Stochastic dominance in multicriterion analysis under risk

Traditionally, in the literature on the modelling of decision aids one notes the propensity to treat expected utility models and outranking relation models as rivals. It may be possible, however, to benefit from the use of both approaches in a risky decision context. Stochastic dominance conditions can be used to establish, for each criterion, the preferences of a decision maker and to characterise them by a concave or convex utility function.Two levels of complexity in preference elicitation, designated as clear and unclear, are distinguished. Only in the case of unclear preferences is it potentially interesting to attempt to estimate the value function of the decision maker, thus obtaining his (her) preferences with a reduced number of questions. The number of questions that must be asked of the decision maker depends upon the level of the concordance threshold that he(she) requires in the construction of the outranking relations using the ELECTRE method.     

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.     

Preferences over consumption and status

Experimental evidence suggests that individual consumption has not only personal value but also enters the social part of the utility. Existing models of social preferences make ad hoc parametric assumptions about the nature of this duality. This creates a problem of experimental identification of preferences since without such assumptions it is impossible to distinguish whether consumption or social concerns are driving the behavior. Given observed choice, the Axiomatic model of preferences in this article makes it possible to unambiguously determine personal and social utility without any assumptions about their relationship. The unique separation can be achieved only if the individual choices in different subgroups of other people are available. Preferences over consumption and status are used as an example to demonstrate how the utility is constructed. The model shows what kind of information about choice is needed to empirically determine the nature of social preferences without making restrictive assumptions. This can help to estimate whether personal consumption or social value is more important in economic decisions.     

The arguments of utility: Preference reversals in expected utility of income models

There is a debate in the literature about the arguments of utility in expected utility theory. Some implicitly assume utility is defined on final wealth whereas others argue it may be defined on initial wealth and income separately. I argue that making income and wealth separate arguments of utility has important implications that may not be widely recognized. A framework is presented that allows the unified treatment of expected utility models and anomalies. I show that expected utility of income models can predict framing induced preference reversals, a willingness to pay-willingness to accept gap for lotteries, and choice-value preference reversals. The main contribution is a theorem. It is proved that for all utility functions where initial wealth and income enter separately, either there will be preference reversals or preferences can be represented by a utility function defined on final wealth alone.     

Expected utility without utility

This paper advances an interpretation of Von Neumann-Morgenstern's expected utility model for preferences over lotteries which does not require the notion of a cardinal utility over prizes and can be phrased entirely in the language of probability. According to it, the expected utility of a lottery can be read as the probability that this lottery outperforms another given independent lottery. The implications of this interpretation for some topics and models in decision theory are considered.     

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.     

Comparing risk preferences over financial and environmental lotteries

This paper investigates whether preferences over environmental risks are best modeled using probability-weighted utility functions or can be reasonably approximated by expected utility (EU) or subjective EU models as is typically assumed. I elicit risk attitudes in the financial and environmental domains using multiple-price list experiment. I examine how subjects?? behavioral, attitudinal, and demographic characteristics affect their probability weighting functions first for financial risks, then for oil-spill risks. I find that most subjects tend to overweight extreme positive outcomes relative to expected utility in both the environmental and financial domains. Subjects are more likely to overemphasize low probability, extreme environmental outcomes than low probability, extreme financial outcomes, leading subjects to offer more support for mitigating environmental gambles than financial gambles with the same odds and equivalent outcomes. I conclude that EU models are likely to underestimate subjects?? willingness to pay for environmental cleanup programs or policies with uncertain outcomes.     

What if utility functions do not exist?

Often the preferences of decision-makers are sufficiently inconsistent so as to preclude the existence of a utility function in the classical sense. Several alternatives for dealing with this situation are discussed. One alternative, that of modifying classical demands on utility functions, is emphasized and described in the context of the theory of measurement developed in recent years by behavioral scientists. The measurement theory approach is illustrated by discussing the concept of the dimension of a partial order. Even if we cannot assign numerical utility or worth values which reflect preferences in the classical utility function sense, from the measurement theory point of view we can still learn a lot about the preferences by finding several measures of worth so that a given alternative x is preferred to an alternative y if and only if x is ranked higher than y on each of the worth scales. If such measures can be found, it follows that the preferences define a partial order, and the smallest number of such scales needed is called the dimension of the partial order. If one-dimensional preferences (those amenable to classical utility assignments) cannot be found, then the next best thing is to search for partially ordered preferences with as small a dimension as possible. Several conditions under which a partial order is two-dimensional are described.The author acknowledges the helpful comments of Joel Spencer and Ralph Strauch. He also thanks Kirby Baker and Peter Fishburn for permission to quote freely from earlier joint work on two-dimensional partial orders.     

The two faces of independence: betweenness and homotheticity

This paper shows that expected utility belongs to the intersection of models satisfying betweenness and a homotheticity condition for risky choice. Betweenness models can accommodate variable risk attitudes, originally highlighted by the Allais paradox, by restricting indifference curves to be linear while allowing non-parallelism. Homotheticity, in contrast, restricts indifference curves to be parallel while permitting non-linearities, such as those highlighted by inverse-S probability weighting. Data from an experiment indicate that approximately 2/3s of participants satisfied homotheticity. Of this group, about half satisfied the expected utility hypothesis. The other half violated expected utility and therefore betweenness. These results indicate that homothetic preferences, and in particular those violating betweenness, can be empirically relevant for decision making under risk.

     

Investigating Risky Choices Over Losses Using Experimental Data

We conduct a battery of experiments in which agents make choices from several pairs of all-loss-lotteries. Using these choices, we estimate a representation of individual preferences over lotteries. We find statistically and economically significant departures from expected utility maximization for many subjects. We also estimate a preference representation based on summary statistics for behavior in the population of subjects, and again find departures from expected utility maximization. Our results suggest that public policies based on an expected utility approach could significantly underestimate preferences and willingness to pay for risk reduction.JEL Classification: C91, D81     

Individual fairness in Harsanyi’s utilitarianism: operationalizing all-inclusive utility

Fairness can be incorporated into Harsanyi’s utilitarianism through all-inclusive utility. This retains the normative assumptions of expected utility and Pareto-efficiency, and relates fairness to individual preferences. It makes utilitarianism unfalsifiable, however, if agents’ all-inclusive utilities are not explicitly specified. This note proposes a two-stage model to make utilitarian welfare analysis falsifiable by specifying all-inclusive utilities explicitly through models of individual fairness preferences. The approach is applied to include fairness in widely discussed allocation examples.     

Supermodularity and the Comparative Statics of Risk

In this article, it is shown that a wide range of comparative statics results from expected utility theory can be extended to generalized expected utility models using the tools of supermodularity theory. In particular, a range of concepts of decreasing absolute risk aversion may be formulated in terms of the supermodularity properties of certainty equivalent representations of preferences.     

Dynamic Choice Mechanisms

A dynamic choice mechanism (e.g. sophisticated choice) is a rule transforming a sequence of orderings into actual choices. The dynamic choice literature analysing such rules is restricted to the case of strict preferences. The present paper allows also for weak preferences. This generalisation is necessary since in dynamic utility models decision makers are typically endowed with orderings which can be represented by continuous utility functions. Such a representation, however, requires the orderings to be a weak ordering. In the presence of weak orderings the classical choice mechanisms have to be re-examined. This paper develops and analyses new choice mechanisms and relates them to the notion of a subgame-perfect equilibrium.     

Nontransitive preferences in decision theory

Intransitive preferences have been a topic of curiosity, study, and debate over the past 40 years. Many economists and decision theorists insist on transitivity as the cornerstone of rational choice, and even in behavioral decision theory intransitivities are often attributed to faulty experiments, random or sloppy choices, poor judgment, or unexamined biases. But others see intransitive preferences as potential truths of reasoned comparisons and propose representations of preferences that accommodate intransitivities. This article offers a partial survey of models for intransitive preferences in a variety of decisional contexts. These include economic consumer theory, multiattribute utility theory, game theory, preference between time streams, and decision making under risk and uncertainty. The survey is preceded by a discussion of issues that bear on the relevance and reasonableness of intransitivity.     

Preferences for information on probabilities versus prizes: The role of risk-taking attitudes

Many real-world decisions entail choices between information on either probabilities or payoffs (i.e., prizes). Simplified versions of such decisions are examined to gain insight into preferences for different types of information as a function of risk-attitudes. General and simple decision rules are derived for cases where the utility function is concave (or convex) over the relevant payoff interval.The article further describes several experiments to test business students' intuitions concerning these optimal decision rules. In general, risk-taking attitudes did not correlate significantly with subjects' preferences for information, in violation of theorems regarding mean-preserving spreads of risk. Other tests, e.g., narrowing certain probability ranges, also resulted in preferences contrary to expected utility (EU) theory.     

Estimating representations of time preferences and models of probabilistic intertemporal choice on experimental data

We here estimate a number of alternatives to discounted-utility theory, such as quasi-hyperbolic discounting, generalized hyperbolic discounting, and rank-dependent discounted utility with three different models of probabilistic choice. The data come from a controlled laboratory experiment designed to reveal individual time preferences in two rounds of 100 binary-choice problems. Rank-dependent discounted utility and its special case—the maximization of present discounted value—turn out to be the best-fitting theory (for about two-thirds of all subjects). For a great majority of subjects (72%), the representation of time preferences in Luce’s choice model provides the best fit.     

Interpersonal dependency of preferences

Standard decision theoretic models disregard the phenomenon of interpersonal dependency of preferences. In this paper it is argued that interpersonal dependency of preferences is a serious challenge for standard utility theory. First we sketch the more philosophical aspects of the problem and then, using a simple, formal model for the two-person case, we show that interpersonal dependency of preferences generally results in indeterminacy of preferences (resp. of subjective utility).     

On the Intuition of Rank-Dependent Utility

Among the most popular models for decision under risk and uncertainty are the rank-dependent models, introduced by Quiggin and Schmeidler. Central concepts in these models are rank-dependence and comonotonicity. It has been suggested that these concepts are technical tools that have no intuitive or empirical content. This paper describes such contents. As a result, rank-dependence and comonotonicity become natural concepts upon which preference conditions, empirical tests, and improvements in utility measurement can be based. Further, a new derivation of the rank-dependent models is obtained. It is not based on observable preference axioms or on empirical data, but naturally follows from the intuitive perspective assumed. We think that the popularity of the rank-dependent theories is mainly due to the natural concepts used in these theories.     

Individual vs. couple behavior: an experimental investigation of risk preferences

In this article, we elicit both individuals’ and couples’ preferences assuming prospect theory (PT) as a general theoretical framework for decision under risk. Our experimental method, based on certainty equivalents, allows to infer measurements of utility and probability weighting at the individual level and at the couple level. Our main results are twofold. First, risk attitude for couples is compatible with PT and incorporates deviations from expected utility similar to those found in individual decision making. Second, couples’ attitudes towards risk are found to be consistent with a mix of individual attitudes, women being more influent on couples’ preferences at low probability levels.