Po Hyun Sung

Working Papers

• Comparative Risk Attitudes in Stochastic Choice [PDF] 

(with Ben Wincelberg) 

Abstract:  Under the CARA and CRRA utility families, Fechnerian models of stochastic choice---a non-parametric class that includes the logit and probit models---are known to suffer from the paradoxical property that a more risk-averse individual is often predicted to choose a riskier lottery more frequently. We show that the paradox persists under broad generalizations: when noise is non-Fechnerian, differs arbitrarily across individuals, and even varies across menus. Paradoxical predictions arise under empirically relevant coefficients of risk aversion and lotteries, revealing that, even theoretically, parameter estimates depend on the observed lottery comparisons. We establish that two utility functions will produce paradoxical reversals whenever the ratio of their second derivatives is unbounded. Using this characterization, we propose a number of parametric utility families that do not suffer from this condition, offering well-behaved alternatives to CARA and CRRA for stochastic choice.

• Monotonicity and Bracketing in Games [arXiv] 

(with Fedor Sandomirskiy, Omer Tamuz, and Ben Wincelberg)

Revise and resubmit, Journal of Political Economy

Abstract: We study solution concepts for normal-form games. We obtain a characterization of Nash equilibria and logit quantal response equilibria, as well as generalizations capturing non-expected utility. Our axioms reflect that players are responsive to payoffs induced by the play of others and, whenever several games are played simultaneously, players may consider each separately.

• Independence of Irrelevant Decisions in Stochastic Choice [arXiv] 

(with Fedor Sandomirskiy, Omer Tamuz, and Ben Wincelberg)

Reject and resubmit, American Economic Review

Abstract: We investigate stochasticity in choice behavior across diverse decisions. Each decision is modeled as a menu of actions with associated outcomes, and a stochastic choice rule assigns probabilities to actions based on the outcome profile. We characterize rules whose predictions are not affected by whether or not additional, irrelevant decisions are included in the model. Our main result is that such rules form the parametric family of mixed-logit rules.

• Connecting Ellsberg and Allais Paradoxes [PDF]

(with Jack Adeney, Charles Sprenger, and Yu-Hsiang Wang)

Abstract: This manuscript identifies a largely unrecognized connection between, and distinction in results for,  Ellsberg's three-color paradox and Allais' common-consequence paradox. Both phenomena derive from reducing a common state payment to zero, but the reactions to this reduction are directionally opposed across the two problems. Using a common experimental framework, we develop intermediate tasks to identify the source of this difference. Key to the difference is the reversal of Allais' common consequence paradox when problem parameters are made more similar to those for Ellsberg.

• Stochastically Ordered Random Utilities

(with Ben Wincelberg)

Draft coming soon!

Abstract: We study the FOSD independent random utility (FIRU) model, in which random utilities are independent and ranked by first-order dominance. This model generalizes the widely used i.i.d. noise model, which includes logit and probit. We provide necessary conditions on binary choice data for it to be rationalized by the FIRU model. When there are three alternatives, these restrictions are sufficient to characterize the model. In this case, the set of binary choice data rationalized by the FIRU model is convex. Thus, the restrictions of the FIRU model extend to the i.i.d. mixture noise model, which includes mixed logit. 

• Measuring Economic Preferences in the Presence of Noise: The Connections Between Choices and Valuations

(with Ted O'Donoghue, Charles Sprenger, and Ben Wincelberg)

Draft coming soon!

Abstract:   The measurement of economic preferences is an essential research objective for experimental economics, yet the literature lacks consensus for which measurement tools to deploy. Prima-facie differences in measurements derived from two principal tools—binary choice and valuation tasks—have led researchers to argue for specific techniques on intuitive grounds, or question the stability of preferences central to utility theory. We theoretically examine the connections between choices and valuations assuming stable preferences, but recognizing that measurements are noisy. Even under strict assumptions for the symmetry of noise and preference heterogeneity, stable preferences do not generally imply identical measurements unless choice and valuation noise are identically distributed, calling into question the standard inference drawn from failures of  "calibration" across the two. Importantly, however, our results state conditions under which  calibration should obtain: when choice experiments are conducted at the mean preference. This testable prediction is evaluated in a dataset that combines the data from McGranaghan et al (2024a) and McGranaghan et al (2024b). This combined dataset consists of 424 paired choice and valuation lottery experiments comprising 68,448 observations. Though these experiments overwhelmingly show patterns associated with inconsistency—individuals are systematically more likely to choose safer options than their valuations imply—calibration largely holds at estimates of the mean preference; an indication of stable preferences once one accounts for noise. The techniques we develop also shed light on how to more credibly identify calibration failures, providing tools for future assessments of preference measures.