Skip to main content
SpringerLink
Log in
Book cover

The Multivariate Algorithmic Revolution and Beyond pp 318–363Cite as

Studies in Computational Aspects of Voting

A Parameterized Complexity Perspective

  • Chapter

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7370))

Abstract

We review NP-hard voting problems together with their status in terms of parameterized complexity results. In addition, we survey standard techniques for achieving fixed-parameter (in)tractability results in voting.

Supported by the DFG, research project PAWS, NI 369/10.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arora, S., Barak, B.: Computational Complexity: A Modern Approach. Cambridge University Press (2009)

    Google Scholar 

  2. Ailon, N.: Aggregation of Partial Rankings, p-Ratings, and Top-m Lists. Algorithmica 57(2), 284–300 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  3. Alon, N., Lokshtanov, D., Saurabh, S.: Fast FAST. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009, Part I. LNCS, vol. 5555, pp. 49–58. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  4. Arrow, K.J., Sen, A.K., Suzumura, K. (eds.): Handbook of Social Choice and Welfare, vol. 1. North-Holland (2002)

    Google Scholar 

  5. Arrow, K.J., Sen, A.K., Suzumura, K. (eds.): Handbook of Social Choice and Welfare, vol. 2. North-Holland (2010)

    Google Scholar 

  6. Alon, N., Yuster, R., Zwick, U.: Color-Coding. Journal of the ACM 42(4), 844–856 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  7. Banks, J.S.: Sophisticated Voting Outcomes and Agenda Control. Social Choice and Welfare 1(4), 295–306 (1985)

    Article  MATH  Google Scholar 

  8. Biedl, T.C., Brandenburg, F.-J., Deng, X.: On the Complexity of Crossings in Permutations. Discrete Mathematics 309(7), 1813–1823 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Betzler, N., Bredereck, R., Niedermeier, R.: Partial Kernelization for Rank Aggregation: Theory and Experiments. In: Raman, V., Saurabh, S. (eds.) IPEC 2010. LNCS, vol. 6478, pp. 26–37. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  10. Betzler, N., Bredereck, R., Niedermeier, R., Uhlmann, J.: On Making a Distinguished Vertex Minimum Degree by Vertex Deletion. In: Černá, I., Gyimóthy, T., Hromkovič, J., Jefferey, K., Králović, R., Vukolić, M., Wolf, S. (eds.) SOFSEM 2011. LNCS, vol. 6543, pp. 123–134. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  11. Betzler, N., Bredereck, R., Niedermeier, R., Uhlmann, J.: On Bounded-Degree Vertex Deletion Parameterized by Treewidth. Discrete Applied Mathematics 160(1–2), 53–60 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  12. Brandt, F., Brill, M., Seedig, H.G.: On the Fixed-Parameter Tractability of Composition-Consistent Tournament Solutions. In: Proceedings of the 22nd International Joint Conference on Artificial Intelligence, pp. 85–90. AAAI Press (2011)

    Google Scholar 

  13. Brandt, F., Conitzer, V., Endriss, U.: Computational Social Choice. In: Weiss, G. (ed.) Multiagent Systems. MIT Press (2012)

    Google Scholar 

  14. Betzler, N., Dorn, B.: Towards a Dichotomy of Finding Possible Winners in Elections Based on Scoring Rules. Journal of Computer and System Sciences 76(8), 812–836 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  15. Bodlaender, H.L., Downey, R.G., Fellows, M.R., Hermelin, D.: On Problems Without Polynomial Kernels. Journal of Computer and System Sciences 75(8), 423–434 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  16. Baumeister, D., Erdélyi, G., Hemaspaandra, E., Hemaspaandra, L.A., Rothe, J.: Computational Aspects of Approval Voting. In: Laslier, J.-F., Remzi Sanver, M. (eds.) Handbook on Approval Voting, ch. 10, pp. 199–251. Springer (2010)

    Google Scholar 

  17. Betzler, N.: A Multivariate Complexity Analysis of Voting Problems. PhD thesis, Friedrich-Schiller-Universität Jena (2010)

    Google Scholar 

  18. Betzler, N.: On Problem Kernels for Possible Winner Determination under the k-Approval Protocol. In: Hliněný, P., Kučera, A. (eds.) MFCS 2010. LNCS, vol. 6281, pp. 114–125. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  19. Brams, S., Fishburn, P.C.: Voting Procedures. In: Arrow, K.J., Sen, A.K., Suzumura, K. (eds.) Handbook of Social Choice and Welfare, vol. 1, pp. 173–236. Elsevier (2002)

    Google Scholar 

  20. Betzler, N., Fellows, M.R., Guo, J., Niedermeier, R., Rosamond, F.A.: Fixed-Parameter Algorithms for Kemeny Rankings. Theoretical Computer Science 410, 4554–4570 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  21. Betzler, N., Guo, J., Komusiewicz, C., Niedermeier, R.: Average Parameterization and Partial Kernelization for Computing Medians. Journal of Computer and System Sciences 77, 774–789 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  22. Betzler, N., Guo, J., Niedermeier, R.: Parameterized Computational Complexity of Dodgson and Young Elections. Information and Computation 208(2), 165–177 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  23. Betzler, N., Hemmann, S., Niedermeier, R.: A Multivariate Complexity Analysis of Determining Possible Winners Given Incomplete Votes. In: Proceedings of the 21st International Joint Conference on Artificial Intelligence, pp. 53–58 (2009)

    Google Scholar 

  24. Betzler, N., Niedermeier, R., Woeginger, G.J.: Unweighted Coalitional Manipulation Under the Borda Rule is NP-hard. In: Proceedings of 22nd International Joint Conference of Artificial Intelligence, pp. 55–60 (2011)

    Google Scholar 

  25. Bartholdi III, J.J., Orlin, J.B.: Single Transferable Vote Resists Strategic Voting. Social Choice and Welfare 8, 341–354 (1991)

    MathSciNet  MATH  Google Scholar 

  26. Bodlaender, H.L.: Kernelization: New Upper and Lower Bound Techniques. In: Chen, J., Fomin, F.V. (eds.) IWPEC 2009. LNCS, vol. 5917, pp. 17–37. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  27. Brams, S., Remzi Sanver, M.: Voting Systems that Combine Approval and Preference. In: Brams, S., Gehrlein, W.V., Roberts, F.S. (eds.) The Mathematics of Preference, Choice, and Order: Essays in Honor of Peter C. Fishburn, pp. 215–237. Springer (2009)

    Google Scholar 

  28. Betzler, N., Slinko, A., Uhlmann, J.: On the Computation of Fully Proportional Representation (2011) (available at Social Science Research Network)

    Google Scholar 

  29. Bartholdi III, J.J., Tovey, C.A., Trick, M.A.: The Computational Difficulty of Manipulating an Election. Social Choice and Welfare 6(3), 227–241 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  30. Bartholdi III, J.J., Tovey, C.A., Trick, M.A.: Voting Schemes for Which It Can Be Difficult to Tell Who Won the Election. Social Choice and Welfare 6(2), 157–165 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  31. Bartholdi III, J.J., Tovey, C.A., Trick, M.A.: How Hard Is It to Control an Election? Mathematical and Computer Modeling 16(8-9), 27–40 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  32. Bodlaender, H.L., Thomassé, S., Yeo, A.: Kernel Bounds for Disjoint Cycles and Disjoint Paths. Theoretical Computer Science 412(35), 4570–4578 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  33. Betzler, N., Uhlmann, J.: Parameterized Complexity of Candidate Control in Elections and Related Digraph Problems. Theoretical Computer Science 410(52), 5425–5442 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  34. Chamberlin, J.R., Courant, P.N.: Representative Deliberations and Representative Decisions: Proportional Representation and the Borda Rule. American Political Science Review 77(3), 718–733 (1983)

    Article  Google Scholar 

  35. Cai, L., Chen, J., Downey, R.G., Fellows, M.R.: Advice Classes of Parameterized Tractability. Annals of Pure and Applied Logic 84, 119–138 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  36. Chevaleyre, Y., Endriss, U., Lang, J., Maudet, N.: A Short Introduction to Computational Social Choice. In: van Leeuwen, J., Italiano, G.F., van der Hoek, W., Meinel, C., Sack, H., Plášil, F. (eds.) SOFSEM 2007. LNCS, vol. 4362, pp. 51–69. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  37. Christian, R., Fellows, M., Rosamond, F., Slinko, A.: On Complexity of Lobbying in Multiple Referenda. Review of Economic Design 11(3), 217–224 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  38. Charon, I., Hudry, O.: Slater Orders and Hamiltonian Paths of Tournaments. Electronic Notes in Discrete Mathematics 5, 60–63 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  39. Chevaleyre, Y., Lang, J., Maudet, N., Monnot, J., Xia, L.: New Candidates Welcome! Possible Winners with Respect to the Addition of New Candidates. In: CoRR, abs/1111.3690 (2011)

    Google Scholar 

  40. Conitzer, V.: Computing Slater Rankings Using Similarities among Candidates. In: Proceedings of the 21st AAAI Conference on Artificial Intelligence, pp. 613–619. AAAI Press (2006)

    Google Scholar 

  41. Conitzer, V.: Making Decisions Based on the Preferences of Multiple Agents. Communications of the ACM 53, 84–94 (2010)

    Article  Google Scholar 

  42. Copeland, A.H.: A ‘Resonable’ Social Welfare Function. Mimeographed (University of Michigan Seminar on Application of Mathematics in Social Science) (1951)

    Google Scholar 

  43. Conitzer, V., Rognlie, M., Xia, L.: Preference Functions That Score Rankings and Maximum Likelihood Estimation. In: Proceedings of the 20th International Joint Conference on Artificial Intelligence, pp. 109–115 (2009)

    Google Scholar 

  44. Conitzer, V., Sandholm, T., Lang, J.: When Are Elections with Few Candidates Hard to Manipulate? Journal of the ACM 54, 1–33 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  45. de Borda, J.-C.: Mémoire sur les élections au scrutin. Histoire de l’Académie Royale des Sciences (1781)

    Google Scholar 

  46. Caritat, M.J.A.N., de Condorcet: Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix. L’Imprimerie Royale, Paris (1785)

    Google Scholar 

  47. Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer (1999)

    Google Scholar 

  48. Dwork, C., Kumar, R., Naor, M., Sivakumar, D.: Rank Aggregation Methods for the Web. In: Proceedings of the 10th International Conference on World Wide Web, pp. 613–622. ACM (2001)

    Google Scholar 

  49. Dwork, C., Kumar, R., Naor, M., Sivakumar, D.: Rank Aggregation Revisited (2001) (manuscript)

    Google Scholar 

  50. Davies, J., Katsirelos, G., Narodytska, N., Walsh, T.: Complexity of and Algorithms for Borda Manipulation. In: Proceedings of the 25th AAAI Conference on Artificial Intelligence, pp. 657–662. AAAI Press (2011)

    Google Scholar 

  51. Dom, M., Lokshtanov, D., Saurabh, S.: Incompressibility through Colors and IDs. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009, Part I. LNCS, vol. 5555, pp. 378–389. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  52. Dodgson, C.: A Method of Taking Votes on More Than Two Issues. Pamphlet printed by the Clarendon Press, Oxford, and headed (1876) (not yet published)

    Google Scholar 

  53. Dorn, B., Schlotter, I.: Multivariate Complexity Analysis of Swap Bribery. Algorithmica (2012) (available electronically)

    Google Scholar 

  54. Downey, R.G., Thilikos, D.M.: Confronting Intractability via Parameters. Computer Science Review 5(4), 279–317 (2011)

    Article  MATH  Google Scholar 

  55. Elkind, E., Faliszewski, P.: Approximation Algorithms for Campaign Management. In: Saberi, A. (ed.) WINE 2010. LNCS, vol. 6484, pp. 473–482. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  56. Erdélyi, G., Fellows, M.R.: Parameterized Control Complexity in Bucklin Voting and in Fallback Voting. In: Proceedings of the 3rd International Workshop on Computational Social Choice, pp. 163–174 (2010)

    Google Scholar 

  57. Erdélyi, G., Fernau, H., Goldsmith, J., Mattei, N., Raible, D., Rothe, J.: The Complexity of Probabilistic Lobbying. In: Rossi, F., Tsoukias, A. (eds.) ADT 2009. LNCS, vol. 5783, pp. 86–97. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  58. Erdélyi, G., Fellows, M.R., Piras, L., Rothe, J.: Control Complexity in Bucklin and Fallback Voting. Technical report, arXiv:1103.2230 (2011)

    Google Scholar 

  59. Elkind, E., Faliszewski, P., Slinko, A.: Swap Bribery. In: Mavronicolas, M., Papadopoulou, V.G. (eds.) SAGT 2009. LNCS, vol. 5814, pp. 299–310. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  60. Elkind, E., Faliszewski, P., Slinko, A.: Cloning in Elections. In: Proceedings of the 24th AAAI Conference on Artificial Intelligence, pp. 768–773. AAAI Press (2010)

    Google Scholar 

  61. Elkind, E., Faliszewski, P., Slinko, A.: On the Role of Distances in Defining Voting Rules. In: Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems, pp. 375–382 (2010)

    Google Scholar 

  62. Erdélyi, G., Nowak, M., Rothe, J.: Sincere-Strategy Preference-Based Approval Voting Fully Resists Constructive Control and Broadly Resists Destructive Control. Mathematical Logic Quaterly 55, 425–443 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  63. Erdélyi, G., Piras, L., Rothe, J.: Control Complexity in Fallback Voting. Technical report, arXiv:1004.3398v1 (2010)

    Google Scholar 

  64. Ephrati, E., Rosenschein, J.S.: The Clarke Tax as a Consensus Mechanism Among Automated Agents. In: Proceedings of the 9th AAAI Conference on Artificial Intelligence, pp. 173–178. AAAI Press (1991)

    Google Scholar 

  65. Ephrati, E., Rosenschein, J.S.: A Heuristic Technique for Multi-Agent Planning. Annals of Mathematics and Artificial Intelligence 20(1–4), 13–67 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  66. Erdélyi, G., Rothe, J.: Control Complexity in Fallback Voting. In: Proceedings of Computing: the 16th Australasian Theory Symposium. Australian Computer Society Conferences in Research and Practice in Information Technology Series, pp. 39–48 (2010)

    Google Scholar 

  67. Faliszewski, P.: Nonuniform Bribery. In: Proceedings of the 7th International Joint Conference on Autonomous Agents and Multiagent Systems. International Foundation for Autonomous Agents and Multiagent Systems, pp. 1569–1572 (2008)

    Google Scholar 

  68. Fellows, M.: Towards Fully Multivariate Algorithmics: Some New Results and Directions in Parameter Ecology. In: Fiala, J., Kratochvíl, J., Miller, M. (eds.) IWOCA 2009. LNCS, vol. 5874, pp. 2–10. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  69. Fernau, H., Fomin, F.V., Lokshtanov, D., Raible, D., Saurabh, S., Villanger, Y.: Kernel(s) for Problems with No Kernel: On Out-Trees with Many Leaves. In: Proceedings of the 26th International Symposium on Theoretical Aspects of Computer Science. LIPIcs, vol. 3, pp. 421–432. Schloss Dagstuhl (2009)

    Google Scholar 

  70. Fernau, H., Fomin, F.V., Lokshtanov, D., Mnich, M., Philip, G., Saurabh, S.: Ranking and Drawing in Subexponential Time. In: Iliopoulos, C.S., Smyth, W.F. (eds.) IWOCA 2010. LNCS, vol. 6460, pp. 337–348. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  71. Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer (2006)

    Google Scholar 

  72. Faliszewski, P., Hemaspaandra, E., Hemaspaandra, L.A.: How Hard Is Bribery in Elections? Journal of Artificial Intelligence Research 35, 485–532 (2009)

    MathSciNet  MATH  Google Scholar 

  73. Faliszewski, P., Hemaspaandra, E., Hemaspaandra, L.A.: Using Complexity to Protect Elections. Communications of the ACM 53(11), 74–82 (2010)

    Article  Google Scholar 

  74. Faliszewski, P., Hemaspaandra, E., Hemaspaandra, L.A.: Multimode Control Attacks on Elections. Journal of Artificial Intelligence Research 40, 305–351 (2011)

    MathSciNet  MATH  Google Scholar 

  75. Faliszewski, P., Hemaspaandra, E., Hemaspaandra, L.A., Rothe, J.: A Richer Understanding of the Complexity of Election Systems. In: Fundamental Problems in Computing: Essays in Honor of Professor Daniel J. Rosenkrantz, pp. 375–406 (2009)

    Google Scholar 

  76. Faliszewski, P., Hemaspaandra, E., Hemaspaandra, L.A., Rothe, J.: Llull and Copeland Voting Computationally Resist Bribery and Constructive Control. Journal of Artificial Intelligence Research 35, 275–341 (2009)

    MathSciNet  MATH  Google Scholar 

  77. Fishburn, P.C.: Condorcet Social Choice Functions. SIAM Journal on Applied Mathematics 33(3), 469–489 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  78. Fellows, M.R., Jansen, B., Lokshtanov, D., Rosamond, F.A., Saurabh, S.: Determining the Winner of a Dodgson Election is Hard. In: Proceedings of the 29th Conference on Foundations of Software Technology and Theoretical Computer Science, pp. 459–469. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2010)

    Google Scholar 

  79. Fagin, R., Kumar, R., Sivakumar, D.: Efficient Similarity Search and Classification via Rank Aggregation. In: Proceedings of the 22nd ACM SIGMOD International Conference on Management of Data, pp. 301–312. ACM (2003)

    Google Scholar 

  80. Fortnow, L., Santhanam, R.: Infeasibility of Instance Compression and Succinct PCPs for NP. Journal of Computer and System Sciences 77(1), 91–106 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  81. Gaertner, W.: A Primer in Social Choice Theory–LSE Perspectives in Economic Analysis, revised edition. Oxford University Press (2009)

    Google Scholar 

  82. Gibbard, A.: Manipulation of Voting Schemes: A General Result. Econometrica 41(4), 587–601 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  83. Guo, J., Moser, H., Niedermeier, R.: Iterative Compression for Exactly Solving NP-Hard Minimization Problems. In: Lerner, J., Wagner, D., Zweig, K.A. (eds.) Algorithmics of Large and Complex Networks. LNCS, vol. 5515, pp. 65–80. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  84. Guo, J., Niedermeier, R.: Invitation to Data Reduction and Problem Kernelization. ACM SIGACT News 38(1), 31–45 (2007)

    Article  Google Scholar 

  85. Goodman, L.A.: On Methods of Amalgamation. In: Thrall, R.M., Coombs, C.H., Davis, R.L. (eds.) Decision Processes, pp. 39–48. John Wiley and Sons, Inc. (1954)

    Google Scholar 

  86. Hemaspaandra, E., Hemaspaandra, L.A., Rothe, J.: Exact Analysis of Dodgson Elections: Lewis Caroll’s 1876 Voting System is Complete for Parallel Access to NP. Journal of the ACM 44(6), 806–825 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  87. Hemaspaandra, E., Hemaspaandra, L.A., Rothe, J.: Anyone but Him: The Complexity of Precluding an Alternative. Artificial Intelligence 171(5-6), 255–285 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  88. Hemaspaandra, E., Hemaspaandra, L.A., Rothe, J.: Hybrid Elections Broaden Complexity-Theoretic Resistance to Control. Mathematical Logic Quarterly 55(4), 397–424 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  89. Hemaspaandra, E., Spakowski, H., Vogel, J.: The Complexity of Kemeny Elections. Theoretical Computer Science 349(3), 382–391 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  90. Hudry, O.: A Note On “Banks Winners in Tournaments Are Difficult to Recognize” by G. J. Woeginger. Social Choice and Welfare 23(1), 113–114 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  91. Impagliazzo, R., Paturi, R.: On the Complexity of k-SAT. Journal of Computer and System Sciences 62, 367–375 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  92. Impagliazzo, R., Paturi, R., Zane, F.: Which Problems Have Strongly Exponential Complexity? Journal of Computer and System Sciences 63(4), 512–530 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  93. Jackson, B.N., Schnable, P.S., Aluru, S.: Consensus Genetic Maps as Median Orders from Inconsistent Sources. IEEE/ACM Transactions on Computational Biology and Bioinformatics 5(2), 161–171 (2008)

    Article  Google Scholar 

  94. Kemeny, J.G.: Mathematics Without Numbers. Daedalus 88, 571–591 (1959)

    Google Scholar 

  95. Konczak, K., Lang, J.: Voting Procedures with Incomplete Preferences. In: Proceedings of IJCAI 2005 Multidisciplinary Workshop on Advances in Preference Handling, pp. 124–129 (2005)

    Google Scholar 

  96. Komusiewicz, C., Niedermeier, R., Uhlmann, J.: Deconstructing Intractability—A Multivariate Complexity Analysis of Interval Constrained Coloring. Journal of Discrete Algorithms 9, 137–151 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  97. Karpinski, M., Schudy, W.: Faster Algorithms for Feedback Arc Set Tournament, Kemeny Rank Aggregation and Betweenness Tournament. In: Cheong, O., Chwa, K.-Y., Park, K. (eds.) ISAAC 2010. LNCS, vol. 6506, pp. 3–14. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  98. Kleinberg, J., Tardos, É.: Algorithm Design. Addison-Wesley (2006)

    Google Scholar 

  99. Lu, T., Boutilier, C.: Budgeted Social Choice: From Consensus to Personalized Decision Making. In: Proceedings of the 22nd International Joint Conference on Artificial Intelligence, pp. 280–286 (2011)

    Google Scholar 

  100. Lenstra, H.W.: Integer Programming with a Fixed Number of Variables. Mathematics of Operations Research 8(4), 538–548 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  101. Levenglick, A.: Fair and Reasonable Election Systems. Behavioral Science 20(1), 34–46 (1975)

    Article  Google Scholar 

  102. Liu, H., Feng, H., Zhu, D., Luan, J.: Parameterized Computational Complexity of Control Problems in Voting Systems. Theoretical Computer Science 410, 2746–2753 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  103. Lokshtanov, D.: New Methods in Parameterized Algorithms and Complexity. PhD thesis, University of Bergen (2009)

    Google Scholar 

  104. Lindner, C., Rothe, J.: Fixed-Parameter Tractability and Parameterized Complexity Applied to Problems From Computational Social Choice. In: Supplement in the Mathematical Programming Glossary (October 2008)

    Google Scholar 

  105. Liu, H., Zhu, D.: Parameterized Complexity of Control Problems in Maximin Election. Information Processing Letters 110(10), 383–388 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  106. Matoušek, J., Gärtner, B.: Understanding and Using Linear Programming (Universitext). Springer (2006)

    Google Scholar 

  107. Monroe, B.L.: Fully Proportional Representation. American Political Science Review 89(4), 925–940 (1995)

    Article  Google Scholar 

  108. Moulin, H.: Axioms of Cooperative Decision Making. Cambridge University Press (1991)

    Google Scholar 

  109. Mahajan, M., Raman, V.: Parameterizing Above Guaranteed Values: MaxSat and MaxCut. Journal of Algorithms 31(2), 335–354 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  110. Mahajan, M., Raman, V., Sikdar, S.: Parameterizing Above or Below Guaranteed Values. Journal of Computer and System Sciences 75, 137–153 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  111. Misra, N., Raman, V., Saurabh, S.: Lower Bounds on Kernelization. Discrete Optimization 8(1), 110–128 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  112. Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press (February 2006)

    Google Scholar 

  113. Niedermeier, R.: Reflections on Multivariate Algorithmics and Problem Parameterization. In: Proceedings of the 27th International Symposium on Theoretical Aspects of Computer Science. LIPIcs, vol. 5, pp. 17–32 (2010)

    Google Scholar 

  114. Nurmi, H.: Comparing Voting Systems. Kluwer Academic Publishers (1987)

    Google Scholar 

  115. Papadimitriou, C.H.: Computational Complexity. Addison-Wesley (1994)

    Google Scholar 

  116. Pini, M.S., Rossi, F., Brent Venable, K., Walsh, T.: Incompleteness and Incomparability in Preference Aggregation: Complexity Results. Artificial Intelligence 175, 1272–1289 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  117. Procaccia, A.D., Rosenschein, J.S., Zohar, A.: On the Complexity of Achieving Proportional Representation. Social Choice and Welfare 30, 353–362 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  118. Rothe, J., Baumeister, D., Lindner, C., Rothe, I.: Einführung in Computational Social Choice: Individuelle Strategien und kollektive Entscheidungen beim Spielen. Spektrum Akademischer Verlag, Wählen und Teilen (2011)

    Google Scholar 

  119. Raman, V., Saurabh, S.: Improved Fixed Parameter Tractable Algorithms for Two “Edge” Problems: MAXCUT and MAXDAG. Information Processing Letters 104(2), 65–72 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  120. Rothe, J., Spakowski, H., Vogel, J.: Exact Complexity of the Winner Problem for Young Elections. Theory of Computing Systems 36(4), 375–386 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  121. Reed, B.A., Smith, K., Vetta, A.: Finding Odd Cycle Transversals. Operations Research Letters 32, 299–301 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  122. Satterthwaite, M.A.: Strategy-Proofness and Arrow’s Conditions: Existence and Correspondence Theorems for Voting Procedures and Social Welfare Functions. Journal of Economic Theory, 187–217 (1975)

    Google Scholar 

  123. Sculley, D.W.: Rank Aggregation for Similar Items. In: Proceedings of the 7th SIAM International Conference on Data Mining, pp. 587–592 (2007)

    Google Scholar 

  124. Schlotter, I., Elkind, E., Faliszewski, P.: Campaign Management under Approval-Driven Voting Rules. In: Proceedings of the 25th AAAI Conference on Artificial Intelligence, pp. 726–731. AAAI Press (2011)

    Google Scholar 

  125. Simjour, N.: Improved Parameterized Algorithms for the Kemeny Aggregation Problem. In: Chen, J., Fomin, F.V. (eds.) IWPEC 2009. LNCS, vol. 5917, pp. 312–323. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  126. Slater, P.: Inconsistencies in a Schedule of Paired Comparisons. Biometrika 48(3-4), 303–312 (1961)

    Article  Google Scholar 

  127. Sniedovich, M.: Wald’s Maximin Model: A Treasure in Disguise! Journal of Risk Finance 9(3), 287–291 (2008)

    Article  Google Scholar 

  128. Taylor, A.D.: Social Choice and the Mathematics of Manipulation. Cambridge University Press (2005)

    Google Scholar 

  129. Wald, A.: Statistical Decision Functions. The Annals of Mathematical Statistics 20(2) (1949)

    Google Scholar 

  130. Walsh, T.: Uncertainty in Preference Elicitation and Aggregation. In: Proceedings of the 22nd AAAI Conference on Artificial Intelligence, pp. 3–8. AAAI Press (2007)

    Google Scholar 

  131. Woeginger, G.J.: Banks Winners in Tournaments are Difficult to Recognize. Social Choice and Welfare 20(3), 523–528 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  132. Xia, L., Conitzer, V.: Determining Possible and Necessary Winners under Common Voting Rules Given Partial Orders. Journal of Artificial Intelligence Research 41, 25–67 (2011)

    MathSciNet  MATH  Google Scholar 

  133. Young, H.P., Levenglick, A.: A Consistent Extension of Condorcet’s Election Principle. SIAM Journal on Applied Mathematics 35(2), 285–300 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  134. Young, H.P.: Extending Condorcet’s Rule. Journal of Economic Theory 16, 335–353 (1977)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Softwaretechnik und Theoretische Informatik, TU Berlin, Germany

    Nadja Betzler, Robert Bredereck, Jiehua Chen & Rolf Niedermeier

Authors
  1. Nadja Betzler
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Robert Bredereck
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jiehua Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Rolf Niedermeier
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Information and Computing Sciences, Utrecht University, P.O. Box 80.089, 3508 TB, Utrecht, The Netherlands

    Hans L. Bodlaender

  2. School of Mathematics, Statistics and Operations Research, Victoria University, P.O. Box 600, Wellington, New Zealand

    Rod Downey

  3. Institute of Informatics, University of Bergen, Postboks 7800, 5020, Bergen, Norway

    Fedor V. Fomin

  4. Computer and Automation Research Institute, Hungarian Academy of Sciences (MTA SZTAKI), Pf. 63, 1518, Budapest, Hungary

    Dániel Marx

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Betzler, N., Bredereck, R., Chen, J., Niedermeier, R. (2012). Studies in Computational Aspects of Voting. In: Bodlaender, H.L., Downey, R., Fomin, F.V., Marx, D. (eds) The Multivariate Algorithmic Revolution and Beyond. Lecture Notes in Computer Science, vol 7370. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30891-8_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-30891-8_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30890-1

  • Online ISBN: 978-3-642-30891-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation