Settling the Score: Portioning with Cardinal Preferences

TL;DR

This paper analyzes various rules for dividing a public resource among agents, showing that a simple averaging rule often best satisfies fairness and strategic properties in a novel setting.

Contribution

It introduces a comprehensive axiomatic analysis of resource partitioning rules, highlighting the effectiveness of the average proposal rule in fairness and strategic considerations.

Findings

The average rule satisfies many fairness and strategyproofness axioms.

The average rule outperforms other rules in fairness properties.

Two characterizations of the average rule are provided.

Abstract

We study a portioning setting in which a public resource such as time or money is to be divided among a given set of candidates, and each agent proposes a division of the resource. We consider two families of aggregation rules for this setting -- those based on coordinate-wise aggregation and those that optimize some notion of welfare -- as well as the recently proposed independent markets rule. We provide a detailed analysis of these rules from an axiomatic perspective, both for classic axioms, such as strategyproofness and Pareto optimality, and for novel axioms, some of which aim to capture proportionality in this setting. Our results indicate that a simple rule that computes the average of the proposals satisfies many of our axioms and fares better than all other considered rules in terms of fairness properties. We complement these results by presenting two characterizations of the average rule.