Reference-dependent subjective expected utility

A reference-dependent generalisation of subjective expected utility theory is presented. In this theory, preferences between acts depend both on final outcomes and on reference points (which may be uncertain acts). It is characterised by a set of axioms in a Savage-style framework. A restricted form of the theory separates attitudes to end states (encoded in a ‘satisfaction function’) from attitudes to gains and losses of satisfaction. Given weak additional assumptions, the restricted theory excludes cycles of choice, explains observed disparities between willingness-to-pay and willingness-to-accept valuations of lotteries, and predicts preference reversal.     

A theory of subjective compound lotteries

We develop a Savage-type model of choice under uncertainty in which agents identify uncertain prospects with subjective compound lotteries. Our theory permits issue preference; that is, agents may not be indifferent among gambles that yield the same probability distribution if they depend on different issues. Hence, we establish subjective foundations for the Anscombe-Aumann framework and other models with two different types of probabilities. We define second-order risk as risk that resolves in the first stage of the compound lottery and show that uncertainty aversion implies aversion to second-order risk which implies issue preference and behavior consistent with the Ellsberg paradox.     

A mechanism for eliciting a probability distribution

This work extends Karni’s direct revelation mechanism for eliciting agents’ subjective beliefs over the distribution of a random variable.     

A subjective model of experimentation

Typically an experiment is defined by a set of possible signals and a likelihood function, and both are specified exogenously—they are taken to be observable by the analyst. This paper renders them subjective by showing that they may be derived from suitable choice behavior. This is done in the context of an axiomatic representation theorem for preference on a suitable domain.     

Subjective probabilities on “small” domains

The Savagian choice-theoretic construction of subjective probability does not apply to preferences, like those in the Ellsberg Paradox, that reflect a distinction between risk and ambiguity. We formulate two representation results—one for expected utility, the other for probabilistic sophistication—that derive subjective probabilities but only on a “small” domain of risky events. Risky events can be either specified exogenously or in terms of choice behavior; in the latter case, both the values and the domain of probability are subjective. The analysis identifies a mathematical structure—called a mosaic—that is intuitive for both exogenous and behavioral specifications of risky events. This structure is weaker than an algebra or even a λ-system.     

Subjective mortality expectations and consumption and saving behaviours among the elderly

Abstract Life expectancy is an important factor that individuals have to take into account for saving and consumption choices. The life‐cycle model of consumption and saving behaviour predicts that consumption growth should decrease with higher mortality rates. The aim of this study is to test this hypothesis based on data about subjective longevity expectations from the Health and Retirement Study merged with detailed consumption data from two waves of the Consumption and Activities Mail Survey. This study finds that an increase in subjective mortality by 1% corresponds to an annual decrease in consumption of non‐durable goods of around 1.8%.     

Subjective random discounting and intertemporal choice

This paper provides an axiomatic foundation for a particular type of preference shock model called the random discounting representation where a decision maker believes that her discount factors change randomly over time. For this purpose, we formulate an infinite horizon extension of [E. Dekel, B. Lipman, A. Rustichini, Representing preferences with a unique subjective state space, Econometrica 69 (2001) 891-934], and identify the behavior that reduces all subjective uncertainties to those about future discount factors. We also show uniqueness of subjective belief about discount factors. Moreover, a behavioral comparison about preference for flexibility characterizes the condition that one's subjective belief second-order stochastically dominates the other. Finally, the resulting model is applied to a consumption-savings problem.     

Act similarity in case-based decision theory

Summary Case-Based Decision Theory (CBDT) postulates that decision making under uncertainty is based on analogies to past cases. In its original version, it suggests that each of the available acts is ranked according to its own performance in similar decision problems encountered in the past.The purpose of this paper is to extend CBDT to deal with cases in which the evaluation of an act may also depend on past performance of different, but similar acts. To this end we provide a behavioral axiomatic definition of the similarity function over problem-act pairs (and not over problem pairs alone, as in the original model).We propose a model in which preferences are context-dependent. For each conceivable history of outcomes (to be thought of as the context of decision) there is a preference order over acts. If these context-dependent preference relations satisfy our consistency-across-contexts axioms, there is an essentially unique similarity function that represents these preferences via the (generalized) CBDT functional.We are grateful to Akihiko Matsui for the discussions that motivated this work. We also thank Enriqueta Aragones, Roger Myerson, Zvika Neeman, Ariel Rubinstein, Peyton Young, and an anonymous referee for their comments. Partial financial support from the Alfred Sloan Foundation is gratefully acknowledged.     

Finite additive utility representations for preferences over menus

I characterize a finite additive utility representation for preferences over menus. The numbers of both positive and negative components in this representation are expressed explicitly in terms of preference. These expressions can be used to characterize models of temptation, perfectionism, context effects, and other phenomena.     

A perspective on subjective probability for prediction and decision

The problem of assigning a meaningful subjective probability measure on a set of predictive models (inductive hypothesis) is considered. An outperformance construct is suggested as a means of reducing this to the more tractable task of assessing the distribution on a set of realizable events. Further issues on the precise interpretation of subjective probability estimation from the perspective of the decision-oriented forecaster are then considered.     

Measuring subjective expectations in developing countries: A critical review and new evidence

The majority of economic decisions are forward-looking and thus involve expectations of future outcomes. Understanding the expectations that individuals have is thus of crucial importance to designing and evaluating policies in health, education, finance, migration, social protection, and many other areas. However, the majority of developing country surveys are static in nature and many do not elicit subjective expectations of individuals. Possible reasons given for not collecting this information include fears that poor, illiterate individuals do not understand probability concepts, that it takes far too much time to ask such questions, or that the answers add little value. This paper provides a critical review and new analysis of subjective expectations data from developing countries and refutes each of these concerns. We find that people in developing countries can generally understand and answer probabilistic questions, such questions are not prohibitive in time to ask, and the expectations are useful predictors of future behavior and economic decisions. The paper discusses the different methods used for eliciting such information, the key methodological issues involved, and the open research questions. The available evidence suggests that collecting expectations data is both feasible and valuable, suggesting that it should be incorporated into more developing country surveys.     

The demand for a risky asset in the presence of a background risk

We examine the demand for a risky asset in the presence of two risks: a financial risk and a background risk which need not be financial. First, we compute the necessary and sufficient condition for a positive demand for a risky asset, showing that it depends on two terms capturing respectively the direct effect of risk premium and the dependence between the two risks. Second, we develop higher order expectation dependence concept and show that the more information about the sign of higher cross derivatives of the utility function we have, the weaker dependence conditions on distribution we achieve.     

Imprecise probabilistic beliefs as a context for decision-making under ambiguity

Coherent imprecise probabilistic beliefs are modeled as incomplete comparative likelihood relations admitting a multiple-prior representation. Under a structural assumption of Equidivisibility, we provide an axiomatization of such relations and show uniqueness of the representation. In the second part of the paper, we formulate a behaviorally general “Likelihood Compatibility” axiom relating preferences and probabilistic beliefs and characterize its implications for the class of “invariant biseparable” preferences that includes the MEU and CEU models among others.     

Subjective conditional probability modelling

Cross-impact analysis is a technique for investigating the effect of interaction of events in future oriented studies. A fundamental difficulty with cross-impact analysis is to determine what respondents mean when they answer the “conditional probability” questions normally posed. This paper offers a heuristic alternative to traditional cross-impact analysis which is applicable to cross-impact situations where the object is to generate scenarios for decision making.     

Co-monotonicity: Toward a utility function capturing envy

Envy affects economic decisions, and can lead to monotonicity violation. We introduce co-monotonicity—a generalization of monotonicity, expected to hold even in the presence of envy. Experimental results and implications for the form of possible utility functions are discussed.     

Preemption in a real option game with a first mover advantage and player-specific uncertainty

In this paper a two-player real option game with a first-mover advantage is analyzed, where payoffs are driven by a player-specific stochastic state variable. It is shown that there exists an equilibrium which has qualitatively different properties from those in standard real option games driven by common stochastic shocks. The properties of the equilibrium are four-fold: (i) preemption does not necessarily occur, (ii) if preemption takes place, the rent-equalization property holds, (iii) for almost all sample paths it is clear ex-ante which player invests first, and (iv) it is possible that both players invest simultaneously, even if that is not optimal. It is argued from simulations that real option games with a common one-dimensional shock do not provide a good approximation for games with player-specific uncertainty, even if these are highly correlated.     

A critical review of multi-criteria decision making methods with special reference to forest management and planning

This paper provides a review of research contributions on forest management and planning using multi-criteria decision making (MCDM) based on an exhaustive literature survey. The review primarily focuses on the application aspects highlighting theoretical underpinnings and controversies. It also examines the nature of the problems addressed and incorporation of risk into forest management and planning decision making. The MCDM techniques covered in this review belong to several schools of thought. For each technique, a variety of empirical applications including recent studies has been reviewed. More than 60 individual studies were reviewed and classified by the method used, country of origin, number and type of criteria and options evaluated. The review serves as a guide to those interested in how to use a particular MCDM approach. Based on the review, some recent trends and future research directions are also highlighted.     

An operational interpretation and existence of the Aumann-Serrano index of riskiness

In this note we provide an operational interpretation of the economic index of riskiness of Aumann and Serrano (2008) and discuss its existence in the case of non-finite gambles.     

The monetary utility premium and interpersonal comparisons

The utility premium is generally defined as the pain or reduction in expected utility caused by an n$n$th-degree risk increase, where n≥2$n\ge 2$. While it is a very useful concept in understanding a decision maker’s choice in uncertain situations, the utility premium is not interpersonally comparable. This note shows that the monetary utility premium–the utility premium divided by the expected marginal utility at the random starting wealth–is interpersonally comparable, and the comparison is characterized by Ross more risk aversion of the corresponding degree.