Networks, Polarization, and Voting: Models for Information Aggregation in Social Settings

Abstract

Social networks, voting, and polarization all fall into the realm of the instrument, process, and consequence of information aggregation in social settings. These are both classical topics that have motivated studies from various disciplines, and active areas in need of new models as novel phenomenon, demand, and proposals continue to emerge in recent years. In this thesis, we study three models for social information aggregation inspired by these three topics respectively.

In the first chapter, we consider how to detect corruption when each network nodes’ true identities are only locally known. In this model, each vertex reports about the types - truthful or corrupt - of its neighbors, where truthful nodes report the true types and corrupt nodes report adversarially. We show that detecting corruption in this model yields linear-time algorithm while the minimal number of nodes the corrupt party needs to control in order to hide all corruption is hard to approximate to any multiplicative factor, assuming the Small Set Expansion Hypothesis.

In the second chapter, we propose a geometric opinion dynamic model where a strong form of polarization in high-dimension emerges: public opinions not only radicalize on each issue, but also correlate across issues. We demonstrate that this type of polarization could arise as an unintended byproduct of influencers’ natural effort to promote a product or an idea. We analyze this mechanism with one or more influencers, sending messages strategically, heuristically, or randomly, and examine the computational aspects of optimal influencing strategy and its effect on polarization.

The third chapter considers whether distributed election procedure can aggregate to good social choice outcomes when voters delegate strategically. We model liquid democracy as a game where voters with continuous-valued preference peaks choose between delegation and learning about policies at a cost and voting directly. We derive the pure-strategy coalition-proof Nash equilibrium and show that equilibrium delegation network varies with learning cost. When cost is low, all voters delegate to the median is a cpNE. As learning cost increases, new forms of cpNE emerge, where extreme voters delegate inward and moderate voters delegate outward to the nearest incentized voters.