DP18958 Ordinal Simplicity and Auditability in Discrete Mechanism Design
Designing mechanisms for environments without transfers, market designers usually restrict attention to ordinal mechanisms. Ordinal mechanisms are simpler for both designers and participants but miss potentially welfare-relevant information. Under what conditions focusing on ordinal mechanisms is without loss? We show that, in general, all group strategy-proof mechanisms are ordinal. All mechanisms maximizing an Arrovian social welfare function are ordinal; in a large class of environments, such Arrovian efficiency is implied by Pareto efficiency and a simple auditability condition. Strategy-proof mechanisms that are simple to audit are also ordinal. As applications, we characterize important classes of mechanisms in public choice as well as single-unit-demand and multiple-unit-demand allocation of private goods.
