A logic for causal reasoning

The POSSIBLE WINNER problem asks whether some distinguished candidate may become the winner of an election when the given incomplete votes are extended into complete ones in a favorable way. POSSIBLE WINNER is NP-complete for common voting rules such as Borda, many other positional scoring rules, Bucklin, Copeland etc. We investigate how three different parameterizations influence the computational complexity of POSSIBLE WINNER for a number of voting rules. We show fixed-parameter tractability results with respect to the parameter "number of candidates" but intractability results with respect to the parameter "number of votes". Finally, we derive fixed-parameter tractability results with respect to the parameter "total number of undetermined candidate pairs" and identify an interesting polynomial-time solvable special case for Borda.

[1]  Pietro Torasso,et al.  On the Relationship between Abduction and Deduction , 1991, J. Log. Comput..

[2]  Nils J. Nilsson,et al.  Artificial Intelligence , 1974, IFIP Congress.

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

[4]  Sarit Kraus,et al.  Nonmonotonic Reasoning, Preferential Models and Cumulative Logics , 1990, Artif. Intell..

[5]  Camilla Schwind,et al.  Causality in Action Theories , 1999, Electron. Trans. Artif. Intell..

[6]  Fangzhen Lin,et al.  Embracing Causality in Specifying the Indeterminate Effects of Actions , 1996, AAAI/IAAI, Vol. 1.

[7]  Hudson Turner.  Strong Equivalence for Logic Programs and Default Theories (Made Easy) , 2001, LPNMR.

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

[9]  Laura Giordano,et al.  Ramification and causality in a modal action logic , 2000, J. Log. Comput..

[10]  David Pearce,et al.  Strongly equivalent logic programs , 2001, ACM Trans. Comput. Log..

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

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

[13]  Hudson Turner,et al.  A Logic of Universal Causation , 1999, Artif. Intell..

[14]  Grigoris Antoniou,et al.  Nonmonotonic reasoning , 1997 .

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

[16]  Leon van der Torre,et al.  Input/Output Logics , 2000, J. Philos. Log..

[17]  Toby Walsh,et al.  Uncertainty in Preference Elicitation and Aggregation , 2007, AAAI.

[18]  Toby Walsh,et al.  Incompleteness and Incomparability in Preference Aggregation , 2007, IJCAI.

[19]  Hudson Turner,et al.  Satisfiability planning with Causal Theories , 1998, KR.

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

[21]  Hudson Turner,et al.  Causal Theories of Action and Change , 1997, AAAI/IAAI.

[22]  Vladimir Lifschitz,et al.  On the Logic of Causal Explanation (Research Note) , 1997, Artif. Intell..

[23]  松本 裕治.  Default Reasoningと非単調論理(海外研究動向) , 1981 .

[24]  Enrico Giunchiglia,et al.  Nonmonotonic causal theories , 2004, Artif. Intell..

[25]  Hector Geffner,et al.  Default reasoning - causal and conditional theories , 1992 .

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

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

[28]  Rolf Niedermeier,et al.  Invitation to Fixed-Parameter Algorithms , 2006 .

[29]  Toby Walsh,et al.  Winner Determination in Sequential Majority Voting , 2007, IJCAI.