Nhan-Tam Nguyen

Fairness and Rank-Weighted Utilitarianism in Resource Allocation

In multiagent resource allocation with indivisible goods, boolean fairness criteria and optimization of inequality-reducing collective utility functions CUFs are orthogonal approaches to fairness. We investigate the question of whether the proposed scale of criteria by Bouveret and Lemaitrei¾?[5] applies to nonadditive utility functions and find that only the more demanding part of the scale remains intact for k-additive utility functions. In addition, we show that the min-max fair-share allocation existence problem is NP-hard and that under strict preferences competitive equilibrium from equal incomes does not coincide with envy-freeness and Pareto-optimality. Then we study the approximability of rank-weighted utilitarianism problems. In the special case of rank dictator functions the approximation problem is closely related to the MaxMin-Fairness problem: Approximation and/or hardness results would immediately transfer to the MaxMin-Fairness problem. For general inequality-reducing rank-weighted utilitarianism we show strong NP-completeness. Experimentally, we answer the question of how often maximizers of rank-weighted utilitarianism satisfy the max-min fair-share criterion, the weakest fairness criterion according to Bouveret and Lemaitres scale. For inequality-reducing weight vectors there is high compatibility. But even for weight vectors that do not imply inequality-reducing CUFs, the Hurwicz weight vectors, we find a high compatibility that decreases as the Hurwicz parameter decreases.

Positional scoring-based allocation of indivisible goods

We define a family of rules for dividing m indivisible goods among agents, parameterized by a scoring vector and a social welfare aggregation function. We assume that agents’ preferences over sets of goods are additive, but that the input is ordinal: each agent reports her preferences simply by ranking single goods. Similarly to positional scoring rules in voting, a scoring vector

radioActive WiFi Sharing for Autonomous Peers

s = (s_1, \ldots , s_m)

Scoring rules for the allocation of indivisible goods

s=(s1,…,sm) consists of m nonincreasing, nonnegative weights, where

Complexity and approximability of social welfare optimization in multiagent resource allocation

s_i

Approximate Solutions To Max-Min Fair and Proportionally Fair Allocations of Indivisible Goods

si is the score of a good assigned to an agent who ranks it in position i. The global score of an allocation for an agent is the sum of the scores of the goods assigned to her. The social welfare of an allocation is the aggregation of the scores of all agents, for some aggregation function