Aggregating Preferences over Lotteries in the Absence of Expected Utility
Mathematics
Final Report Abstract
Aggregating the preferences of multiple agents over various social alternatives into a collective preference relation is a basic economic problem. In cases of interest, randomizations over alternatives, called lotteries, frequently also qualify as outcomes. This project set out to improve our theoretical understanding of how to aggregate preferences over lotteries. It intentionally departed from much of the previous work on this problem by not assuming that preferences over lotteries are based on expected utility maximization. This is motivated by experimental results that suggest that real-world agents frequently do not behave like expected utility maximizers as witnessed by the Allais Paradox (Allais, 1953) and the preference reversal phenomenon (Grether and Plott, 1979) for instance. The main tool was axiomatic analysis. That is, one formulates desirable properties of aggregation methods mathematically and then studies which aggregation methods satisfy those. The findings comprise three parts. First, we studied preference aggregation for convex preferences over lotteries, which constitute a much larger class than expected utility preferences. The main result characterizes a unique aggregation method by the axioms in Arrow’s seminal impossibility theorem (Arrow, 1951). In particular, Arrow’s theorem ceases to hold for interesting domains of convex preferences. This work appeared in Econometrica, one of the most prestigious journals for economic research. Second, we studied preference aggregation under uncertainty, where outcomes are not lotteries but uncertain acts. In contrast to lotteries which specify objective probabilities for alternatives, agents may disagree on the probability that an uncertain act yields a specific alternative. We considered preferences over acts that maximize subjective expected utility as introduced by Savage (1954) and characterized the aggregation method that averages the agents’ probability assessments and sums up their utility functions. Preference aggregation under uncertainty was not originally planned as a part of the project but turned out to be interesting as well as fruitful. Third, the aggregation method associates with every profile of individual preferences a set of lotteries by choosing the lotteries that are maximal for the corresponding collective preferences. We studied various axiomatic properties of these lotteries with analytical tools and by running extensive computer simulations. Moreover, we showed that they arise from a simple procedure for collective decisionmaking, which has analogs in physics, biology, and chemistry.
Publications
- Arrovian aggregation of convex preferences. Econometrica, 88 (2):799–844, 2020
F. Brandl and F. Brandt
(See online at https://doi.org/10.3982/ECTA15749) - Belief-averaging and relative utilitarianism: Savage meets Arrow. 2020
F. Brandl
- A natural adaptive process for collective decision-making. 2021
F. Brandl and F. Brandt
