We generalize the classic problem of fairly allocating indivisible goods to the problem of fair public decision making, in which a decision must be made on several social issues simultaneously, and, unlike the classic se ing, a decision can provide positive utility to multiple players. We extend the popular fairness notion of proportionality (which is not guaranteeable) to our more general se ing, and introduce three novel relaxations proportionality up to one issue, round robin share, and pessimistic proportional share -that are also interesting in the classic goods allocation se ing. We show that the Maximum Nash Welfare solution, which is known to satisfy appealing fairness properties in the classic se ing, satis es or approximates all three relaxations in our framework. We also provide polynomial time algorithms and hardness results for nding allocations satisfying these axioms, with or without insisting on Pareto optimality. 1 at said, there is a recent line of work on implicit utilitarian voting that a empts to maximize an objective with respect to the cardinal utilities underlying the ordinal preferences [7, 29] , and is therefore closer to our work.
To address this problem, REF defined proportionality up to one issue in the public decision making framework, inspired by related notions for private goods.
Fair Public Decision Making
EC '17
Business Computer Science