Strategyproof and Proportionally Fair Facility Location
Haris Aziz, Alexander Lam, Barton E. Lee, Toby Walsh

TL;DR
This paper investigates strategyproof and proportionally fair mechanisms for a one-dimensional facility location problem, characterizing their properties, uniqueness, and approximation guarantees for social welfare and costs.
Contribution
It introduces a hierarchy of fairness axioms, characterizes strategyproof mechanisms satisfying these axioms, and identifies the unique Uniform Phantom mechanism with optimal approximation guarantees.
Findings
Many fairness axioms become equivalent under strategyproofness.
The Uniform Phantom mechanism is unique and strategyproof, satisfying multiple fairness axioms.
It achieves the best approximation of social welfare among strategyproof, fair mechanisms.
Abstract
We focus on a simple, one-dimensional collective decision problem (often referred to as the facility location problem) and explore issues of strategyproofness and proportionality-based fairness. We introduce and analyze a hierarchy of proportionality-based fairness axioms of varying strength: Individual Fair Share (IFS), Unanimous Fair Share (UFS), Proportionality (as in Freeman et al, 2021), and Proportional Fairness (PF). For each axiom, we characterize the family of mechanisms that satisfy the axiom and strategyproofness. We show that imposing strategyproofness renders many of the axioms to be equivalent: the family of mechanisms that satisfy proportionality, unanimity, and strategyproofness is equivalent to the family of mechanisms that satisfy UFS and strategyproofness, which, in turn, is equivalent to the family of mechanisms that satisfy PF and strategyproofness. Furthermore,…
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Taxonomy
TopicsGame Theory and Voting Systems · Experimental Behavioral Economics Studies · Auction Theory and Applications
