Fair Public Decision Making

Abstract

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 setting, 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 setting, 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 setting. We show that the Maximum Nash Welfare solution, which is known to satisfy appealing fairness properties in the classic setting, satisfies or approximates all three relaxations in our framework. We also provide polynomial time algorithms and hardness results for finding allocations satisfying these axioms, with or without insisting on Pareto optimality.

Fair Allocation of Indivisible Public Goods

“…In particular, for the public decision making framework, the private goods setting, and multiwinner elections (a.k.a. Knapsack with unit sizes), there is an outcome whose guarantee for every coalition is close to the guarantee that Conitzer et al provide to individual agents [10].…”

“…We consider a fairly broad model for public goods allocation that generalizes much of previous work [24,10,11,3,12,9,30]. There is a set of voters (or agents) N = [n].…”

“…To address this issue, [10] introduced the novel relaxation of proportionality up to one issue in their public decision making framework, inspired by a similar relaxation called envy-freeness up to one good in the private goods setting [24,9]. They say that an outcome c of a public decision making problem satisfies proportionality up to one issue if for all agents i ∈ N , there exists an outcome c ′ that differs from c only on a single issue and u i (c ′ ) ≥ P rop i .…”

“…In fact, it may produce an outcome that may be construed as unfair if it does not reflect the wishes of large groups of voters. Thus, in this work, we address the following question posed by [10]:…”

On the Proximity of Markets with Integral Equilibria

“…A well-studied solution concept in this line of work is envy-freeness up to one good [Bud11]: an (integral) allocation is said to be envy-free up to one good (EF1) iff each agent prefers its own bundle over the bundle of any other agent up to the removal of one good. Along the lines of EF1, a surrogate of proportionalitycalled proportionality up to one good-has also been considered in prior work [CFS17]. In particular, an allocation is said to be proportional up to one good (PROP1) iff each agent receives its proportional share after the inclusion of one extra good in its bundle.…”