Power and Freedom in Mechanisms

TL;DR

This paper introduces a framework to measure agents' influence in strategy-proof mechanisms, distinguishing between their freedom to affect their own outcomes and their power over others, with applications to assignment rules.

Contribution

It generalizes existing concepts of opportunity and power, providing new characterizations of mechanisms like top trading cycles and bipolar serial dictatorships based on freedom and power.

Findings

Constrained efficient mechanisms maximize agents' freedom.

Top trading cycles rule is characterized by high freedom.

Bipolar serial dictatorships exhibit specific power and freedom properties.

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.