Do Trade Union Leaders Violate Subjective Expected Utility? Some Insights From Experimental Data

This paper presents the results of two experiments designed to test violations of Subjective Expected Utility Theory (SEUT) within a sample of Italian trade union delegates and leaders. Subjects priced risky and ambiguous prospects in the domain of gains. Risky prospects were based on games of chance, while ambiguous prospects were built on the standard Ellsberg paradox and on event lotteries whose outcomes were based either on the results of a fictional election or on the future results of the 1999 European Parliamentary election in Italy and the U.K. The experiments show that, although risky prospects were priced at their expected values on average, trade union delegates and leaders did violate SEUT when assessing ambiguous prospects. Moreover, their behaviour depended on the source of uncertainty (Ellsberg paradox vs. electoral results; fictional vs. real election; Italy vs. U.K. election outcomes). We discuss the implications of these results for the economic theory of the trade union.     

Nondegenerate Intervals of No-Trade Prices for Risk Averse Traders

According to the local risk-neutrality theorem an agent who has the opportunity to invest in an uncertain asset does not buy it or sell it short iff its expected value is equal to its price, independently of the agent's attitude towards risk. Contrary to that it is shown that, in the context of expected utility theory with differentiable vNM utility function, but without the assumption of stochastic constant returns to scale, nondegenerate intervals of no-trade prices may exist. With a quasiconcave expected utility function they do if, and only if, the agent is risk averse of order one.     

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.     

Indirect methods for valuing changes in environmental risks with nonexpected utility preferences

Theoretical models for estimating individuals' values for sure improvements in environmental quality are well developed. These models can be classified as being based on averting behavior, hedonic prices, or weak complementarity. Some of these models have also been applied to the task of valuing changes in risk based on expected utility theory. This article provides a systematic development of these models for changes in either the probability or the magnitude of an uncertain event and shows that the derived expressions for individual marginal willingness to pay can be generalized to nonexpected utility preferences as long as the index of preferences is continuous, convex, and twice differentiable.     

Expected utility with lower probabilities

An uncertain and not just risky situation may be modeled using so-called belief functions assigning lower probabilities to subsets of outcomes. In this article we extend the von Neumann-Morgenstern expected utility theory from probability measures to belief functions. We use this theory to characterize uncertainty neutrality and different degrees of uncertainty aversion.We are grateful to Birgit Grodal, Salvatore Modica, David Schmeidler, and an anonymous referee for comments, help, and encouragement. Financial support from the Danish Social Sciences Research Council is acknowledged.     

Convex stochastic dominance with finite consequence sets

Stochastic dominance is a notion in expected-utility decision theory which has been developed to facilitate the analysis of risky or uncertain decision alternatives when the full form of the decision maker's von Neumann-Morgenstern utility function on the consequence space X is not completely specified. For example, if f and g are probability functions on X which correspond to two risky alternatives, then f first-degree stochastically dominates g if, for every consequence x in X, the chance of getting a consequence that is preferred to x is as great under f as under g. When this is true, the expected utility of f must be as great as the expected utility of g.Most work in stochastic dominance has been based on increasing utility functions on X with X an interval on the real line. The present paper, following [1], formulates appropriate notions of first-degree and second-degree stochastic dominance when X is an arbitrary finite set. The only structure imposed on X arises from the decision maker's preferences. It is shown how typical analyses with stochastic dominance can be enriched by applying the notion to convex combinations of probability functions. The potential applications of convex stochastic dominance include analyses of simple-majority voting on risky alternatives when voters have similar preference orders on the consequences.     

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.      

Advances in prospect theory: Cumulative representation of uncertainty

We develop a new version of prospect theory that employs cumulative rather than separable decision weights and extends the theory in several respects. This version, called cumulative prospect theory, applies to uncertain as well as to risky prospects with any number of outcomes, and it allows different weighting functions for gains and for losses. Two principles, diminishing sensitivity and loss aversion, are invoked to explain the characteristic curvature of the value function and the weighting functions. A review of the experimental evidence and the results of a new experiment confirm a distinctive fourfold pattern of risk attitudes: risk aversion for gains and risk seeking for losses of high probability; risk seeking for gains and risk aversion for losses of low probability.This article has benefited from discussions with Colin Camerer, Chew Soo-Hong, David Freedman, and David H. Krantz. We are especially grateful to Peter P. Wakker for his invaluable input and contribution to the axiomatic analysis. We are indebted to Richard Gonzalez and Amy Hayes for running the experiment and analyzing the data. This work was supported by Grants 89-0064 and 88-0206 from the Air Force Office of Scientific Research, by Grant SES-9109535 from the National Science Foundation, and by the Sloan Foundation.     

Two-parameter decision models and rank-dependent expected utility

This paper extends the existing literature concerning the relationship between two parameter decision models and those based on expected utility in two main directions. The first relaxes Meyer's location and scale (or Sinn's linear class) condition and shows that a two-parameter representation of preferences over uncertain prospects and the expected utility representation yield consistent rankings of random variables when the decision maker's choice set is restricted to random variables differing by mean shifts and monotone meanpreserving spreads. The second shows that the rank-dependent expected utility model is also consistent with two-parameter ranking methods if the probability transform satisfies certain dominance conditions. The main implication of these results is that the simple two-parameter model can be used to analyze the comparative statics properties of a wide variety of economic models, including those with multiple sources of uncertainty when the random variables are comonotonic. To illustrate this point, we apply our results to the problem of optimal portfolio investment with random initial wealth. We find that it is relatively easy to obtain strong global comparative statics results even if preferences do not satisfy the independence axiom.     

Optimal insurance without expected utility: The dual theory and the linearity of insurance contracts

Models of the insurance markets and institutions are routinely based on expected utility. Since EU is being challenged by an increasing number of decision models, we examine whether EU-based models are robust in their predictions. To do so, we rework some basic models of optimal insurance contracts and equilibrium using the “dual” theory to EU of Yaari. When there is a single, insurable source of risk, dual theory permits only corner solutions if the contract itself is linear. This contrasts sharply with EU. Nonlinearity, and thereby the possibility of interior solutions, is introduced in two ways. First, the contract itself is nonlinear, i.e., a deductible insurance policy. Or second, the decision maker is subject to some background risk such as uninsurable risky assets or default of the insurer. When decision problems are subject to nonlinearity, the predictions on optimal insurance are more similar to, though not identical with, those generated with EU.     

It is Whether You Win or Lose: The Importance of the Overall Probabilities of Winning or Losing in Risky Choice

Imagine that you own a five-outcome gamble with the following payoffs and probabilities: ($100, .20; $50, .20; Imagine that you own a five-outcome gamble with the following payoffs and probabilities: ($100, .20; $50, .20; $0, .20; –$25, .20; –$50, .20). What happens when the opportunity to improve such a gamble is provided by a manipulation that adds value to one outcome versus another outcome, particularly when the opportunity to add value to one outcome versus another outcome changes the overall probability of a gain or the overall probability of a loss? Such a choice provides a simple test of the expected utility model (EU), original prospect theory (OPT), and cumulative prospect theory (CPT). A study of risky choices involving 375 respondents indicates that respondents were most sensitive to changes in outcome values that either increased the overall probability of a strict gain or decreased the overall probability of a strict loss. These results indicate more support for OPT rather than CPT and EU under various assumptions about the shape of the utility and value and weighting functions. Most importantly, the main difference between the various expectation models of risky choice occurs for outcomes near the reference value. A second study of risky choice involving 151 respondents again demonstrated the sensitivity of subjects to reducing the probability of a strict loss even at the cost of reduced expected value. Consequently, we argue that theories of how people choose among gambles that involve three or more consequences with both gains and losses need to include measures of the overall probabilities of a gain and of a loss.JEL Classification  D81     

Evidence for multiple strategies in choice under risk

This paper describes an experimental study that yields evidence for the coexistence of two decision strategies of choice under risk. Under the first strategy, choices are made based on aspiration levels – a heuristic that simplifies risky decisions. Under the second strategy, which can be used when aspiration levels are not determinative, choices are made based on preferences for positive skewness. Our model fitting confirms the efficacy of a two-pronged approach that can marshal either strategy depending on specific features of the risky prospects under consideration.     

At the nexus of risk and time preferences: An experimental investigation

Although many economic decisions involve choices between uncertain outcomes occurring at different times, most theoretical and empirical work restricts attention to one dimension or another. In this paper, we investigate whether both risk and time preferences can be represented by a single parameter. We collect experimental data to estimate models which allows for a disentanglement of risk and time preferences. Results reveal that the discounted expected utility model assumption, that risk and time preferences can be explained by a single parameter, is not supported by the data. The model estimates imply people prefer to delay the resolution of risky outcomes.     

Estimating individual and group preference functionals using experimental data

In this paper, the empirical performance of several preference functionals is assessed using individual and group experimental data. We investigate if there is a risky choice theory that fits group decisions better than alternative theories, and if there are significant differences between individual and group choices. Experimental findings reported in this paper provide answers to both of those questions showing that expected utility gains a “winning” position over higher-level functionals (we considered disappoint aversion and two variants of rank-dependent utility) when risky choices are undertaken by individuals as well as by small groups. However, in the group experiment, alternatives (and, most notably, disappoint aversion) improve their relative performance, a fact that hints at the existence of differences between individual and group choices. We interpreted this result as evidence that feelings-like disappointment aversion become stronger in group decision.     

Individual behavior under risk and under uncertainty: An experimental study

These experiments are concerned with individual behavior under risk and under uncertainty. By exploiting the isolation effect the experiments were able to offer to 134 subjects the possibility of actually gaining or losing an important sum of money.The experimental data show that under risk as well as under complete ignorance the subjects' attitudes towards prospects of gains and towards prospects of losses are totally unrelated.The data also show that when facing prospects of gains, the subjects generally take the exact probabilities of the events into account, whereas, when facing prospects of losses many of then have only recourse to coarser categories of plausibility, or even no longer use their information at all.     

Exchange rate systems and relative prices

The article relaxes one of the assumptions required for exchange-rate-system neutrality, without abandoning flexible prices. It assumes that taxes or restrictions on international transactions are expected to differ under pegged and flexible exchange rates. Governments are more willing to impose restrictions or taxes when they have a low level of international reserves and operate under a system of pegged exchange rates where further losses are possible. Expectations about these policy reactions change the behavior of equilibrium relative prices: they may vary less under pegged than under flexible exchange rates, as they appear to do in the real world.     

Heterogeneity in life-duration preferences: Are risky recreationists really more risk loving?

We conduct multiple price list experiments that elicit life duration risk preferences from amateur auto racers, technical rock climbers, SCUBA divers, and a student control group. We posit a preference function that allows for risk aversion and probability weighting. We are particularly interested in whether the behavior of risk takers, such as risky recreationists or smokers, is best explained by a risk-tolerant utility function or if immunity to possibility bias arising from overweighting of low probabilities is a more important motivator of the choice to engage in risky activities. We find that amateur auto racers are more rational than either students or other risky recreationists because they are less likely to overemphasize low-probability events. Women, older subjects, and rock climbers are more susceptible to possibility bias than others, making them likely to overinvest in disease treatments that have a low probability of success.     

Are Preference Reversals Errors? An Experimental Investigation

This paper investigates whether some part of the preference reversal phenomenon can be attributed to errors in the responses of subjects in experiments. Such errors have been well documented in other investigations of behaviour in risky decision problems, but their relevance to the preference reversal phenomenon has not been explored. Building on earlier work, we develop an extended error model and apply it to the results of an experiment in which subjects tackle risky choice problems on five separate occasions. In this experiment subjects had to answer choice questions in three occasions and to state selling and buying prices in the remaining two occasions. Our results indicate that scale compatibility can be ruled out as a significant sole explanation of the preference reversal phenomenon. Moreover, we can show that a considerable fraction of observed preference reversals can be classified as pricing errors, whereas choice errors turn out to play a minor role.