2026 Theses Doctoral

Essays on Decisions Under Risk

Zhang, Hanyao

This dissertation studies the topic of decision making under risk from three main perspectives: (1) The roles played by preferences, complexity, and mistakes in shaping observed decisions; (2) How to robustly identify preferences from observed decisions; and (3) The decision making procedures underlying observed decisions. The dissertation studies these questions by developing new experimental and analytical methods.

In Chapter 1, I study the procedural aspects of decision making under risk by introducing a novel experimental design tracking experimental subjects’ calculations when valuing lotteries. The calculations predominantly fall into three groups: expected values, linear functions of monetary outcomes, or those unmatched to lottery primitives. Calculations exhibit remarkable within-subject stability alongside substantial between-subject heterogeneity. Calculations strongly predict valuations: subjects performing expected values-related calculations display near risk-neutrality, while on average, other subjects’ valuations display extreme unresponsiveness to changes in probabilities. An analysis by calculation group reveals distinct behavioral mechanisms driving behaviors: adoption of expected-value calculations is consistent with the reductions in implementation costs from the provided calculator, while the linear functions of monetary outcomes are consistent with the theory of attribute substitution (Kahneman and Frederick, 2002).

In Chapter 2, I turn to the statistical aspects of decision making under risk by decomposing the observed decisions into preferences and mistakes. Risk preferences recovered from lottery valuation data are not robust to unverifiable assumptions about the structure of mistakes in the valuations. To address this, I develop a novel approach utilizing Oprea’s (2024b) deterministic mirrors – deterministic payments that preserve key structural features of lotteries. I estimate the mistake structure in deterministic mirrors – where certain payments enable identification of mistake patterns – through a mixture model incorporating two types of mistakes frequently observed, then apply these estimates to correct lottery valuations. The corrected valuations are closer to risk neutrality than raw valuations; when they deviate from risk neutrality, they are predominantly risk averse. The corrected valuations are more aligned with expected utility theory, in contrast to the raw valuations which exhibit strong probability weighting. Our approach offers a generalizable framework for preference recovery: researchers can use auxiliary tasks with known correct answers to discipline assumptions about mistakes.

In Chapter 3, joint with Mark Dean, we revisit the debate between Oprea (2024b) on the one side, and Banki et al. (2025) and Wu (2025) on the other side, over whether the apparent fourfold pattern (FFP) of risk in mirrors, documented in Oprea (2024b), reflects complexity or confusion. In response to Oprea, Wu (2025) makes several changes from the experimental design of Oprea aimed at reducing confusion. Wu reports an absence of FFP in mirrors, and interprets this as evidence against Oprea’s interpretation of his data. In this Chapter, we present results from a new set of experiments that suggest that this is not the case. Building off the experiments of Wu, which were designed to eliminate these sources of confusion, we find robust evidence for the four fold pattern for mirrors. The difference in results is instead be driven by two other sources. First, the choices in Wu are designed to be symmetric around the expected value of the lottery, meaning that ‘trembling hand’ errors do not contribute to the four fold pattern. It turns out this channel is important. Second, the training regime of Wu appears to teach subjects how to calculate expected values, rather than simply removing confusion.