Strategyproof Linear Regression in High Dimensions

TL;DR

This paper introduces a family of group strategyproof linear regression mechanisms for high-dimensional data, ensuring truthful responses from agents with single-peaked preferences, by leveraging a connection to the Ham Sandwich Theorem.

Contribution

It presents generalized resistant hyperplane mechanisms that are group strategyproof in any number of dimensions, extending previous two-dimensional results.

Findings

Existence of group strategyproof mechanisms in high dimensions

Connection established between mechanism properties and the Ham Sandwich Theorem

Mechanisms ensure truthful responses from agents with single-peaked preferences

Abstract

This paper is part of an emerging line of work at the intersection of machine learning and mechanism design, which aims to avoid noise in training data by correctly aligning the incentives of data sources. Specifically, we focus on the ubiquitous problem of linear regression, where strategyproof mechanisms have previously been identified in two dimensions. In our setting, agents have single-peaked preferences and can manipulate only their response variables. Our main contribution is the discovery of a family of group strategyproof linear regression mechanisms in any number of dimensions, which we call generalized resistant hyperplane mechanisms. The game-theoretic properties of these mechanisms -- and, in fact, their very existence -- are established through a connection to a discrete version of the Ham Sandwich Theorem.