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.

Myopic risk-seeking: The impact of narrow decision bracketing on lottery play

In two experiments conducted with low-income participants, we find that individuals are more likely to buy state lottery tickets when they make several purchase decisions one-at-a-time, i.e. myopically, than when they make one decision about how many tickets to purchase. These results extend earlier findings showing that “broad bracketing” of decisions encourages behavior consistent with expected value maximization. Additionally, the results suggest that the combination of myopic decision making and the “peanuts effect”—greater risk seeking for low stakes than high stakes gambles—can help explain the popularity of state lotteries.

Stochastic expected utility theory

This paper proposes a new decision theory of how individuals make random errors when they compute the expected utility of risky lotteries. When distorted by errors, the expected utility of a lottery never exceeds (falls below) the utility of the highest (lowest) outcome. This assumption implies that errors are likely to overvalue (undervalue) lotteries with expected utility close to the utility of the lowest (highest) outcome. Proposed theory explains many stylized empirical facts such as the fourfold pattern of risk attitudes, common consequence effect (Allais paradox), common ratio effect and violations of betweenness. Theory fits the data from ten well-known experimental studies at least as well as cumulative prospect theory.

One-reason decision-making: Modeling violations of expected utility theory

People violate expected utility theory and this has been traditionally modeled by augmenting its weight-and-add framework by nonlinear transformations of values and probabilities. Yet individuals often use one-reason decision-making when making court decisions or choosing cellular phones, and institutions do the same when creating rules for traffic safety or fair play in sports. We analyze a model of one-reason decision-making, the priority heuristic, and show that it simultaneously implies common consequence effects, common ratio effects, reflection effects, and the fourfold pattern of risk attitude. The preferences represented by the priority heuristic satisfy some standard axioms. This work may provide the basis for a new look at bounded rationality.

Pre-commitment and flexibility in a time decision experiment

An agent with dynamically inconsistent preferences may deviate from her plan of action as the future draws near. An exponential discounter may do exactly the same when facing an uncertain future. Through an experiment we compare preference-based vs. uncertainty-based explanations for choice reversal over time by eliciting choices for pre-commitment and flexibility. Evidence of widespread commitment favors a preference-based explanation.

The relationship between individual expectations and behaviors: Mortality expectations and smoking decisions

Using data from the Health and Retirement Study, we assess the accuracy of subjective beliefs about mortality and objectively estimated probabilities for individuals in the same sample. Overall, subjective beliefs and objective probabilities are very close. However, there are differences conditional on behaviors, with current smokers being relatively optimistic and never smokers relatively pessimistic in their assessments. In the aggregate, individuals accurately predict longevity, but at the individual level, subjective beliefs provide information in addition to the estimated objective probabilities in predicting actual events, which may arise from the effect of past or anticipated decisions on these beliefs.

Learning from mistakes: What do inconsistent choices over risk tell us?

We implement a risk experiment that allows for judgment errors to investigate who makes mistakes and whether it matters. The experiments are conducted with a random sample of the adult population in Rwanda, and data on financial decisions are collected. We find a high proportion of inconsistent choices, with over 50% of the participants making at least one mistake. Importantly, errors are informative. While risk aversion alone does not explain financial decisions, risk aversion and inconsistent choices interact in significant and sensible ways. As we would expect, risk-averse individuals are more likely to belong to a savings group and less likely to take out an informal loan. For those more likely to make mistakes, however, as they become more risk averse, they are less likely to belong to a savings group and more likely to take up informal credit, suggesting that mistakes correlate with less than optimal behavior.

Self-protection and insurance with interdependencies

We study optimal investment in self-protection of insured individuals when they face interdependencies in the form of potential contamination from others. If individuals cannot coordinate their actions, then the positive externality of investing in self-protection implies that, in equilibrium, individuals underinvest in self-protection. Limiting insurance coverage through deductibles or selling “at-fault” insurance can partially internalize this externality and thereby improve individual and social welfare.

Individual decision-making experiments with risk and intertemporal choice

Many decisions require tradeoffs over time and in the presence of risk. To examine interactions between risk and intertemporal effects we developed a laboratory experiment. In the experiment, subjects choose between payoffs that take place at different points in time. We find that very few subjects are consistently risk averse or risk loving. Instead, we find that subjects are less patient in the presence of risk. We also find that increased risk decreases subjects’ patience levels. However, we do not find evidence that the effect of risk on the intertemporal decision depends on the length of the temporal delay.

Perception of own death risk

Individuals’ perception of their own road-traffic and overall mortality risks are examined in this paper. Perceived risk is compared with the objective risk of the respondents’ peers, i.e. their own gender and age group, and the results suggest that individuals’ risk perception of their own risk is biased. For road-traffic risk we obtain similar results to what have been found previously in the literature, overassessment and underassessment among low- and high-risk groups, respectively. For overall risk we find that all risk groups underestimate their risk. The results also indicate that men's risk bias is larger than women’s.

A tractable method to measure utility and loss aversion under prospect theory

This paper provides an efficient method to measure utility under prospect theory. Our method minimizes both the number of elicitations required to measure utility and the cognitive burden for subjects, being based on the elicitation of certainty equivalents for two-outcome prospects. We applied our method in an experiment and were able to replicate the main findings on prospect theory, suggesting that our method measures what it is intended to. Our data confirmed empirically that risk seeking and concave utility can coincide under prospect theory. Utility did not depend on the probability used in the elicitation, which offers support for the validity of prospect theory.

Gender,risk and stereotypes

This paper reports results from an economic experiment where respondents are asked to make choices between risky outcomes for themselves and others. We investigate whether subjects’ own risk preferences and gender stereotypes are reflected in the predictions they make for the risk preferences of others and the way this occurs. When predicting other people’s risk preferences, the respondents tend to use a combination of their own risk preferences and stereotypes. Moreover, when making risky choices for others, the respondents generally use a combination of their own risk preferences and their average predicted risk preference of the targeted group.

Naive,resolute or sophisticated? A study of dynamic decision making

Dynamically inconsistent decision makers have to decide, implicitly or explicitly, what to do about their dynamic inconsistency. Economic theorists have identified three possible responses—to act naively (thus ignoring the dynamic inconsistency), to act resolutely (not letting their inconsistency affect their behaviour) or to act sophisticatedly (hence taking into account their inconsistency). We use data from a unique experiment (which observes both decisions and evaluations) in order to distinguish these three possibilities. We find that the majority of subjects are either naive or resolute (with slightly more being naive) but very few are sophisticated. These results have important implications for predicting the behaviour of people in dynamic situations.

Eliciting decision weights by adapting de Finetti’s betting-odds method to prospect theory

This paper extends de Finetti’s betting-odds method for assessing subjective beliefs to ambiguous events. Thus, a tractable manner for measuring decision weights under ambiguity is obtained. De Finetti’s method is so transparent that decision makers can evaluate the relevant tradeoffs in complex situations. The resulting data can easily be analyzed, using nonparametric techniques. Our extension is implemented in an experiment on predicting next-day’s performance of the Dow Jones and Nikkei stock indexes, where we test the existence and nature of rank dependence, finding usual patterns. We also find violations of rank dependence.

Conspicuous conservatism in risk choice

We analyze the risk levels chosen by agents who have private information regarding their quality, and whose performance will be judged and rewarded by outsiders. Assume that risk choice is observable. Agents will choose risk strategically to enhance their expected reputations. We show that conspicuous conservatism results: agents of different qualities choose levels below those that would be chosen if quality were observable. This happens because bad agents must cloak their identity by choosing the same risk level as good agents, and good agents are more likely to distinguish themselves if they reduce the risk level. Our results contrast starkly with those for the case when risk choice cannot be observed.

Risk preferences and changes in background risk

We present two theorems that yield necessary and sufficient conditions for first- and second-degree stochastic dominance deteriorations of background risk to increase risk aversion with respect to foreground risk. We require that any change in a foreground risk that is undesirable remains so after a background risk changes in a way that is either unfair, undesirable in the sense of reducing expected utility, or undesirable in the sense of increasing expected marginal utility. Our results thus characterize utility functions that are, respectively, vulnerable, proper, or standard with respect to changes in background risk.

Can ranking techniques elicit robust values?

This paper reports two experiments which examine the use of ranking methods to elicit ‘certainty equivalent’ values. It investigates whether such methods are able to eliminate the disparities between choice and value which constitute the ‘preference reversal phenomenon’ and which thereby pose serious problems for both theory and policy application. The results show that ranking methods are vulnerable to distorting effects of their own, but that when such effects are controlled for, the preference reversal phenomenon, previously so strong and striking, is very considerably attenuated.

Whom should we believe? Aggregation of heterogeneous beliefs

We examine the collective risk attitude of a group with heterogeneous beliefs. We prove that the wealth-dependent probability distribution used by the representative agent is biased in favor of the beliefs of the more risk tolerant consumers. Moreover, increasing disagreement on the state probability raises the state probability of the representative agent. It implies that when most disagreements are concentrated in the tails of the distribution, the perceived collective risk is magnified. This can help to solve the equity premium puzzle. We show that the trade volume and the equity premium are positively correlated.