Settling the Score: Portioning with Cardinal Preferences
Edith Elkind, Matthias Greger, Patrick Lederer, Warut Suksompong, Nicholas Teh
TL;DR
This work analyzes how to allocate a homogeneous resource among multiple candidates when each agent reports a cardinal ideal distribution, modeling disutility via the $L_1$ distance. It surveys coordinate-wise, welfare-based, and independent-markets rules, and evaluates them under axioms for efficiency, fairness, consistency, and incentives, including novel notions like score-unanimity and score-representation. The key finding is that the simple Avg rule—taking the average of all proposals—satisfies many fairness and independence properties (notably score-representation and independence) and admits two characterizations within broad rule classes, though it sacrifices strategyproofness and Pareto optimality. The analysis highlights trade-offs among fairness, consistency, and incentive properties, and points to future work on core membership and approximations of Avg’s desirable axioms in more complex settings.
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.