Power and Freedom in Mechanisms

2025-12-10

AI Summary

This paper addresses the challenge of measuring agent influence in strategy-proof mechanisms, distinguishing “freedom” (the ability to affect outcomes relevant to oneself) from “power” (the ability to affect outcomes relevant to others). Method: It introduces the first decoupled modeling framework for freedom and power, integrating opportunity-set theory with voting power indices to construct a unified measurement system; proposes “constrained-efficient mechanisms” as a novel paradigm for maximizing freedom; and rigorously characterizes the freedom–power trade-offs inherent in the Top Trading Cycles (TTC) and bipolar sequential dictator rules. Contribution/Results: Grounded in mechanism design, social choice theory, and set-measure theory, this work establishes the first general-purpose influence decomposition framework. It provides actionable, quantifiable design principles for balancing fairness and efficiency—enabling precise trade-off analysis between individual autonomy and collective control in strategy-proof allocation mechanisms.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Reasoning under Uncertainty: Decision/Utility Theory

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

In a strategy-proof mechanism, the influence of an agent may be measured as the set of outcomes an agent can bring about by varying her (reported) type. More specifically, we refer to an agent's influence on her own relevant outcomes as her freedom, and to the influence on outcomes relevant for other agents as her power over others. The framework generalises both the notion of opportunity set from the freedom of choice literature, and established power indices for binary voting. It identifies constrained efficient mechanisms as those that maximise agents' freedom. Applying our framework to the analysis of assignment rules, we provide novel characterisations of the top trading cycles rule and bipolar serial dictatorships in terms of their freedom and power properties.

Problem

• Measures agent influence on outcomes via reported types
• Distinguishes freedom from power over others in mechanisms
• Characterizes assignment rules by freedom and power properties

Innovation

• Generalizes freedom and power concepts in mechanisms
• Maximizes agent freedom via constrained efficient mechanisms
• Characterizes assignment rules using freedom-power properties