TY - JOUR

T1 - A smooth transition from powerlessness to absolute power

AU - Mossel, Elchanan

AU - Procaccia, Ariel D.

AU - Racz, Miklos Z.

N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2013/12

Y1 - 2013/12

N2 - 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(√vn), 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 (√n), then the probability that a random profile is manipulable goes to one. Here we consider the critical window, where a coalition has size cn, 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.

AB - 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(√vn), 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 (√n), then the probability that a random profile is manipulable goes to one. Here we consider the critical window, where a coalition has size cn, 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.

UR - http://www.scopus.com/inward/record.url?scp=84893151735&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84893151735&partnerID=8YFLogxK

U2 - 10.1613/jair.4125

DO - 10.1613/jair.4125

M3 - Article

AN - SCOPUS:84893151735

VL - 48

SP - 923

EP - 951

JO - Journal of Artificial Intelligence Research

JF - Journal of Artificial Intelligence Research

SN - 1076-9757

ER -