An impossibility theorem concerning positive involvement in voting

2024-01-11

Economics Letters

AI Summary

This paper addresses the feasibility of the *positive participation* axiom—requiring that adding support for a candidate should never cause that candidate to lose—in social choice theory. Using axiomatic analysis and ordinal preference modeling, we construct rigorous counterexamples demonstrating an irreconcilable conflict between positive participation and several foundational democratic principles. Specifically, we prove that no voting rule can simultaneously satisfy positive participation, non-dictatorship, no-veto-power, the Condorcet winner and loser criteria, resolvability, and majority-margin ranking invariance. This constitutes a novel impossibility theorem, challenging the intuitive appeal of participation axioms and establishing a fundamental theoretical boundary for voting mechanism design. The result underscores the inherent trade-offs embedded in democratic aggregation procedures.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Decision/Utility Theory

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Problem

• Proves no ordinal voting method satisfies positive involvement
• Shows incompatibility with Condorcet winner and loser criteria
• Demonstrates conflict with resolvability and invariance properties

Innovation

• Proves impossibility theorem for voting methods
• Links positive involvement to Condorcet criteria
• Analyzes ordinal preferences and majority margins