A Few Queries Go a Long Way: Information-Distortion Tradeoffs in Matching

TL;DR

This paper explores how limited cardinal information obtained through a small number of queries can significantly improve the efficiency of one-sided matching problems compared to using only ordinal preferences.

Contribution

It introduces a framework analyzing the tradeoff between the number of queries per agent and the resulting distortion in matching problems.

Findings

Limited queries lead to substantial reduction in distortion.

Partial cardinal information improves matching efficiency.

Tradeoff between query complexity and social welfare achieved.

Abstract

We consider the one-sided matching problem, where n agents have preferences over n items, and these preferences are induced by underlying cardinal valuation functions. The goal is to match every agent to a single item so as to maximize the social welfare. Most of the related literature, however, assumes that the values of the agents are not a priori known, and only access to the ordinal preferences of the agents over the items is provided. Consequently, this incomplete information leads to loss of efficiency, which is measured by the notion of distortion. In this paper, we further assume that the agents can answer a small number of queries, allowing us partial access to their values. We study the interplay between elicited cardinal information (measured by the number of queries per agent) and distortion for one-sided matching, as well as a wide range of well-studied related problems. Qualitatively, our results show that with a limited number of queries, it is possible to obtain significant improvements over the classic setting, where only access to ordinal information is given.