Parametric multi-attribute utility functions for optimal profit under risk constraints

We provide an economic interpretation of the practice consisting in incorporating risk measures as constraints in an expected prospect maximization problem. For what we call the infimum of expectations class of risk measures, we show that if the decision maker (DM) maximizes the expectation of a random prospect under constraint that the risk measure is bounded above, he then behaves as a “generalized expected utility maximizer” in the following sense. The DM exhibits ambiguity with respect to a family of utility functions defined on a larger set of decisions than the original one; he adopts pessimism and performs first a minimization of expected utility over this family, then performs a maximization over a new decisions set. This economic behaviour is called “maxmin under risk” and studied by Maccheroni (Econ Theory 19:823–831, 2002). As an application, we make the link between an expected prospect maximization problem, subject to conditional value-at-risk being less than a threshold value, and a non-expected utility economic formulation involving “loss aversion”-type utility functions.     

The Likelihood Method for Decision under Uncertainty

This paper introduces the likelihood method for decision under uncertainty. The method allows the quantitative determination of subjective beliefs or decision weights without invoking additional separability conditions, and generalizes the Savage–de Finetti betting method. It is applied to a number of popular models for decision under uncertainty. In each case, preference foundations result from the requirement that no inconsistencies are to be revealed by the version of the likelihood method appropriate for the model considered. A unified treatment of subjective decision weights results for most of the decision models popular today. Savage’s derivation of subjective expected utility can now be generalized and simplified. In addition to the intuitive and empirical contributions of the likelihood method, we provide a number of technical contributions: We generalize Savage’s nonatomiticy condition (“P6”) and his assumption of (sigma) algebras of events, while fully maintaining his flexibility regarding the outcome set. Derivations of Choquet expected utility and probabilistic sophistication are generalized and simplified similarly. The likelihood method also reveals a common intuition underlying many other conditions for uncertainty, such as definitions of ambiguity aversion and pessimism.     

Bayesian decision theory,rule utilitarianism,and Arrow's impossibility theorem

The first part of this paper reexamines the logical foundations of Bayesian decision theory and argues that the Bayesian criterion of expected-utility maximization is the only decision criterion consistent with rationality. On the other hand, the Bayesian criterion, together with the Pareto optimality requirement, inescapably entails a utilitarian theory of morality. The next sections discuss the role both of cardinal utility and of cardinal interpersonal comparisons of utility in ethics. It is shown that the utilitarian welfare function satisfies all of Arrow's social choice postulates avoiding the celebrated impossibility theorem by making use of information which is unavailable in Arrow's original framework. Finally, rule utilitarianism is contrasted with act utilitarianism and judged to be preferable for the purposes of ethical theory.     

Dopamine receptor genes predict risk preferences,time preferences,and related economic choices

Outside of economics, researchers have recently identified genetic predictors of “sensation-seeking” that have been linked to risky and impulsive behaviors. We examine the implications of these genetic polymorphisms for economic behavior. Our analysis indicates that the 7-repeat allele of the DRD4 gene that regulates dopamine uptake in the brain predicts risk-taking and time preferences in economic experiments that allow for ambiguity, losses and discounting. These genetic polymorphisms can also be used to directly predict financial choice patterns that are consistent with previous findings in the behavioral genetics literature.     

The Value of a Probability Forecast from Portfolio Theory

A probability forecast scored ex post using a probability scoring rule (e.g. Brier) is analogous to a risky financial security. With only superficial adaptation, the same economic logic by which securities are valued ex ante – in particular, portfolio theory and the capital asset pricing model (CAPM) – applies to the valuation of probability forecasts. Each available forecast of a given event is valued relative to each other and to the “market” (all available forecasts). A forecast is seen to be more valuable the higher its expected score and the lower the covariance of its score with the market aggregate score. Forecasts that score highly in trials when others do poorly are appreciated more than those with equal success in “easy” trials where most forecasts score well. The CAPM defines economically rational (equilibrium) forecast prices at which forecasters can trade shares in each other’s ex post score – or associated monetary payoff – thereby balancing forecast risk against return and ultimately forming optimally hedged portfolios. Hedging this way offers risk averse forecasters an “honest” alternative to the ruse of reporting conservative probability assessments.     

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.

Testing transitivity in choice under risk

Recently proposed models of risky choice imply systematic violations of transitivity of preference. This study explored whether people show the predicted intransitivity of the two models proposed to account for the certainty effect in Allais paradoxes. In order 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 preferences that need not be transitive. Error rate for a choice is estimated from preference reversals between repeated presentations of the same choice. Results showed that few people repeated intransitive patterns. We can retain the hypothesis that all participants were transitive.     

Dynamic Choice, Independence and Emotions

From the viewpoint of the independence axiom of expected utility theory, an interesting empirical dynamic choice problem involves the presence of a “global risk,” that is, a chance of losing everything whichever safe or risky option is chosen. In this experimental study, participants have to allocate real money between a safe and a risky project. Treatment variable is the particular decision stage at which a global risk is resolved: (i) before the investment decision; (ii) after the investment decision, but before the resolution of the decision risk; (iii) after the resolution of the decision risk. The baseline treatment is without global risk. Our goal is to investigate the isolation effect and the principle of timing independence under the different timing options of the global risk. In addition, we examine the role played by anticipated and experienced emotions in the choice problem. Main findings are a violation of the isolation effect, and support for the principle of timing independence. Although behavior across the different global risk cases shows similarities, we observe clear differences in people’s affective responses. This may be responsible for the conflicting results observed in earlier experiments. Dependent on the timing of the global risk different combinations of anticipated and experienced emotions influence decision making.      

Elementary proof that mean–variance implies quadratic utility

An extensive literature overlapping economics, statistical decision theory and finance, contrasts expected utility [EU] with the more recent framework of mean–variance (MV). A basic proposition is that MV follows from EU under the assumption of quadratic utility. A less recognized proposition, first raised by Markowitz, is that MV is fully justified under EU, if and only if utility is quadratic. The existing proof of this proposition relies on an assumption from EU, described here as “Buridan’s axiom” after the French philosopher’s fable of the ass that starved out of indifference between two bales of hay. To satisfy this axiom, MV must represent not only “pure” strategies, but also their probability mixtures, as points in the (σ, μ) plane. Markowitz and others have argued that probability mixtures are represented sufficiently by (σ, μ) only under quadratic utility, and hence that MV, interpreted as a mathematical re-expression of EU, implies quadratic utility. We prove a stronger form of this theorem, not involving or contradicting Buridan’s axiom, nor any more fundamental axiom of utility theory.     

Two-sided intergenerational moral hazard,long-term care insurance,and nursing home use

Two-sided intergenerational moral hazard occurs (i) if the parent’s decision to purchase long-term care (LTC) coverage undermines the child’s incentive to exert effort because the insurance protects the bequest from the cost of nursing home care, and (ii) when the parent purchases less LTC coverage, relying on child’s effort to keep him out of the nursing home. However, a “net” moral hazard effect obtains only if the two players’ responses to exogenous shocks fail to neutralize each other, entailing a negative relationship between child’s effort and parental LTC coverage. We focus on outcomes out of equilibrium, interpreting them as a break in the relationship resulting in no informal care provided and hence high probability nursing home admission. Changes in the parent’s initial wealth, LTC subsidy received, and child’s expected inheritance are shown to induce “net” moral hazard, in contradistinction to changes in child’s opportunity cost and share in the bequest.     

Choosing monetary sequences: theory and experimental evidence

We formulate and investigate experimentally a model of how individuals choose between time sequences of monetary outcomes. The model assumes that a decision maker uses, sequentially, two criteria to screen options. Each criterion only permits a decision between some pairs of options, while the other options are incomparable according to that criterion. When the first criterion is not decisive, the decision maker resorts to the second criterion to select an alternative. We find that: (1) traditional economic models based on discounting alone cannot explain a significant (almost 30%) proportion of the data no matter how much variability in the discount functions is allowed; (2) our model, despite considering only a specific (exponential) form of discounting, can explain the data much better solely thanks to the use of the secondary criterion; (3) our model explains certain specific patterns in the choices of the “irrational” people. We reject the hypothesis that anomalous behavior is due simply to random “mistakes” around the basic predictions of discounting theories: deviations are not random and there are clear systematic patterns of association between “irrational” choices.     

Valuing Others’ Information under Imperfect Expectations

Sometimes we believe that others receive harmful information. However, Marschak’s value of information framework always assigns non-negative value under expected utility: it starts from the decision maker’s beliefs – and one can never anticipate information’s harmfulness for oneself. The impact of decision makers’ capabilities to process information and of their expectations remains hidden behind the individual and subjective perspective Marschak’s framework assumes. By introducing a second decision maker as a point of reference, this paper introduces a way for evaluating others’ information from a cross-individual, imperfect expectations perspective for agents maximising expected utility. We define the cross-value of information that can become negative – then the information is “harmful” from a cross-individual perspective – and we define (mutual) cost of limited information processing capabilities and imperfect expectations as an opportunity cost from this same point of reference. The simple relationship between these two expected utility-based concepts and Marschak’s framework is shown, and we discuss evaluating short-term reactions of stock market prices to new information as an important domain of valuing others’ information.      

Great Expectations. Part I: On the Customizability of Generalized Expected Utility

We propose a generalization of expected utility that we call generalized EU (GEU), where a decision maker’s beliefs are represented by plausibility measures and the decision maker’s tastes are represented by general (i.e., not necessarily real-valued) utility functions. We show that every agent, “rational” or not, can be modeled as a GEU maximizer. We then show that we can customize GEU by selectively imposing just the constraints we want. In particular, we show how each of Savage’s postulates corresponds to constraints on GEU.     

Is There a “Pessimistic” Bias in Individual Beliefs? Evidence from a Simple Survey

It is an important issue for economic and finance applications to determine whether individuals exhibit a behavioral bias toward pessimism in their beliefs, in a lottery or more generally in an investment opportunities framework. In this paper, we analyze the answers of a sample of 1,540 individuals to the following question “Imagine that a coin will be flipped 10 times. Each time, if heads, you win $10\texttt{C}\!\!\!\rule[2.3pt]{.4em}{.3pt}\!\!\rule[3.3pt]{.4em}{.3pt}It is an important issue for economic and finance applications to determine whether individuals exhibit a behavioral bias toward pessimism in their beliefs, in a lottery or more generally in an investment opportunities framework. In this paper, we analyze the answers of a sample of 1,540 individuals to the following question “Imagine that a coin will be flipped 10 times. Each time, if heads, you win . How many times do you think that you will win?” The average answer is surprisingly about 3.9 which is below the average 5, and we interpret this as a pessimistic bias. We find that women are more “pessimistic” than men, as are old people relative to young. We also analyze how our notion of pessimism is related to more general notions of pessimism previously introduced in psychology.     

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.

Context dependence and consistency in dynamic choice under uncertainty: the case of anticipated regret

We examine if and to what extent choice dispositions can allow dependence on contexts and maintain consistency over time, in a dynamic environment under uncertainty. We focus on one of the context dependence properties, opportunity dependence because of being affected by anticipated regret, where the consequentialist choice framework is maintained. There are two sources of potential inconsistency: one is arrival of information, and the other is changing opportunities. First, we go over the general method of resolution of potential inconsistency, by taking any kinds of inconsistency as given constraints. Second, we characterize a class of choice dispositions that are consistent to information arrival, but may be inconsistent to changing opportunities. Finally, we consider the overall requirement of dynamic consistency and show that it necessarily implies each of consistency to information arrival and independence of choice opportunities. The last result states that the two kinds of potential inconsistency cannot “compensate” each other to recover dynamic consistency overall.     

Preference stability and substitution of indifferents: a rejoinder to Seidenfeld

Seidenfeld (Seidenfeld, T. [1988a], Decision theory without 'Independence' or without 'Ordering', Economics and Philosophy 4: 267-290) gave an argument for Independence based on a supposition that admissibility of a sequential option is preserved under substitution of indifferents at choice nodes (S). To avoid a natural complaint that (S) begs the question against a critic of Independence, he provided an independent proof of (S) in his (Seidenfeld, T. [1988b], Rejoinder [to Hammond and McClennen], Economics and Philosophy 4: 309-315). In reply to my (Rabinowicz, W. [1995], To have one's cake and eat it too: Sequential choice and expected-utility violations, The Journal of Philosophy 92: 586-620), in which I argue that the proof is invalid, Seidenfeld (Seidenfeld, T. [2000], Substitution of indifferent options at choice nodes and admissibility: A reply to Rabinowicz, Theory and Decision 48: 305–310 this issue) submits that I fail to give due consideration to one of the underlying assumptions of his derivation: it is meant to apply only to those cases in which the agent's preferences are stable throughout the sequential decision process. The purpose of this note is to clarify the notion of preference stability so as meet this objection.     

The ostrich effect: Selective attention to information

We develop and test a model which links information acquisition decisions to the hedonic utility of information. Acquiring and attending to information increases the psychological impact of information (an impact effect), increases the speed of adjustment for a utility reference-point (a reference-point updating effect), and affects the degree of risk aversion towards randomness in news (a risk aversion effect). Given plausible parameter values, the model predicts asymmetric preferences for the timing of resolution of uncertainty: Individuals should monitor and attend to information more actively given preliminary good news but “put their heads in the sand” by avoiding additional information given adverse prior news. We test for such an “ostrich effect” in a finance context, examining the account monitoring behavior of Scandinavian and American investors in two datasets. In both datasets, investors monitor their portfolios more frequently in rising markets than when markets are flat or falling.

Political influence in multi-choice institutions: cyclicity,anonymity, and transitivity

We study political influence in institutions where each member chooses a level of support for a collective goal. These individual choices determine the degree to which the goal is reached. Influence is assessed by newly defined binary relations, each of which ranks members on the basis of their relative performance at a corresponding level of participation. For institutions with three options (e.g., voting games in which each voter may vote “yes”, “abstain”, or vote “no”), we obtain three influence relations, and show that their strict components may be cyclic. This latter property describes a “paradox of power” which contrasts with the transitivity of the unique influence relation of binary voting games. Weak conditions of anonymity suffice for each of these relations to be transitive. We also obtain a necessary and sufficient condition for each of these relations to be complete. Further, we characterize institutions in which the rankings induced by these relations, and the Banzhaf–Coleman and Shapley–Shubik power indices coincide. We argue that extending the influence relations to firms would be useful in efficiently assigning workers to different units of production. Finally, we provide applications to various forms of political and economic organizations.     

On the Robustness of the Winner’s Curse Phenomenon

We set out to find ways to help decision makers overcome the “winner’s curse,” a phenomenon commonly observed in asymmetric information bargaining situations, and instead found strong support for its robustness. In a series of manipulations of the “Acquiring a Company Task,” we tried to enhance decision makers’ cognitive understanding of the task. We did so by presenting them with different parameters of the task, having them compare and contrast these different parameters, giving them full feedback on their history of choices and resulting outcomes, and allowing them to interact with a human opponent instead of a computer program. Much to our surprise, none of these manipulations led to a better understanding of the task. Our results demonstrate and emphasize the robustness of the winner’s curse phenomenon.