Aggregating Information and Preferences with Bounded-Size Deviations

TL;DR

This paper analyzes strategic voting with coalition limits, characterizing when the majority's preferred outcome is stable under Bayesian equilibrium, revealing complex relationships between coalition size and majority influence.

Contribution

It provides a complete characterization of equilibrium regions in a voting model with coalition size constraints and introduces the ex-ante Bayesian $k$-strong equilibrium concept.

Findings

Stable majority outcomes depend on coalition size and majority strength.

The equilibrium region boundary shows non-linear relationships.

Results highlight the strategic complexity in coalition-based voting.

Abstract

We investigate a voting scenario with two groups of agents whose preferences depend on a ground truth that cannot be directly observed. The majority's preferences align with the ground truth, while the minorities disagree. Focusing on strategic behavior, we analyze situations where agents can form coalitions up to a certain capacity and adopt the concept of ex-ante Bayesian $k$-strong equilibrium, in which no group of at most $k$ agents has an incentive to deviate. Our analysis provides a complete characterization of the region where equilibria exist and yield the majority-preferred outcome when the ground truth is common knowledge. This region is defined by two key parameters: the size of the majority group and the maximum coalition capacity. When agents cannot coordinate beyond a certain threshold determined by these parameters, a stable outcome supporting the informed majority emerges. The boundary of this region exhibits several distinct segments, notably including a surprising non-linear relationship between majority size and deviation capacity. Our results reveal the complexity of the strategic behaviors in this type of voting game, which in turn demonstrate the capability of the ex-ante Bayesian $k$-strong equilibrium to provide a more detailed analysis.