The Pareto Frontier for Random Mechanisms

TL;DR

This paper characterizes the Pareto frontier of random mechanisms balancing manipulability and performance measures like efficiency or fairness, providing algorithms to compute optimal trade-offs in voting settings.

Contribution

It introduces a structural characterization of the Pareto frontier for trade-offs in random mechanisms and develops algorithms to compute it.

Findings

The Pareto frontier can be explicitly characterized structurally.

Algorithms efficiently compute optimal trade-offs between manipulability and performance.

Results demonstrate the shape of the Pareto frontier in voting scenarios with multiple alternatives.

Abstract

We study the trade-offs between strategyproofness and other desiderata, such as efficiency or fairness, that often arise in the design of random ordinal mechanisms. We use approximate strategyproofness to define manipulability, a measure to quantify the incentive properties of non-strategyproof mechanisms, and we introduce the deficit, a measure to quantify the performance of mechanisms with respect to another desideratum. When this desideratum is incompatible with strategyproofness, mechanisms that trade off manipulability and deficit optimally form the Pareto frontier. Our main contribution is a structural characterization of this Pareto frontier, and we present algorithms that exploit this structure to compute it. To illustrate its shape, we apply our results for two different desiderata, namely Plurality and Veto scoring, in settings with 3 alternatives and up to 18 agents.