Risky Utility Research Articles

Chance theory: A separation of riskless and risky utility

In a temporal context, sure outcomes may yield higher utility than risky ones as they are available for the execution of plans before the resolution of uncertainty. By observing a disproportionate preference for certainty, empirical research points to a fundamental difference between riskless and risky utility. Chance Theory (CT) accounts for this difference and, in contrast to earlier approaches to separate risky and riskless utility, does not violate basic rationality principles like first-order stochastic dominance or transitivity. CT evaluates the lowest outcome of an act with the riskless utility v and the increments over that outcome, called chances, by subjective expected utility (EU) with a risky utility u. As a consequence of treating sure outcomes differently to risky ones, CT is able to explain the EU-paradoxes of Allais (Econometrica, 21(4): 503–546, 1953) that rely on the certainty effect, and also the critique to EU put forward by Rabin (Econometrica, 68(5): 1281–1292, 2000). Moreover, CT separates risk attitudes in the strong sense, captured entirely by u, from attitude towards wealth reflected solely through the curvature ofv.

Transforming Ordinal Riskless Utility into Cardinal Risky Utility: A Comment on Chung, Glimcher, and Tymula (2019)

Chung, Glimcher, and Tymula (2019) observed both consumers’ choices over commodity bundles and choices under risk. They assumed a cardinal riskless utility function V representing consumer choices and a cardinal risky utility function U.The two were inconsistent. This note shows that the two functions can be reconciled if we assume that V is ordinal. Then one utility function U can accommodate both risky and riskless choices. (JEL C91, D12, D81)

Effects of downstream entry in a supply chain with a spot market

This article contributes to research at the interface of marketing, operations, and risk management by investigating the effects of downstream entry in a two-echelon supply chain with risk-averse supply chain members and a liquid spot market for trading intermediate goods. We find that at downstream entry, the upstream supplier may decrease the contract price of the intermediate goods to balance its risk-free utility from the contract channel and its risky utility from the spot market; correspondingly, downstream manufacturers may increase their contract quantities. As a result, downstream entry may hurt the supplier and benefit the incumbent manufacturers. We also identify situations where downstream entry can lead to a “win-win-win” situation, where the supplier, incumbent manufacturers, and final product consumers all benefit from downstream entry. Furthermore, when spot price volatility is high, the supplier may engage in speculative trading, but downstream entry discourages this speculative behavior. We conclude that these results are driven by the combined effects of spot trading and the risk attitudes of supply chain members. Specifically, the effects of downstream entry are dramatically affected by the risk attitude of manufacturers, but only slightly affected by that of the supplier. Finally, we find that the main results hold when the supplier’s capacity level is endogenous.

Reconciling introspective utility with revealed preference: Experimental arguments based on prospect theory

In an experiment, choice-based (revealed-preference) utility of money is derived from choices under risk, and choiceless (non-revealed-preference) utility from introspective strength-of-preference judgments. The well-known inconsistencies of risky utility under expected utility are resolved under prospect theory, yielding one consistent cardinal utility index for risky choice. Remarkably, however, this cardinal index also agrees well with the choiceless utilities, suggesting a relation between a choice-based and a choiceless concept. Such a relation implies that introspective judgments can provide useful data for economics, and can reinforce the revealed-preference paradigm. This finding sheds new light on the classical debate on ordinal versus cardinal utility.

La réconciliation des mesures des préférences sur la santé dans le certain et dans le risque

Cet article étudie la possibilité de réconcilier l’utilité sur la santé dans le certain et dans le risque en interprétant cette dernière à l’aide des hypothèses de la théorie des perspectives de Kahneman et Tversky: la déformation subjective des probabilités et l’aversion pour les pertes. Il postule aussi que certains biais attribués à un comportement d’aversion pour les pertes peuvent être justifiés, de manière alternative, par le fait que les personnes interrogées ne sont pas certaines de leurs préférences. Ces hypothèses sont testées lors d’une étude de mesure des préférences sur trois états de santé hypothétiques. L’identité entre l’utilité certaine et risquée interprétée dans le cadre de la théorie des perspectives est obtenue pour deux des trois états de santé. Les résultats suggèrent que révéler les préférences à l’aide de choix réversibles peut éviter certains biais résultant de l’incertitude sur les préférences.

Deriving quality-adjusted life years (QALYs) from constant proportional time tradeoff and risk posture conditions

With foundations in decision theory, Quality-Adjusted Life Years (QALYs) are the most important measure of health outcome in medical decision making. Constant proportional time tradeoff (CP-TTO) is a condition on riskless value with empirical support in the QALY literature. The primary use of CP-TTO in previous axiomatizations of QALYs has been to guarantee that the utility of health state and survival duration is a power function of duration. We show that CP-TTO has other useful applications in QALY research. Under mild conditions CP-TTO implies an additive value function. Furthermore, CP-TTO can be combined with assumptions of risky utility to yield several different parametric QALY representations, including one that is inconsistent with utility independence. We find that CP-TTO simplifies axiomatizations of QALY representations in the sense that if CP-TTO is among the assumptions of a QALY axiomatization, other standard preference assumptions, e.g., double cancellation or utility independence, become redundant and can be dropped from the axiom system. This can be desirable if it allows one to drop from the axiomatization an assumption that is practically difficult to test, e.g., double cancellation.

Determinants of risk-taking: Behavioral and economic views

The concept of risk-taking is examined from various perspectives: economic, decision theoretic, and psychological. Multiple factors are discussed as complicating the extraction of any presumed risk-taking propensity from a person's real-world behavior.Problem structuring, beliefs, andvalues (defined here as riskless as opposed to risky utility) may of course underlie differences in risk behavior. In addition,context andprocess factors can induce variance in risk-bearing. Also,portfolio effects (including cross-sectional, multiattribute, and longitudinal) may greatly complicate the measurement of risk-taking propensity. Lastly, the presence of incompletemarkets (via which risks can be partially diversified and traded) may further mask the link between intrinsic and observed risk-taking. This article examines each of these measurement obstacles and sources of variance.

Group Preference Aggregation Rules Based on Strength of Preference

In many decision problems, the consequences of an action may impact several individuals, and the decision may be based on the preferences of those who are affected. The rule for aggregating these individual preferences is called a group preference aggregation rule. In this paper we present a theory for group preference aggregation rules based on the concept of strength of preference. This concept is operationalized by asking an individual to order differences in his strength of preference between pairs of alternatives. A preference representation function that reproduces this ordering is called a measurable value function. In general we cannot expect a measurable value function and a utility function obtained from lottery questions to bear any particular relation to each other. A group preference aggregation rule based on the measurable value functions of individuals can be used under conditions of certainty without introducing lotteries into the preference assessment procedure. In addition, it facilitates the difficult problem of making interpersonal utility comparisons. We also establish several relationships between the group preference aggregation rules based on measurable value functions and previous work based on risky utility functions. These relationships allow either one of these preference aggregation rules to be transformed into the other after obtaining only a minimal amount of information from a group member. These relationships also raise several fundamental questions about the effects of the introduction of risk on the preferences of an individual and on the preferences of a group. We offer some preliminary comments and results regarding these issues.

Multidimensional utility models for risky and riskless choice

Subjects evaluated 27 hypothetical job offers using both riskless rating scale and risky utility response modes. These preference judgments were then analyzed using both statistical and conjoint measurement procedures. Additive statistical models provided excellent approximations to both the riskless and risky responses of every subject. Nonetheless, half of the subjects showed statistically significant, and in some cases, substantial departures from additivity. Despite the predictive success of the additive and multiplicative models studied, the conjoint measurement analysis revealed that several subjects substantially violated the ordinal properties shared by both additive and multiplicative models. In addition, all subjects showed some minor violations of the conjoint measurement axioms. A simple numerical analysis showed, however, that most of these minor violations may have been due to random error.