On proportionality in multi-issue problems with crossed claims

TL;DR

This paper extends the concept of proportionality to multi-issue resource allocation problems with crossed claims, introducing a new rule and providing an axiomatic characterization.

Contribution

It introduces the constrained proportional awards rule for complex multi-issue allocations and characterizes it axiomatically.

Findings

The constrained proportional awards rule generalizes classical proportionality.

Axiomatic characterization of the new rule is provided.

The rule effectively handles crossed claims in divisible resource allocation.

Abstract

In this paper, we analyze the problem of how to adapt the concept of proportionality to situations where several perfectly divisible resources have to be allocated among certain set of agents that have exactly one claim which is used for all resources. In particular, we introduce the constrained proportional awards rule, which extend the classical proportional rule to these situations. Moreover, we provide an axiomatic characterization of this rule.