Aggregating Information and Preferences with Bounded-Size Deviations

2025-05-15

AI Summary

This paper studies voting games under unobservable ground truth with two heterogeneous voter types: a majority whose preferences align with the truth, and a minority whose preferences systematically deviate. Focusing on bounded cooperation—where coalition size is capped at $k$—we introduce the *prior Bayesian $k$-strong equilibrium* to characterize equilibrium existence and its ability to guarantee majority-preferred outcomes. Theoretically, we establish, for the first time, a precise nonlinear piecewise boundary delineating the equilibrium existence region in terms of majority size and coalition capacity $k$, thereby overcoming classical assumptions of full rationality or unlimited coalition formation. Empirically, our framework captures intricate strategic interactions and fully identifies the parameter region ensuring stable realization of majority-preferred outcomes—revealing counterintuitive non-monotonicities along certain boundaries.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Social Networks and Social Media: Media and governance, opinion dynamics, filter bubbles, polarization
• Security and Privacy: Privacy-enhancing technologies

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.

Problem

• Analyzing voting scenarios with majority-minority preference conflicts
• Characterizing equilibrium conditions for coalition formation in voting games
• Exploring non-linear relationships between majority size and deviation capacity

Innovation

• Ex-ante Bayesian k-strong equilibrium analysis
• Majority-minority preference alignment with truth
• Non-linear majority-deviation capacity relationship