risk seeking over losses, displaying a “reflection effect” and (ii) they are ambiguity neutral over gains and are mildly ambiguity seeking over losses. Further analysis shows that on an individual level, and with respect to both risky and ambiguous prospects, there is limited incidence of a reflection effect where subjects are risk/ambiguity averse (seeking) in gains and seeking (averse) in losses, though this incidence is higher for ambiguous prospects. A very high proportion of such cases of reflection exhibit risk (ambiguity) aversion in gains and risk (ambiguity) seeking in losses, with the reverse effect being significantly present in the case of risk but almost absent in case of ambiguity. Our results suggest that reflection across gains and losses is not a stable individual characteristic, but depends upon whether the form of uncertainty is precise or ambiguous, since we rarely find an individual who exhibits reflection in both risky and ambiguous prospects. We also find that correlations between attitudes towards risk and ambiguity were domain dependent.      

An experimental investigation of violations of transitivity in choice under uncertainty

Several models of decision-making imply systematic violations of transitivity of preference. Our experiments explored whether people show patterns of intransitivity predicted by regret theory and majority rule. To distinguish “true” violations from those produced by “error,” a model was fit in which each choice can have a different error rate and each person can have a different pattern of true preferences that need not be transitive. Error rate for a choice is estimated from preference reversals between repeated presentations of that same choice. Our results showed that very few people repeated intransitive patterns. We can retain the hypothesis that transitivity best describes the data of the vast majority of participants.

Reporting probabilistic expectations with dynamic uncertainty about possible distributions

We study how experimental subjects report subjective probability distributions in the presence of ambiguity characterized by uncertainty over a fixed set of possible probability distributions generating future outcomes. Subjects observe draws from the true but unknown probability distribution generating outcomes at the beginning of each period of the experiment and state at selected periods a) the likelihoods that each probability distribution in the set is the true distribution, and b) the likelihoods of future outcomes. We estimate heterogeneity of rules used to update uncertainty about the true distribution and rules used to report distributions of future outcomes. We find that approximately 65% of subjects report distributions by properly weighing the possible distributions using their expressed uncertainty over them, while 22% of subjects report distributions close to the distribution they perceive as most likely. We find significant heterogeneity in how subjects update their expressed uncertainty. On average, subjects tend to overweigh the importance of their prior uncertainty relative to new information, leading to ambiguity that is substantially more persistent than would be predicted using Bayes’ rule. Counterfactual simulations suggest that this persistence will likely hold in settings not covered by our experiment.     

The Likelihood Method for Decision under Uncertainty

This paper introduces the likelihood method for decision under uncertainty. The method allows the quantitative determination of subjective beliefs or decision weights without invoking additional separability conditions, and generalizes the Savage–de Finetti betting method. It is applied to a number of popular models for decision under uncertainty. In each case, preference foundations result from the requirement that no inconsistencies are to be revealed by the version of the likelihood method appropriate for the model considered. A unified treatment of subjective decision weights results for most of the decision models popular today. Savage’s derivation of subjective expected utility can now be generalized and simplified. In addition to the intuitive and empirical contributions of the likelihood method, we provide a number of technical contributions: We generalize Savage’s nonatomiticy condition (“P6”) and his assumption of (sigma) algebras of events, while fully maintaining his flexibility regarding the outcome set. Derivations of Choquet expected utility and probabilistic sophistication are generalized and simplified similarly. The likelihood method also reveals a common intuition underlying many other conditions for uncertainty, such as definitions of ambiguity aversion and pessimism.