Random Rank: The One and Only Strategyproof and Proportionally Fair Randomized Facility Location MechanismDownload PDF

Published: 31 Oct 2022, 18:00, Last Modified: 12 Oct 2022, 12:36NeurIPS 2022 AcceptReaders: Everyone
Keywords: Facility location, Randomized Social Choice, Fairness in Collective Decision Problems, Voting
TL;DR: We find a unique characterization of randomized mechanisms which satisfy truthfulness, anonymity and proportional fairness.
Abstract: Proportionality is an attractive fairness concept that has been applied to a range of problems including the facility location problem, a classic problem in social choice. In our work, we propose a concept called Strong Proportionality, which ensures that when there are two groups of agents at different locations, both groups incur the same total cost. We show that although Strong Proportionality is a well-motivated and basic axiom, there is no deterministic strategyproof mechanism satisfying the property. We then identify a randomized mechanism called Random Rank (which uniformly selects a number $k$ between $1$ to $n$ and locates the facility at the $k$'th highest agent location) which satisfies Strong Proportionality in expectation. Our main theorem characterizes Random Rank as the unique mechanism that achieves universal truthfulness, universal anonymity, and Strong Proportionality in expectation among all randomized mechanisms. Finally, we show via the AverageOrRandomRank mechanism that even stronger ex-post fairness guarantees can be achieved by weakening universal truthfulness to strategyproofness in expectation.
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