Essays on Social Learning and Social Choice

Citation

Hann-Caruthers, Wade Daniel (2023) Essays on Social Learning and Social Choice. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/4v8h-z740. https://resolver.caltech.edu/CaltechTHESIS:06012023-000259864

Abstract

This dissertation contains three essays, two which contribute to the study of social learning (Chapters 1 and 2) and one which contributes to the study of social choice (Chapter 3).

In Chapter 1, I introduce a fully rational model of social learning on networks with endogenous action timing. I show that the structure of the network can play an important role in the aggregation of information. When the social network contains high-degree vertices, agents can be arbitrarily likely to make good choices. In contrast, when the social network is linear, there is a bound on how likely agents are to make good choices which holds regardless of how patient they are. The main contribution of this chapter is the identification of a novel mechanism through which strategic behavior can substantially impede the flow of information through a social network.

In Chapter 2, co-authored with Vadim Martynov and Omer Tamuz, we study the asymptotic rate at which the probability of taking the correct action converges to 1 in the classical sequential learning model with unbounded signals. We provide a characterization of the asymptotic law of motion of the public belief, and we use this characterization to show that convergence occurs more slowly than when agents directly observe private signals, and that the expected time until the last incorrect action can be finite or infinite.

In Chapter 3, co-authored with Laurent Bartholdi, Maya Josyula, Omer Tamuz, and Leeat Yariv, we introduce equitability as a less stringent alternative to symmetry for modeling egalitarianism in voting rules. We then use techniques from group theory to show that equitable voting rules can have minimal winning coalitions comprising a vanishing fraction of the population, but they cannot be smaller than the square root of the population size.

Thesis Files