Copeland voting: ties matter

We study the complexity of manipulation for a family of election systems derived from Copeland voting via introducing a parameter α that describes how ties in head-to-head contests are valued. We show that the thus obtained problem of manipulation for unweighted Copelandα elections is NP-complete even if the size of the manipulating coalition is limited to two. Our result holds for all rational values of α such that 0 < α < 1 except for α = 1/2. Since it is well known that manipulation via a single voter is easy for Copeland, our result is the first one where an election system originally known to be vulnerable to manipulation via a single voter is shown to be resistant to manipulation via a coalition of a constant number of voters.

[1]  Ariel D. Procaccia,et al.  Junta distributions and the average-case complexity of manipulating elections , 2006, AAMAS '06.

[2]  Vincent Conitzer,et al.  Nonexistence of Voting Rules That Are Usually Hard to Manipulate , 2006, AAAI.

[3]  Inon Zuckerman,et al.  Universal Voting Protocol Tweaks to Make Manipulation Hard , 2003, IJCAI.

[4]  Moni Naor,et al.  Rank aggregation methods for the Web , 2001, WWW '01.

[5]  Edith Hemaspaandra,et al.  Dichotomy for voting systems , 2005, J. Comput. Syst. Sci..

[6]  Ronen I. Brafman,et al.  CP-nets: A Tool for Representing and Reasoning withConditional Ceteris Paribus Preference Statements , 2011, J. Artif. Intell. Res..

[7]  Lirong Xia,et al.  Strongly Decomposable Voting Rules on Multiattribute Domains , 2007, AAAI.

[8]  David C. Mcgarvey.  A THEOREMI ON THE CONSTRUCTION OF VOTING PARADOXES , 1953 .

[9]  John J. Bartholdi,et al.  Single transferable vote resists strategic voting , 2015 .

[10]  Ariel D. Procaccia,et al.  On the robustness of preference aggregation in noisy environments , 2007, AAMAS '07.

[11]  Vincent Conitzer,et al.  When are elections with few candidates hard to manipulate? , 2007, J. ACM.

[12]  Eithan Ephrati,et al.  Multi-Agent Planning as a Dynamic Search for Social Consensus , 1993, IJCAI.

[13]  Piotr Faliszewski,et al.  Llull and Copeland Voting Broadly Resist Bribery and Control , 2007, AAAI.

[14]  Richard Edwin Stearns,et al.  The Voting Problem , 1959 .

[15]  M. Trick,et al.  The computational difficulty of manipulating an election , 1989 .

[16]  M. Trick,et al.  Voting schemes for which it can be difficult to tell who won the election , 1989 .

[17]  Edith Elkind,et al.  Hybrid Voting Protocols and Hardness of Manipulation , 2005, ISAAC.

[18]  Ariel D. Procaccia,et al.  Algorithms for the coalitional manipulation problem , 2008, SODA '08.

[19]  Arnold B. Urken,et al.  Classics of social choice , 1995 .