TY - GEN

T1 - New approximation for borda coalitional manipulation

AU - Keller, Orgad

AU - Hassidim, Avinatan

AU - Hazon, Noam

N1 - Publisher Copyright:
© Copyright 2017, International Foundation for Autonomous Agents and Multiagent Systems (www.ifaamas.org). All Rights Reserved.

PY - 2017

Y1 - 2017

N2 - We study the problem of Borda Unweighted Coal it ion al Manipulation, where k manipulators try to manipulate an election on m candidates under the Borda protocol. This problem is known to be NP-hard. While most recent approaches to approximation tried to minimize fc, the number of manipulators needed to make the preferred candidate win (thus assuming that the number of manipulators is not limited in advance), we focus instead on minimizing the maximum score obtainable by a non-preferred candidate. We provide a randomized, additive O(k√m log m) approximation to this value; in other words, if there exists a strategy enabling the preferred candidate to win by an Ω(k√m logm) margin, our method, with high probability, will find a strategy enabling her to win (albeit with a possibly smaller margin). It thus provides a somewhat stronger guarantee compared to the previous methods, where the addition of an extra manipulator implied (with respect to the original k) a strategy that provides an ft(m)-Additive approximation to a runner-up's score: When k is o(√m/logm), our strategy provides a stronger approximation. Our algorithm can also be viewed as a (1 + o(l))-multiplicative approximation since the value we approximate has a natural Q(fcm) lower bound. Our methods are novel and adapt techniques from multiprocessor scheduling by carefully rounding an exponentially-large configuration linear program that is solved by using the ellipsoid method with an efficient separation oracle. We be-lieve that such methods could be beneficial in approximating coalitional manipulation in other election protocols as well.

AB - We study the problem of Borda Unweighted Coal it ion al Manipulation, where k manipulators try to manipulate an election on m candidates under the Borda protocol. This problem is known to be NP-hard. While most recent approaches to approximation tried to minimize fc, the number of manipulators needed to make the preferred candidate win (thus assuming that the number of manipulators is not limited in advance), we focus instead on minimizing the maximum score obtainable by a non-preferred candidate. We provide a randomized, additive O(k√m log m) approximation to this value; in other words, if there exists a strategy enabling the preferred candidate to win by an Ω(k√m logm) margin, our method, with high probability, will find a strategy enabling her to win (albeit with a possibly smaller margin). It thus provides a somewhat stronger guarantee compared to the previous methods, where the addition of an extra manipulator implied (with respect to the original k) a strategy that provides an ft(m)-Additive approximation to a runner-up's score: When k is o(√m/logm), our strategy provides a stronger approximation. Our algorithm can also be viewed as a (1 + o(l))-multiplicative approximation since the value we approximate has a natural Q(fcm) lower bound. Our methods are novel and adapt techniques from multiprocessor scheduling by carefully rounding an exponentially-large configuration linear program that is solved by using the ellipsoid method with an efficient separation oracle. We be-lieve that such methods could be beneficial in approximating coalitional manipulation in other election protocols as well.

KW - Borda voting protocol

KW - Coalitional manipulation

KW - Elections

UR - http://www.scopus.com/inward/record.url?scp=85046429887&partnerID=8YFLogxK

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AN - SCOPUS:85046429887

T3 - Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS

SP - 606

EP - 614

BT - 16th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2017

A2 - Durfee, Edmund

A2 - Das, Sanmay

A2 - Larson, Kate

A2 - Winikoff, Michael

T2 - 16th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2017

Y2 - 8 May 2017 through 12 May 2017

ER -