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Making Serial Dictatorships Fair

Adam Hamdan

Abstract

In priority-based matching, serial dictatorship (SD) is simple, strategyproof, and Pareto efficient, but not free of justified envy (i.e. fair). This paper studies how to fairly order agents in SD as a function of their priorities. I show that if preferences are identical across agents and uniformly distributed, and objects have unit capacities, the serial order that minimizes the expected number of justified envy cases is the Kemeny ranking of agents' priorities. If any of these assumptions -- identical preferences, uniformly distributed preferences, or unit capacities -- is relaxed, the optimal SD follows a weighted Kemeny ranking. Broadly, these results demonstrate how insights from social choice theory can inform the design of practical matching mechanisms.

Making Serial Dictatorships Fair

Abstract

In priority-based matching, serial dictatorship (SD) is simple, strategyproof, and Pareto efficient, but not free of justified envy (i.e. fair). This paper studies how to fairly order agents in SD as a function of their priorities. I show that if preferences are identical across agents and uniformly distributed, and objects have unit capacities, the serial order that minimizes the expected number of justified envy cases is the Kemeny ranking of agents' priorities. If any of these assumptions -- identical preferences, uniformly distributed preferences, or unit capacities -- is relaxed, the optimal SD follows a weighted Kemeny ranking. Broadly, these results demonstrate how insights from social choice theory can inform the design of practical matching mechanisms.
Paper Structure (6 sections, 4 theorems, 15 equations)

This paper contains 6 sections, 4 theorems, 15 equations.

Table of Contents

  1. Introduction
  2. Model
  3. Examples
  4. Results
  5. Conclusion
  6. Appendix

Key Result

Theorem 1

If preferences are identical across agents and uniformly distributed, the serial order that minimizes the expected number of justified envy cases is the Kemeny ranking of agents' priorities.

Theorems & Definitions (10)

  • Example 1: Priority Dominance
  • Example 2: Unknown Preferences
  • Theorem 1
  • proof
  • Proposition 1
  • Proposition 2
  • Proposition 3
  • Remark 1
  • proof
  • proof