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.

Time,bounded utility,and the St. Petersburg paradox

The assumption of bounded utility function resolves the St. Petersburg paradox. The justification for such a bound is provided by Brito, who argues that limited time will bound the utility function. However, a reformulated St. Petersburg game, which is played for both money and time, effectively circumvents Brito's justification for a bound. Hence, no convincing justification for bounding the utility function yet exists.     

A test of generalized expected utility theory

In two experiments we test Machina's Hypothesis II (fanning-out). In each experiment we analyze patterns of responses to hypothetical lottery choice questions within a Marschak-Machina triangle. One set of questions involves lotteries on the border of the triangle, an the other set of questions involves lotteries in the interior of the triangle (off the border). Our results show that a large proportion of the observed patterns in the on-border treatment support Hypothesis II, with a considerable amount of fanning-out behavior observed. The patterns observed in the off-border treatment are significantly different from those in the on-border treatment. Hypothesis II performs well in the off-border treatment because expected utility theory itself, which satisfies the restrictions of Hypothesis II, performs well.This is an expanded version of a paper originally prepared for presentation at the Fifth International Conference on the Foundation and Applications of Utility, Risk, and Decision Theories, held June 9–13, 1990 at Duke University, Durham, NC. We acknowledge helpful comments made by participants at that conference, especially those of Mark Machina.     

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.

Subjective expected utility theory revisited: A reductio ad absurdum paradox

A paradox is posed and analyzed in which people reverse their preferences for information on probabilities versus prizes once the range of the unknown probabilities is sufficiently narrowed. This reversal is shown to be incompatible with both objective expected utility (EU) as well as subjective versions in which the same probability transformation applies to all random variables. Experimental data are presented showing that the reversals occur with small, medium and large payoffs.The present paradox is compared with those of Allais and Ellsberg, and found to differ in substantive ways. It raises further questions about the normative status of expected utility theory, especially its treatment of probability and value. The paradox specifically calls into question EU's substitution and compound probability axioms.     

Individual and group decision making under risk: An experimental study of Bayesian updating and violations of first-order stochastic dominance

This paper reports the results of experiments designed to test whether individuals and groups abide by monotonicity with respect to first-order stochastic dominance and Bayesian updating when making decisions under risk. The results indicate a significant number of violations of both principles. The violation rate when groups make decisions is substantially lower, and decreasing with group size, suggesting that social interaction improves the decision-making process. Greater transparency of the decision task reduces the violation rate, suggesting that these violations are due to judgment errors rather than the preference structure. In one treatment, however, less complex decisions result in a higher error rates.

The price of risk with incomplete knowledge on the utility function*

When a risk is exchanged, the exact value for the minimum price (positive or negative) that the purchaser (investor, or insurer) is willing to pay is given by the certainty equivalent wealth level, which in turn depends on his specific utility function. When this utility function is unknown, then only a sufficient condition on the price can ever be found. This paper provides methods for calculating such a sufficient condition, when only limited information on the utility function is known.     

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.     

The gradual decline of cooperation: Endgame effects in evolutionary game theory

The article provides an evolutionary analysis of a finitely iterated Prisoner's Dilemma. The backward induction reasoning for a breakdown of cooperation in this game is transformed to an evolutionary degradation effect. After the introduction of random variations in the strategies' population size, however, cyclical variations of cooperativeness may appear. A breakdown of cooperation is no longer inevitable. An analysis for all possible payoff relations in Prisoner's Dilemma matrices shows that only four qualitatively different dynamical flows can emerge.     

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.      

Correcting expected utility for comparisons between alternative outcomes: A unified parameterization of regret and disappointment

A unified parameterization of an expected utility model corrected for regret and disappointment effects is presented, constrained to conform to a well-known choice pattern, the common consequence effect, a special case of the Allais paradox. For choices subject to regret and disappointment effects to be consistent with this choice pattern, the function that corrects the utility of the obtained outcome has to have a positive second derivative for its regret component and a negative second derivative for its disappointment component. These hypothesized functional forms make predictions about the relative effect that small vs. large differences between obtained and alternative outcomes should have on people’s experiences of regret or disappointment.

Different experimental procedures for obtaining valuations of risky actions: Implications for utility theory

Three different methods of obtaining certainty equivalent valuations of four simple gambles were used with a sample of 358 people paid entirely according to their decisions. The results caution against oversimplistic utility models, and exhibit various characteristics that invite further investigation, including: a marked tendency to round valuations up or down; a tendency to value riskier actions more highly than less risky actions; and multimodal distributions of valuations which, despite their unusual shape, appeared to constitute an identifiable pattern of behaviour.     

Research Review: Family group decision-making: a promising practice in need of more programme theory and research

The use of family group decision‐making (FGDM) in child protection is rapidly increasing throughout the world. This paper provides a brief overview of the research evidence from 1996 to 2005 and proposes future directions for both practice and research. The purpose of the review is to help move the discussion of FGDM from a promising practice to an evidence‐based practice. The research review considers what is known about the child welfare outcomes of FGDM. The paper then turns to research concerning which families are offered FGDM and which FGDM processes appear to be important. The paper concludes with specific suggestions for developing FGDM programmes that can improve child protection practice and then testing these specific programmes in rigorous trials.     

Involvement of Ministries of Health in Health Service Coverage Decisions: Is England an Aberrant Case?

This article examines the involvement of ministries of health in making health service coverage decisions in Denmark, England, France and Germany. The study aims to inform debate in England about the feasibility of reducing perceived ministerial and bureaucratic ‘interference’ in decisions affecting the National Health Service, based on interviews with senior government officials and other health system stakeholders. Ministries of health differ in their involvement in health system governance and coverage decisions (‘the benefits package’), reflecting differences in institutional arrangements. In all four countries, organizations at arm's length or independent from government are either involved in providing technical advice to the ministry of health or have been mandated to take these decisions themselves. However, ministries of health occasionally intervene in the decision‐making process or ignore the advice of these organizations. The Department of Health in England is not an aberrant case, at least in relation to coverage decisions. Indeed, ministries of health in Denmark and France play a larger role in making these decisions. Public pressure, often amplified by the media, is a shared reason for ministerial and ministry involvement in all four countries. This dynamic may thus limit the feasibility of attempts to further separate the NHS from both the Department of Health and wider political pressures.     

New technology and unemployment: A simulation of macroeconomic impacts and responses in Canada

This paper addresses macroeconomic issues of the debate over high technology and unemployment. A macroeconometric simulation model with a number of special features is used to examine alternative scenarios of enhanced productivity performance in Canada over the next decade. Responses of wages, prices, and the monetary authorities are shown to be quantitatively important in determining the impact on employment. The type of productivity change and aggregate fiscal-policy response are shown to be less importance.     

A paradox in decision theory and some experimental results: The relative nature of decisions

A simple two-choice single outcome valued decision under risk is presented which should show up the limitations in the classical approach of von Neumann, its extensions and its alternatives. An empirical testing of this hypothesis strongly supports this criticism. A rationale for explaining the apparent irrational decision is put forward and the case is made for understanding the relative nature of decision choices especially when multi-criteria are involved.