Taking the final step to a full dichotomy of the possible winner problem in pure scoring rules

The POSSIBLE WINNER problem asks, given an election where the voters' preferences over the candidates are specified only partially, whether a designated candidate can be made win. Betzler and Dorn [1] proved a result that is only one step away from a full dichotomy of this problem for the important class of pure scoring rules in the case of unweighted voters and an unbounded number of candidates: POSSIBLE WINNER is NP-complete for all pure scoring rules except plurality, veto, and the scoring rule with vector (2,1,…,1,0), but is solvable in polynomial time for plurality and veto. We take the final step to a full dichotomy by showing that POSSIBLE WINNER is NP-complete also for the scoring rule with vector (2,1,…,1,0).

[1]  Jörg Rothe,et al.  Taking the Final Step to a Full Dichotomy of the Possible Winner Problem in Pure Scoring Rules , 2010, ECAI.

[2]  Piotr Faliszewski,et al.  Copeland voting: ties matter , 2008, AAMAS.

[3]  Toby Walsh,et al.  Complexity of and Algorithms for Borda Manipulation , 2011, AAAI.

[4]  Jérôme Monnot,et al.  Possible winners when new alternatives join: new results coming up! , 2011, AAMAS.

[5]  Nadja Betzler,et al.  Towards a Dichotomy of Finding Possible Winners in Elections Based on Scoring Rules , 2009, MFCS.

[6]  Toby Walsh,et al.  Manipulation of Nanson's and Baldwin's Rules , 2011, AAAI.

[7]  Piotr Faliszewski,et al.  Using complexity to protect elections , 2010, Commun. ACM.

[8]  Gerhard J. Woeginger,et al.  Unweighted Coalitional Manipulation under the Borda Rule Is NP-Hard , 2011, IJCAI.

[9]  Vincent Conitzer,et al.  A scheduling approach to coalitional manipulation , 2010, EC '10.

[10]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[11]  Jörg Rothe,et al.  Computational complexity of two variants of the possible winner problem , 2011, AAMAS.

[12]  Vincent Conitzer,et al.  Determining Possible and Necessary Winners under Common Voting Rules Given Partial Orders , 2008, AAAI.

[13]  Piotr Faliszewski,et al.  Manipulation of copeland elections , 2010, AAMAS.

[14]  Piotr Faliszewski,et al.  A Richer Understanding of the Complexity of Election Systems , 2006, Fundamental Problems in Computing.

[15]  Yann Chevaleyre,et al.  Possible Winners when New Candidates Are Added: The Case of Scoring Rules , 2010, AAAI.

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

[17]  Nadja Betzler,et al.  Towards a dichotomy for the Possible Winner problem in elections based on scoring rules , 2009, J. Comput. Syst. Sci..

[18]  Omer Lev,et al.  An algorithm for the coalitional manipulation problem under Maximin , 2011, AAMAS.

[19]  L. A. Hemaspaandra,et al.  Computational Aspects of Approval Voting , 2010 .

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

[21]  ConitzerVincent.  Making decisions based on the preferences of multiple agents , 2010 .

[22]  Piotr Faliszewski,et al.  AI's War on Manipulation: Are We Winning? , 2010, AI Mag..

[23]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[24]  Piotr Faliszewski,et al.  Swap Bribery , 2009, SAGT.

[25]  Jérôme Lang,et al.  Voting procedures with incomplete preferences , 2005 .

[26]  Thomas J. Schaefer,et al.  The complexity of satisfiability problems , 1978, STOC.

[27]  Ariel D. Procaccia,et al.  Complexity of unweighted coalitional manipulation under some common voting rules , 2009, IJCAI 2009.

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