Axiomatic Characterizations of Draft Rules

TL;DR

This paper characterizes draft rules as allocation procedures that satisfy priority respect, envy-freeness up to one object, non-wastefulness, and resource monotonicity, highlighting their properties and limitations.

Contribution

It provides a simple axiomatic characterization of draft rules and explores their strategic properties and limitations under various conditions.

Findings

Draft rules are uniquely characterized by RP, EF1, NW, and RM.

Draft rules satisfy maxmin strategy-proofness.

Impossibility results show RP and EF1 are incompatible with strategy-proofness.

Abstract

Drafts are sequential round-robin allocation procedures for distributing heterogeneous and indivisible objects among agents subject to some priority order (e.g., allocating players' contract rights to teams in professional sports leagues). Agents report ordinal preferences over objects and bundles are partially ordered by pairwise comparison. We provide a simple characterization of draft rules: they are the only allocation rules that are respectful of a priority (RP), envy-free up to one object (EF1), non-wasteful (NW), and resource monotonic (RM). RP and EF1 are crucial for competitive balance in sports leagues. We also prove two related impossibility theorems showing that the competitive-balance axioms RP and EF1 are generally incompatible with strategy-proofness. Nevertheless, draft rules satisfy maxmin strategy-proofness. If agents may declare some objects unacceptable, then draft rules are characterized by RP, EF1, NW, and RM, in conjunction with individual rationality and truncation invariance.