Statistics Papers

Document Type

Journal Article

Date of this Version

12-2013

Publication Source

Journal of Artificial Intelligence Research

Volume

48

Start Page

923

Last Page

951

DOI

10.1613/jair.4125

Abstract

We study the phase transition of the coalitional manipulation problem for generalized scoring rules. Previously it has been shown that, under some conditions on the distribution of votes, if the number of manipulators is o(√n), where n is the number of voters, then the probability that a random profile is manipulable by the coalition goes to zero as the number of voters goes to infinity, whereas if the number of manipulators is ω(√n), then the probability that a random profile is manipulable goes to one. Here we consider the critical window, where a coalition has size c√n, and we show that as c goes from zero to infinity, the limiting probability that a random profile is manipulable goes from zero to one in a smooth fashion, i.e., there is a smooth phase transition between the two regimes. This result analytically validates recent empirical results, and suggests that deciding the coalitional manipulation problem may be of limited computational hardness in practice.

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Date Posted: 27 November 2017

This document has been peer reviewed.