Models of Manipulation on Aggregation of Binary Evaluations

TL;DR

This paper explores the problem of aggregating binary evaluations in societal decision-making, analyzing strategy-proofness under various definitions and the feasibility of designing anonymous, strategy-proof aggregation rules.

Contribution

It introduces three natural definitions of strategy-proofness and examines the possibility of creating anonymous, strategy-proof aggregation rules within this framework.

Findings

Multiple definitions of strategy-proofness are considered.

Feasibility of anonymous, strategy-proof rules is analyzed.

The framework models various aggregation scenarios like preference and judgment aggregation.

Abstract

We study a general aggregation problem in which a society has to determine its position on each of several issues, based on the positions of the members of the society on those issues. There is a prescribed set of feasible evaluations, i.e., permissible combinations of positions on the issues. Among other things, this framework admits the modeling of preference aggregation, judgment aggregation, classification, clustering and facility location. An important notion in aggregation of evaluations is strategy-proofness. In the general framework we discuss here, several definitions of strategy-proofness may be considered. We present here 3 natural \textit{general} definitions of strategy-proofness and analyze the possibility of designing an annonymous, strategy-proof aggregation rule under these definitions.