For decades, discrete choice modelling was practically dominated by only two models: multinomial probit and logit. This paper presents a novel alternative—harmonic choice model. It is qualitatively similar to multinomial probit and logit: if one choice alternative greatly exceeds all (falls below at least one of) other alternatives in terms of utility then it is chosen with probability close to one (zero). Compared to probit and logit, the new model has relatively flat tails and it is steeper in the neighborhood (...) of zero (when all alternatives yield the same utility and the decision maker chooses among them at random). (shrink)

Elicitation methods in decision-making under risk allow us to infer the utilities of outcomes as well as the probability weights from the observed preferences of an individual. An optimally efficient elicitation method is proposed, which takes the inevitable distortion of preferences by random errors into account and minimizes the effect of such errors on the inferred utility and probability weighting functions. Under mild assumptions, the optimally efficient method for eliciting utilities and probability weights is the following three-stage procedure. First, a (...) probability is elicited whose subjective weight is one half. Second, the utility function is elicited through the midpoint chaining certainty equivalent method using the probability elicited at the first stage. Finally, the probability weighting function is elicited through the probability equivalent method. (shrink)

Standard axioms of additively separable utility for choice over time and classic axioms of expected utility theory for choice under risk yield a generalized expected additively separable utility representation of risk-time preferences over probability distributions over sure streams of intertemporal outcomes. A dual approach is to use the analogues of the same axioms in a reversed order to obtain a generalized additively separable expected utility representation of time–risk preferences over intertemporal streams of probability distributions over sure outcomes. The paper proposes (...) an additional axiom, which is called risk-time reversal, for obtaining a special case of the two representations—expected discounted utility. The axiom of risk-time reversal postulates that if a risky lottery over streams of sure intertemporal outcomes and an intertemporal stream of risky lotteries yield the same probability distribution of possible outcomes in every point in time then a decision-maker is indifferent between the two. This axiom is similar to assumption 2 “reversal of order in compound lotteries” in Anscombe and Aumann :199–205, 1963, p. 201). (shrink)

Empirical research often requires a method how to convert a deterministic economic theory into an econometric model. A popular method is to add a random error term on the utility scale. This method, however, ignores stochastic dominance. A modification of this method is proposed to account for stochastic dominance. The modified model compares favorably to other existing models in terms of goodness of fit to experimental data. The modified model can rationalize the preference reversal phenomenon. An intuitive axiomatic characterization of (...) the modified model is provided. Important microeconomic concept of risk aversion is well defined in the modified model. (shrink)

In binary choice between discrete outcome lotteries, an individual may prefer lottery L1 to lottery L2 when the probability that L1 delivers a better outcome than L2 is higher than the probability that L2 delivers a better outcome than L1. Such a preference can be rationalized by three standard axioms (solvability, convexity and symmetry) and one less standard axiom (a fanning-in). A preference for the most probable winner can be represented by a skew-symmetric bilinear utility function. Such a utility function (...) has the structure of a regret theory when lottery outcomes are perceived as ordinal and the assumption of regret aversion is replaced with a preference for a win. The empirical evidence supporting the proposed system of axioms is discussed. (shrink)

Uncertain or ambiguous events cannot be objectively measured by probabilities, i.e. different decision-makers may disagree about their likelihood of occurrence. This paper proposes a new decision-theoretical approach on how to measure ambiguity that is analogous to axiomatic risk measurement in finance. A decision-theoretical measure of ambiguity is a function from choice alternatives to non-negative real numbers. Our proposed measure of ambiguity is derived from a novel assumption that ambiguity of any choice alternative can be decomposed into a left-tail ambiguity and (...) a right-tail ambiguity. This decomposability assumption is combined with two standard assumptions: ambiguity sources are independent from outcomes and any elementary increase in uncertainty necessarily increases ambiguity. (shrink)

Discounted utility theory and its generalizations use discount functions for weighting utilities of outcomes received in different time periods. We propose a new simple test of convexity–concavity of discount function. This test can be used with any utility function and any preferences over risky lotteries. The data from a controlled laboratory experiment show that about one third of experimental subjects reveal a concave discount function and another one third of subjects reveal a convex discount function.

This paper presents a new decision theory for modelling choice under risk. The new theory is a two-parameter generalization of expected utility theory. The proposed theory assumes that a decision maker: behaves as if maximizing expected utility; but may experience disappointment when the utility of a lottery’s outcome falls short of the expected utility of the lottery; and may have a preference for gambling. The proposed theory can rationalize the fourfold pattern of risk attitudes; the common ratio effect and the (...) reverse thereof ; the Allais paradox in classical common consequence problems and the reverse Allais paradox—in common consequence problems with an even split of a probability mass; violations of the betweenness axiom; switching behavior in the Samuelson’s example; violations of ordinal, upper and lower cumulative independence ; and preference reversals between valuations and choice. In application to insurance, the theory can rationalize full insurance with an actuarially unfair premium and aversion to probabilistic insurance. In application to optimal portfolio investment, the theory can rationalize the equity premium puzzle. (shrink)

Prospect theory emerged as one of the leading descriptive decision theories that can rationalize a large body of behavioral regularities. The methods for eliciting prospect theory parameters, such as its value function and probability weighting, are invaluable tools in decision analysis. This paper presents a new simple method for eliciting prospect theory’s value function without any auxiliary/simplifying parametric assumptions. The method is applicable both to choice under ambiguity (Knightian uncertainty) and risk (when events are characterized by objective probabilities). Our new (...) elicitation method is implemented in a simple paper-and-pencil experiment (via an iterative multiple price list format). This is one of the first experiments that elicits non-parametric prospect theory’s value function with salient rewards. The collected data generally confirm findings in the existing literature: the value function is S-shaped (concave in the gain domain and convex in the loss domain) though there is a weaker loss aversion on the aggregate level and a substantial heterogeneity in loss aversion on the individual level (41% loss averse, 6% loss neutral and 53% gain seeking). (shrink)

Debreu (American Economic Review 50:186–188, 1960) famously criticized Luce (Individual choice behavior, Wiley, New York, 1959) choice model with what became known as the red-bus blue-bus example: if a choice set contains two distinct alternatives C (car) and B (blue bus) then adding a third alternative A (red bus) that is essentially identical to B does not affect the choice probability of C but reduces the choice probability of B by half. Debreu’s critique highlights the existence of substitution effects violating (...) the principle of independence from irrelevant alternatives—the cornerstone of Luce (Individual choice behavior, Wiley, New York, 1959) choice model. This paper weakens this principle to construct a model of probabilistic choice satisfying Debreu’s critique. (shrink)

In the television show Deal or No Deal, a contestant is endowed with a sealed box containing a monetary prize between one cent and half a million euros. In the course of the show, the contestant is offered to exchange her box for another sealed box with the same distribution of possible monetary prizes inside. This offers a unique natural experiment for studying endowment effects under high monetary incentives. We find evidence of only a weak endowment effect when contestants exchange (...) their box for another box with the same distribution of possible prizes. (shrink)

Standard models of portfolio investment rely on various statistical measures of dispersion. Such measures favor returns smoothed over all states of the world and penalize abnormally low as well as abnormally high returns. A model of portfolio investment based on the tradeoff between expected return and expected loss considers only abnormally low returns as undesirable. Such a model has a comparative advantage over other existing models in that a first-order stochastically dominant portfolio always has a higher expected return and a (...) lower expected loss. Expected return—expected loss model of portfolio investment can rationalize the equity premium puzzle. Two random variables are not comoving if there is at least one state of the world in which one random variable yields a positive return and the other—a negative return. Such random variables provide hedging benefits from diversification in portfolio investment according to the expected return—expected loss model. A special case of this model, when an investor linearly trade-offs expected returns and expected losses, is also a special case of the prospect theory when a decision-maker has a piece-wise linear value function without any probability weighting. (shrink)

The problem of intertemporal choice arises when outcomes are received in different moments of time. This paper presents an axiomatic model of intertemporal choice when consumption in the previous moment of time contributes to utility evaluation of consumption in the current moment. This model generalizes classic discounted utility theory (also known as constant or exponential discounting) in two ways. First, in every moment of time, a decision maker derives utility not only from current consumption but also from “residual” consumption in (...) the previous moment of time. Second, these utilities are discounted with weights that are essentially a quasi-hyperbolic discounting function. The paper presents an application of the proposed model to the problem of optimal consumption and savings given a fixed income (wealth). When a decision maker derives satisfaction from both instantaneous consumption as well as a share of consumption in the previous moment of time, optimal consumption path is cyclic—periods of relatively high consumption are interchanged with periods of relatively low consumption. These cycles decay over time. Asymptotically, the consumption path exhibits conventional properties (constant, increasing or decreasing over time when a gross interest rate multiplied by discount factor is correspondingly equal to, greater than, or less than one). (shrink)

This article investigates how subjects determine minimum selling prices for lotteries. We design an experiment where subjects have at every moment an incentive to state their minimum selling price and to adjust the price, if they believe that the price that they stated initially was not optimal. We observe frequent and sizeable price adjustments. We find that random pricing models cannot explain the observed price patterns. We show that earlier prices contain information about future price adjustments. We propose a model (...) of Stochastic Pricing that offers an intuitive explanation for these price adjustment patterns. (shrink)

Risk preferences of Australian academics are elicited by analyzing the aggregate distribution of their retirement funds across available investment options. Not more than 10 % of retirement funds are invested as if their owners maximize expected utility under the assumption of constant relative risk aversion with an empirically plausible level of risk aversion. An implausibly high level of risk aversion is required to rationalize any investment into bonds when stocks are available. Not more than 36.54 % of all investments can (...) be rationalized by a model of loss averse preferences. Moreover, the levels of loss aversion typically reported in the experimental studies imply overinvestment in bonds, which is not observed in the data. Up to 67.18 % of all investments can be rationalized by rank-dependent utility or Yaari’s dual model with empirically plausible parameters. A median Australian academic behaves as if maximizing rank-dependent utility with parameter γ∈[0.76,0.79]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma \in [0.76, 0.79]$$\end{document} in a Tversky and Kahneman probability weighting function. (shrink)

In decision theory, the betweenness axiom postulates that a decision maker who chooses an alternative A over another alternative B must also choose any probability mixture of A and B over B itself and can never choose a probability mixture of A and B over A itself. The betweenness axiom is a weaker version of the independence axiom of expected utility theory. Numerous empirical studies documented systematic violations of the betweenness axiom in revealed individual choice under uncertainty. This paper shows (...) that these systematic violations can be linked to another behavioral regularity—choice shifts in a group decision making. Choice shifts are observed if an individual faces the same decision problem but makes a different choice when deciding alone and in a group. (shrink)

This paper presents an overlapping generations household model with positive assortative matching, incomplete information about partner’s type and a gender pay gap on the labor market. In equilibrium, a gender pay gap creates an excess supply of desirable husbands and women marry early to increase their chance of being matched with an ideal partner, which results in a gender age gap on the marriage market. A modified model with asymmetric information yields a similar result. An extended model where individuals have (...) an option to remain single yields a similar result as well. (shrink)

The voting paradox occurs when a democratic society seeking to aggregate individual preferences into asocialpreference reaches an intransitive ordering. However it is not widely known that the paradox may also manifest for anindividualaggregating over attributes of risky objects to form a preference over those objects. When this occurs, the relation ‘stochastically greater than’ is not always transitive and so transitivity need not hold between those objects. We discuss the impact of other decision paradoxes to address a series of philosophical and (...) economic arguments against intransitive (cyclical) choice, before concluding that intransitive choices can be justified. (shrink)

In the television show Deal or No Deal a contestant is endowed with a sealed box, which potentially contains a large monetary prize. In the course of the show the contestant learns more information about the distribution of possible monetary prizes inside her box. Consider two groups of contestants, who learned that the chances of their boxes containing a large prize are 20% and 80% correspondingly. Contestants in both groups receive qualitatively similar price offers for selling the content of their (...) boxes. If contestants are less risk averse when facing unlikely gains, the price offer is likely to be more frequently rejected in the first group than in the second group. However, the fraction of rejections is virtually identical across two groups. Thus, contestants appear to have identical risk attitudes over (large) gains of low and high probability. (shrink)

Investors who are more willing to accept risks when evaluating their investments less frequently are said to exhibit myopic loss aversion (MLA). Several recent experimental studies found that, on average, subjects bet significantly higher amounts on a risky lottery when they observe only a cumulative outcome of several realizations of the lottery (long evaluation period). In this article, we reexamine these empirical findings by analyzing individual rather than aggregate choice patterns. The behavior of the majority of subjects is inconsistent with (...) the hypothesis of MLA: they bet an intermediate fraction of their initial endowment and these bets, on average, are not significantly different across two treatments with short and long evaluation period. We discuss several alternative explanations of this finding, including the Fechner model of random errors and the financial asset pricing model. (shrink)