Non-expected Utility Models Research Articles

Why environmental and resource economists should care about non-expected utility models

Experimental and theoretical analysis has shown that the conventional expected utility (EU) and subjective expected utility (SEU) models, which are linear in probabilities, have serious limitations in certain situations. We argue here that these limitations are often highly relevant to the work that environmental and natural resource economists do. We discuss some of the experimental evidence and alternatives to the SEU. We consider the theory used, the problems studied, and the methods employed by resource economists. Finally, we highlight some recent work that has begun to use some of the alternatives to the EU and SEU frameworks and discuss areas where much future work is needed.

A new approach to modeling decision-making under uncertainty

This paper presents two axiomatic models of decision making under uncertainty that avoid the use of a state space. The first is a subjective expected utility model with action-dependent subjective probabilities and effect-dependent preferences (the case of effect-independent preferences is obtained as a special instance). The second is a nonexpected utility model involving well-defined families of action-dependent subjective probabilities on effects and a utility representation that is not necessarily linear in these probabilities (a probabilistic sophistication version of this model, with action-dependent subjective probabilities is obtained as a special case).

A theoretically-consistent empirical model of non-expected utility: An application to nuclear-waste transport

Few theoretically-consistent empirical models addressing the relationship between ambiguity, risk, and preferences for health and safety exist. To fill this gap, we propose a theoretical non-expected-utility model (NEUM) that is relatively easy to estimate using an interval-data model. The NEUM we develop hinges upon two sources of variability, one over risk and the other over ambiguity about the risk. Using data from a survey of Nevada residents concerning risks from nuclear-waste transport, we provide individual-specific welfare estimate for a risk increase. Our findings suggest that negative externalities from nuclear-waste transport perceived risks and ambiguity may be substantial.

A GMM test of the precautionary saving hypothesis with nonexpected-utility preferences

Using GMM estimation with the US data from January 1967 to April 2003, the precautionary saving hypothesis is tested using time-varying consumption uncertainty and a nonexpected-utility model of intertemporal optimal consumption. Overidentifying restrictions of the model specification are also tested for both expected and nonexpected utility using Hansen's J-statistics. It was found that the precautionary saving hypothesis did not hold under expected-utility preferences but did hold partly under nonexpected-utility preferences.

Likely Events and Possible States

This paper provides a recipe to generate definitions of possibility, which is equivalent to the standard approach of deriving possibility from belief/knowledge. Savage's notion of nonnullity is therefore an example that fits into our framework. The recipe is used to create a new definition of possibility, which is logically coherent for all weakly monotonic preferences. For various nonexpected utility models of preference, our new definition improves nonnullity and its existing alternatives.

Entscheidungskalküle jenseits des subjektiven Erwartungsnutzens

Starting point are the well-known empirical violations of axioms of Bernoulli Rationality and the discussion about its prescriptive exclusivity. The paper classifies non-expected utility models into categories which are suitable to model different kinds of violations, depending on whether they follow either Allais or Ellsberg. The argument is brought forward that a modification of Hurwicz’s Criterion is a good compromise, provided that lower and upper probabilities exist: the model is axiomatically founded, practicable — that means simply applicable, clearly interpretable and compatible with expected utility — and allows the modelling of an important class of descriptive violations. The new aspects of the article are firstly a frame of reference for the use of the models depending on the type of violation. Secondly, an axiomatic bracing of the modified Hurwicz Criterion is given by characterizing it as a special case of the Choquet expected utility when lower and upper state-probabilities occur. Thirdly, for these probabilities a clear interpretation is given within the classic probability framework.

A theory of quantifiable beliefs

Building upon the works of Anscombe and Amuann [Ann. Math. Stat. 34 (1963) 199] and Karni and Schmeidler [An expected utility theory for state-dependent preferences. Working Paper 48-80, Foerder Institute for Economic Research, Tel Aviv University], we develop a general axiomatic theory of quantifiable beliefs—a form of probabilistic sophistication that does not preclude state-dependent preferences and does not require the reduction of compound lotteries. The theory includes the state-dependent expected utility model of Karni and Schmeidler [An expected utility theory for state-dependent preferences. Working Paper 48-80, Foerder Institute for Economic Research, Tel Aviv University] and the state-independent non-expected utility model of Machina and Schmeidler [J. Econ. Theory 67 (1995) 106] as special cases. The theory is flexible enough to admit recursivity in the decision-making process.

Normal-randomness expected utility, time preference and emotional distortions

A simple non-expected utility model, “normal-randomness expected utility” (NREU), is formulated. In addition to permanent wealth effects captured by expected utility, individuals anticipate temporary emotional reactions to the resolution of uncertainty in the form of elation and disappointment. Therefore, time preference plays an important part in determining risk attitudes. A higher rate of time preference and emotional sensitivity induces distortions similar, but not identical to, rank-dependent expected utility (RDEU). A specific reaction pattern is postulated by the “NREU” model, in which individuals react more heavily to events falling outside of expected “normal” deviations. This pattern induces S-shaped transformation of probability weights.

The politics of redistributive social insurance

This paper analyses the political support for a social insurance that includes elements of redistribution when there exists an imperfect private insurance alternative. Individuals differ both in their income and risk. The social insurance is compulsory and charges an income-related contribution with pooling of risks. The private insurance is voluntary and charges a contribution based on individual risks. However due to the adverse selection problem, private insurance companies provide only partial insurance. Adopting a non-expected utility model, we show that there is a general majority support for social insurance and that this support is increasing with risk aversion. We also show that a mixed insurance is politically impossible, regardless of the degree of redistribution of social insurance and the joint distribution of risk and income in the population. Lastly, we analyse how the political support for social insurance is affected by any change in its redistributive component and the possibility of using genetic tests.

Risk, Ambiguity, and the Separation of Utility and Beliefs

We introduce a general model of static choice under uncertainty, arguably the weakest model achieving a separation of cardinal utility and a unique representation of beliefs. Most of the nonexpected utility models existing in the literature are special cases of it. Such separation is motivated by the view that tastes are constant, whereas beliefs change with new information. The model has a simple and natural axiomatization. Elsewhere (forthcoming), we show that it can be very helpful in the characterization of a notion of ambiguity aversion, as separating utility and beliefs allows us to identify and remove aspects of risk attitude from the decision maker's behavior. Here we show that the model allows us to generalize several results on the characterization of risk aversion in betting behavior. These generalizations are of independent interest, as they show that some traditional results for subjective expected utility preferences can be formulated only in terms of binary acts.

Lottery Dependent Utility: a Reexamination

In order to accommodate empirically observed violations of the independence axiom of expected utility theory Becker and Sarin (1987) proposed their model of lottery dependent utility in which the utility of an outcome may depend on the lottery being evaluated. Although this dependence is intuitively very appealing and provides a simple functional form of the resulting decision criterion, lottery dependent utility has been nearly completely neglected in the recent literature on decision making under risk. The goal of this paper is to revive the lottery dependent utility model. Therefore, we derive first a sound axiomatic foundation of lottery dependent utility. Secondly, we develop a discontinuous variant of the model which can accommodate boundary effects and may lead to a lexicographic non-expected utility model. Both analyses are accompanied by considering some functional specifications which are in accordance with recent experimental results and may have significant applications in business and management science.

The Politics of Redistributive Social Insurance

This paper analyses the political support for social insurance that includes elements of redistribution when there exists an imperfect private insurance alternative. Individuals differ both in their income and risk. The social insurance is compulsory and charges an income-related contribution with pooling of risks. The private insurance is voluntary and charges a contribution based on individuals. However due to the adverse selection problem, private insurance companies provide only partial insurance. Adopting a non-expected utility model, we show that there is a general majority support for social insurance and that this support is increasing with risk aversion and correlation between risk and income. We also show that a mixed insurance is politically impossible, regardless of the degree of redistribution of social insurance and the joint distribution of risk and income in the population. Lastly, we analyse how the political support for social insurance is affected by any change in its redistributive component and the possibility of using genetic tests.

A Theory of Quantifiable Beliefs

Building upon the works of Anscombe and Aumann (1963) and Karni and Schmeidler (1981), we develop a general axiomatic theory of quantifiable beliefs - a form of probabilistic sophistication that does not preclude state-dependent preferences and does not require the reduction of compound lotteries. The theory includes the state-dependent expected utility model of Karni and Schmeidler (1981) and the state-independent non-expected utility model of Machina and Schmeidler (1995) as special cases. The theory is flexible enough to admit recursivity in the decision-making process. One specific example of this recursive class is shown to be compatible with a quantifiable beliefs version of Schmeidler's (1989) Choquet expected utility maximizing model and thus capable of rationalizing Ellsberg-paradox type behavior.

Risk, Ambiguity, and the Separation of Utility and Beliefs

We introduce a general model of static choice under uncertainty, arguably the weakest model achieving a separation of cardinal utility and a unique representation of beliefs. Most of the non-expected utility models existing in the literature are special cases of it. Such separation is motivated by the view that tastes are constant, whereas beliefs change with new information. The model has a simple and natural axiomatization. Elsewhere [13] we show that it can be very helpful in the characterization of a notion of ambiguity aversion, as separating utility and beliefs allows to identify and remove aspects of risk attitude from the decision maker?s behavior. Here we show that the model allows to generalize several results on the characterization of risk aversion in betting behavior. These generalizations are of independent interest, as they show that some traditional results for subjective expected utility preferences can be formulated only in terms of binary acts.

Comonotonic Book-Making With Nonadditive Probabilities

This paper shows how de Finetti's book-making principle, commonly used to justify additive subjective probabilities, can be modified to agree with some nonexpected utility models. More precisely, a new foundation of the rank-dependent models is presented that is based on a comonotonic extension of the book-making principle. The extension excludes book-making only if all gambles considered induce a same rank-ordering of the states of nature through favorableness of their associated outcomes, and allows for nonadditive probabilities. Typical features of rank-dependence, hedging, ambiguity aversion, and pessimism and optimism, can be accommodated.

Knightian Uncertainty in Financial Markets: An Assessment

Following the Savage paradigm, the theory of portfolio choice and asset pricing under uncertainty assume that the agent's beliefs about future states of the world are represented by a unique additive probability measure, either objective or Bayesian prior. Given absence of arbitrage, agent optimality and market equilibrium, the price of any security is the discounted state-price weighted sum of its future payoffs. Each asset is valued by the expectation of its random payments with respect to the probability distribution over the state space. However, puzzling behavior such as price booms and crashes, excess volatility of asset prices, violation of call and put parity, bid and ask spreads and portfolio rigidities has been observed, in financial markets. All these phenomena can be explained by introducing transaction costs, asymmetric information, incomplete markets into standard financial market theory. In the last decade, following a reexamination process that has involved expected utility theory, several non-expected utility models have appeared in economic literature. The starting point is the distinction between risk, where the agent's beliefs are represented by a unique additive probability distribution, and Knightian uncertainty, where information is too vague and imprecise to be summarized by a unique additive probability measure. Since Knightian uncertainty is more common than risk in economic decision-making, researchers have introduced the agent's attitude towards ambiguity, proving that it plays a crucial role in asset price determination and portfolio choice. This provided an alternative explanation of financial market failures and enabled puzzles to be solved. In static and dynamic models, it was proved that Knightian uncertainty, summarized by a capacity or multiple priors, is a sufficient condition to induce phenomena such as price indeterminacy, price volatility, bid and ask spreads, portfolio inertia, violation of call and put parity and market breakdowns.

Certainty preference and the Arrow-Pratt measure

In Schmidt (1998) a new axiomatic model of decision making under risk has been developed, which can accommodate the certainty effect and is, apart from this property, equivalent to expected utility in all other choice problems. A central feature of this model, termed expected utility with certainty preference, is to allow for a measurement of the certainty effect analogously to the measurement of risk aversion by the Arrow-Pratt measure. The purpose of the present paper is to provide a complete characterization of certainty preference. Therefore, among other things, all standard concepts in the theory of risk aversion are defined and analyzed in the framework of certainty preference. This investigation reveals that the measurement of the certainty effect has the same theoretical capabilities as the measurement of risk aversion by the Arrow-Pratt measure. Additionally, expected utility with certainty preference is compared with the existing literature on non-expected utility models. Key words: Certainty effect - risk aversion - Arrow-Pratt measure Non-expected utility theory

Restricting independence to convex cones

Several nonexpected utility models restrict the independence axiom to particular families of convex cones. The present paper considers this possibility from an abstract point of view. A vector space is endowed with a complete and archimedean preorder satisfying independence on each convex cone of an arbitrary family covering the entire space. Necessary and sufficient conditions are given for the representability of the preorder by a functional which is linear on each cone of the family.

SUBJECTIVE RATIONALITY OF INITIATORS AND OF THRESHOLD-THEORETICAL BEHAVIOR OF FOLLOWERS IN COLLECTIVE ACTION

This article brings a rational-choice perspective to bear on (1) some utility characteristics of people who initiate collective action and (2) reasons why such initiators' actions induce followers who appear to act according to the threshold theory described by Granovetter. This article also identifies certain personality/psychological factors and their interactions with individual costs/benefits of alternative choices that determine (1) the relative utility of taking Action versus Non-action and (2) individual thresholds of choosing Action. Among personality/psychological factors, this article examines the effect of uncertainty preference, susceptibility to rumor or prophecy, and personal efficacy. Certain parametric non-expected utility models and a binary choice model are used to accommodate those factors into a rational-choice framework. Three examples, including two situations of collective action, are discussed. One is a case of Mertonian self-fulfilling prophecy where the initially groundless rumor of a bank's insolvency causes bankruptcy. The second is a case of participation in a risky social/political movement. As a third example, the famous Allais paradox is revisited to show how the parametric non-expected utility models employed provide a rational explanation for this empirically observed paradox.

Temporal Resolution of Uncertainty and Recursive Non-expected Utility Models

If an agent (weakly) prefers early resolution of uncertainty then the recursive forms of both the most commonly used non-expected utility models, betweenness and rank dependence, almost reduce to Kreps & Porteus’s (1978) recursive expected utility.