TL;DR
This paper explores how to order agents fairly in serial dictatorship matching by using social choice theory, specifically Kemeny rankings, to minimize justified envy under various assumptions.
Contribution
It introduces a method to determine the optimal agent ordering in serial dictatorship to reduce envy, based on Kemeny rankings and their weighted variants.
Findings
Kemeny ranking minimizes envy under identical, uniformly distributed preferences with unit capacities.
Weighted Kemeny rankings are optimal when preferences are not identical or capacities vary.
Insights connect social choice theory with practical matching mechanism design.
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.
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Taxonomy
TopicsGame Theory and Voting Systems · Auction Theory and Applications · Experimental Behavioral Economics Studies