Violations of betweenness and choice shifts in groups

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.     

A simple framework for the axiomatization of exponential and quasi-hyperbolic discounting

The main goal of this paper is to investigate which normative requirements, or axioms, lead to exponential and quasi-hyperbolic forms of discounting. Exponential discounting has a well-established axiomatic foundation originally developed by Koopmans (Econometrica 28(2):287–309, 1960, 1972) and Koopmans et al. (Econometrica 32(1/2):82–100, 1964) with subsequent contributions by several other authors, including Bleichrodt et al. (J Math Psychol 52(6):341–347, 2008). The papers by Hayashi (J Econ Theory 112(2):343–352, 2003) and Olea and Strzalecki (Q J Econ 129(3):1449–1499, 2014) axiomatize quasi-hyperbolic discounting. The main contribution of this paper is to provide an alternative foundation for exponential and quasi-hyperbolic discounting, with simple, transparent axioms and relatively straightforward proofs. Using techniques by Fishburn (The foundations of expected utility. Reidel Publishing Co, Dordrecht, 1982) and Harvey (Manag Sci 32(9):1123–1139, 1986), we show that Anscombe and Aumann’s (Ann Math Stat 34(1):199–205, 1963) version of Subjective Expected Utility theory can be readily adapted to axiomatize the aforementioned types of discounting, in both finite and infinite horizon settings.     

A multiattribute decision time theory

In this study, we analyze choice in the presence of some conflict that affects the decision time (response time), a subject that has been documented in the literature. We axiomatize a multiattribute decision time (MDT) representation, which is a dynamic extension of the classic multiattribute expected utility theory that allows potentially incomplete preferences. Under this framework, one alternative is preferred to another in a certain period if and only if the weighted sum of the attribute-dependent expected utility induced by the former alternative is larger than that induced by the latter for all attribute weights in a closed and convex set. MDT uniquely determines the decision time as the earliest period at which the ranking between alternatives becomes decisive. The comparative statics result indicates that the decision time provides useful information to locate indifference curves in a specific setting. MDT also explains various empirical findings in economics and other relevant fields.     

The influence of fear in decisions: Experimental evidence

This article studies decisions made under conditions of fear, when a catastrophic outcome is introduced in a lottery. It reports on experimental results and seeks to compare the predictions of the expected utility (EU) framework with those of a new axiomatic treatment of choice under uncertainty that takes explicit account of emotions such as fear (Chichilnisky 1996, 2000, 2002, 2009). Results provide evidence that fear influences the cognitive process of decision-making by leading some subjects to focus excessively on catastrophic events. Such heterogeneity in subjects’ behavior, while not consistent with EU-based functions, is fully consistent with the new type of utility function implied by the new axioms.     

A note on identification in discrete choice models with partial observability

This note establishes a new identification result for additive random utility discrete choice models. A decision-maker associates a random utility \(U_{j}+m_{j}\) to each alternative in a finite set \(j\in \left\{ 1,\ldots ,J\right\} \), where \(\mathbf {U}=\left\{ U_{1},\ldots ,U_{J}\right\} \) is unobserved by the researcher and random with an unknown joint distribution, while the perturbation \(\mathbf {m}=\left( m_{1},\ldots ,m_{J}\right) \) is observed. The decision-maker chooses the alternative that yields the maximum random utility, which leads to a choice probability system \(\mathbf { m\rightarrow }\left( \Pr \left( 1|\mathbf {m}\right) ,\ldots ,\Pr \left( J| \mathbf {m}\right) \right) \). Previous research has shown that the choice probability system is identified from the observation of the relationship \( \mathbf {m}\rightarrow \Pr \left( 1|\mathbf {m}\right) \). We show that the complete choice probability system is identified from observation of a relationship \(\mathbf {m}\rightarrow \sum _{j=1}^{s}\Pr \left( j|\mathbf {m} \right) \), for any \(s<J\). That is, it is sufficient to observe the aggregate probability of a group of alternatives as it depends on \(\mathbf {m}\). This is relevant for applications where choices are observed aggregated into groups while prices and attributes vary at the level of individual alternatives.     

Intertemporal utility smoothing under uncertainty

This paper axiomatizes a recursive utility model that captures both intertemporal utility smoothing defined across time and ambiguity aversion defined over states. The resulting representation adapts Wakai (Econometrica 76:137–153, 2008) model of intertemporal utility smoothing as an aggregator function, where the utility of the certainty equivalent of future uncertainty is computed by Gilboa and Schmeidler (J Math Econ 18:141–153, 1989) multiple-priors utility. The model also permits the separation of intertemporal utility smoothing from ambiguity aversion.     

Risk preferences of Australian academics: where retirement funds are invested tells the story

Risk preferences of Australian academics are elicited by analyzing the aggregate distribution of their retirement funds (superannuation) 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 (Econometrica 55:95–115 1987) dual model with empirically plausible parameters. A median Australian academic behaves as if maximizing rank-dependent utility with parameter \(\gamma \in [0.76, 0.79]\) in a Tversky and Kahneman (J Risk Uncertain 5:297–323 1992) probability weighting function.     

Risk preferences and changes in background risk

We present two theorems that yield necessary and sufficient conditions for first- and second-degree stochastic dominance deteriorations of background risk to increase risk aversion with respect to foreground risk. We require that any change in a foreground risk that is undesirable remains so after a background risk changes in a way that is either unfair, undesirable in the sense of reducing expected utility, or undesirable in the sense of increasing expected marginal utility. Our results thus characterize utility functions that are, respectively, vulnerable, proper, or standard with respect to changes in background risk.

Harsanyi’s critical rule utilitarianism

In his recent book,Rational Behaviour and Bargaining Equilibrium In Games and Social Situations, John C. Harsanyi devotes a chapter to his new theory of morality, which he calls ‘Critical Rule Utilitarianism’, and which contains his solution to the problem of the interpersonal comparison of utility. After a detailed exposition of his theory, arguments will be presented to show that:

1. there are certain formal difficulties in the solution that he offers which leads to a rejection of the axiom that there is to be agreement between an individualj’s personal preferences and individuali’s (i ≠j) extended utility function out of which the social welfare function is to be constructed; and
2. Harsanyi’s theory of critical rule utilitarianism cannot be accepted as a theory of morality because it presupposes a more fundamental theory in its actual construction.

     

Optimal inequality behind the veil of ignorance

In Rawls’ (A theory of justice. Harvard University Press, Cambridge, 1971) influential social contract approach to distributive justice, the fair income distribution is the one that an individual would choose behind a veil of ignorance. Harsanyi (J Polit Econ 61:434–435, 1953, J Polit Econ 63:309–332, 1955, Am Polit Sci Rev 69:594–606, 1975) treated this situation as a decision under risk and arrived at utilitarianism using expected utility theory. This paper investigates the implications of applying cumulative prospect theory instead, which better describes behavior under risk. I find that the specific type of inequality in bottom-heavy right-skewed income distributions, which includes the log-normal income distribution, could be perceived as desirable. This optimal inequality result contrasts the implications of other social welfare criteria.     

What can multiple price lists really tell us about risk preferences?

Multiple price lists have emerged as a simple and popular method for eliciting risk preferences. Despite their popularity, a key downside of multiple price lists has not been widely recognized — namely that the approach is unlikely to generate sufficient information to accurately identify different dimensions of risk preferences. The most popular theories of decision making under risk posit that preferences for risk are driven by a combination of two factors: the curvature of the utility function and the extent to which probabilities are weighted non-linearly. In this paper, we show that the widely used multiple price list introduced by Holt and Laury (The American Economic Review 92(5) 1644–1655 2002) is likely more accurate at eliciting the shape of the probability weighting function, and we construct a different multiple price list that is likely more accurate at eliciting the shape of the utility function. We show that by combining information from different multiple price lists, greater predictive performance can be achieved.     

Loss aversion leading to advantageous selection

Some insurance markets are characterized by “advantageous selection”, that is, ex-post risk and coverage are negatively correlated. We show that expectation-based loss aversion as in K?szegi and Rabin (Quarterly Journal of Economics, 121(4), 1133–1165, 2006; The American Economic Review, 97(4), 1047–1073, 2007) provides a natural explanation for this phenomenon in environments in which risk aversion models do not, e.g., when agents face modest-scale risks and/or in absence of moral hazard. More exposure to risk has two competing effects on an agent’s willingness to pay for insurance: a positive effect, as in standard expected utility models; and a negative one, due to a reference effect. We determine conditions under which an insurance provider optimally sets a high price at which only low risk agents buy.     

Towards a more precise decision framework

The terms negative utility of gambling and risk aversion conflate three things:

Additive representation of separable preferences over infinite products

Let \(\mathcal{X }\) be a set of outcomes, and let \(\mathcal{I }\) be an infinite indexing set. This paper shows that any separable, permutation-invariant preference order \((\succcurlyeq )\) on \(\mathcal{X }^\mathcal{I }\) admits an additive representation. That is: there exists a linearly ordered abelian group \(\mathcal{R }\) and a ‘utility function’ \(u:\mathcal{X }{{\longrightarrow }}\mathcal{R }\) such that, for any \(\mathbf{x},\mathbf{y}\in \mathcal{X }^\mathcal{I }\) which differ in only finitely many coordinates, we have \(\mathbf{x}\succcurlyeq \mathbf{y}\) if and only if \(\sum _{i\in \mathcal{I }} \left[u(x_i)-u(y_i)\right]\ge 0\) . Importantly, and unlike almost all previous work on additive representations, this result does not require any Archimedean or continuity condition. If \((\succcurlyeq )\) also satisfies a weak continuity condition, then the paper shows that, for any \(\mathbf{x},\mathbf{y}\in \mathcal{X }^\mathcal{I }\) , we have \(\mathbf{x}\succcurlyeq \mathbf{y}\) if and only if \({}^*\!\sum _{i\in \mathcal{I }} u(x_i)\ge {}^*\!\sum _{i\in \mathcal{I }}u(y_i)\) . Here, \({}^*\!\sum _{i\in \mathcal{I }} u(x_i)\) represents a nonstandard sum, taking values in a linearly ordered abelian group \({}^*\!\mathcal{R }\) , which is an ultrapower extension of \(\mathcal{R }\) . The paper also discusses several applications of these results, including infinite-horizon intertemporal choice, choice under uncertainty, variable-population social choice and games with infinite strategy spaces.     

Stochastic expected utility theory

This paper proposes a new decision theory of how individuals make random errors when they compute the expected utility of risky lotteries. When distorted by errors, the expected utility of a lottery never exceeds (falls below) the utility of the highest (lowest) outcome. This assumption implies that errors are likely to overvalue (undervalue) lotteries with expected utility close to the utility of the lowest (highest) outcome. Proposed theory explains many stylized empirical facts such as the fourfold pattern of risk attitudes, common consequence effect (Allais paradox), common ratio effect and violations of betweenness. Theory fits the data from ten well-known experimental studies at least as well as cumulative prospect theory.

A tractable method to measure utility and loss aversion under prospect theory

This paper provides an efficient method to measure utility under prospect theory. Our method minimizes both the number of elicitations required to measure utility and the cognitive burden for subjects, being based on the elicitation of certainty equivalents for two-outcome prospects. We applied our method in an experiment and were able to replicate the main findings on prospect theory, suggesting that our method measures what it is intended to. Our data confirmed empirically that risk seeking and concave utility can coincide under prospect theory. Utility did not depend on the probability used in the elicitation, which offers support for the validity of prospect theory.

Moment characterization of higher-order risk preferences

This article presents a characterization of higher-order risk preferences such as prudence or temperance in terms of statistical moments. Our results, which are generalizations of Roger (Theory Decis, 70(1):27–44, 2011) and Ekern (Econ Lett, 6(4), 329–333, 1980), give a better understanding of how higher-order risk preferences relate to skewness preference and kurtosis aversion. While they are not based on expected utility theory, an implication within that theory is that all commonly used utility functions exhibit skewness preference and kurtosis aversion.     

Making social trade-offs among lives,disabilities, and cost

Applying cost/benefit techniques to issues of life and death generally requires a single index, comparable to gross domestic product, describing the welfare of any community in terms of the health, quality of life, wealth, and longevity of its population. While such indices, based on economic and multiattribute utility theory, do exist, they generally require detailed information on the preferences of the affected individuals. Since gathering such detailed information is often prohibitively expensive and time-consuming, this article derives a simpler index of community welfare. Our index evaluates any proposed government project using a weighted geometric average of the project's anticipated impact on

?per capita wealth less the weighted proportion of individuals with various disabilities, and

?per capita life expectancy adjusted to discount future years of life.

Since the criterion measures the overall utility of society, it can also be used to compare quality of life in various countries.     

Ensemble prospectism

Incomplete preferences displaying ‘mildly sweetened’ structure are common, yet theoretically problematic. This paper examines the properties of the rankings induced by the set of all coherent completions of the mildly sweetened partial preference structure. Building on these properties, I propose an ensemble-based refinement of Hare’s (Analysis 70:237–247, 2010) prospectism criterion for rational choice when preferences are incomplete. Importantly, this ensemble-based refinement is immune to Peterson’s (Theory and Decision 78:451–456, 2015) weak money pump argument. Hence, ensemble prospectism ensures outcome rationality. Furthermore, by recognizing the structural isomorphism between mildly sweetened preference structures and Cover’s splitting rule in Blackwell’s Pick the Largest Number problem (Ann Math Stat 22:393–399, 1951), ensemble prospectism can be shown to yield better-than-even odds of selecting the ex-post higher utility option—despite the absence of all-things-considered preferences ex ante.     

Axiomatizing bounded rationality: the priority heuristic

This paper presents an axiomatic framework for the priority heuristic, a model of bounded rationality in Selten’s (in: Gigerenzer and Selten (eds.) Bounded rationality: the adaptive toolbox, 2001) spirit of using empirical evidence on heuristics. The priority heuristic predicts actual human choices between risky gambles well. It implies violations of expected utility theory such as common consequence effects, common ratio effects, the fourfold pattern of risk taking and the reflection effect. We present an axiomatization of a parameterized version of the heuristic which generalizes the heuristic in order to account for individual differences and inconsistencies. The axiomatization uses semiorders (Luce, Econometrica 24:178–191, 1956), which have an intransitive indifference part and a transitive strict preference component. The axiomatization suggests new testable predictions of the priority heuristic and makes it easier for theorists to study the relation between heuristics and other axiomatic theories such as cumulative prospect theory.