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

TLDR; Proportionality is an attractive fairness concept that has been applied to a range of problems including the facility location problem. 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 there is no deterministic strategyproof mechanism satisfying the property.