Optimal Budget Aggregation with Single-Peaked Preferences
CoRR(2024)
摘要
We study the problem of aggregating distributions, such as budget proposals,
into a collective distribution. An ideal aggregation mechanism would be Pareto
efficient, strategyproof, and fair. Most previous work assumes that agents
evaluate budgets according to the ℓ_1 distance to their ideal budget. We
investigate and compare different models from the larger class of star-shaped
utility functions - a multi-dimensional generalization of single-peaked
preferences. For the case of two alternatives, we extend existing results by
proving that under very general assumptions, the uniform phantom mechanism is
the only strategyproof mechanism that satisfies proportionality - a minimal
notion of fairness introduced by Freeman et al. (2021). Moving to the case of
more than two alternatives, we establish sweeping impossibilities for ℓ_1
and ℓ_∞ disutilities: no mechanism satisfies efficiency,
strategyproofness, and proportionality. We then propose a new kind of
star-shaped utilities based on evaluating budgets by the ratios of shares
between a given budget and an ideal budget. For these utilities, efficiency,
strategyproofness, and fairness become compatible. In particular, we prove that
the mechanism that maximizes the Nash product of individual utilities is
characterized by group-strategyproofness and a core-based fairness condition.
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