Guarantees for the success frequency of an algorithm for finding Dodgson-election winners

Journal of Heuristics

Volumn 15, Issue 4, 2009, Pages 403-423

  Homan, Christopher M ^a   Hemaspaandra, Lane A ^b  

^a Rochester Institute of Technology   (United States)

^b University of Rochester   (United States)

Author keywords

Computational social choise; Dodgson elections; Frequently self knowingly correct heuristics; Lewis Carroll

Indexed keywords

COMPUTATIONAL SOCIAL CHOISE; DODGSON ELECTIONS; FREQUENTLY SELF-KNOWINGLY CORRECT HEURISTICS; GREEDY ALGORITHMS; LEWIS CARROLL; POLYNOMIAL HIERARCHIES; POLYNOMIAL-TIME; VOTING SYSTEMS;

HEURISTIC METHODS; VOTING MACHINES;

POLYNOMIALS;

EID: 67651043683     PISSN: 13811231     EISSN: 15729397     Source Type: Journal    
DOI: 10.1007/s10732-007-9068-5     Document Type: Article

References (52)

1. G. Ausiello P. Crescenzi M. Protasi 1995 Approximate solution of NP optimization problems Theor. Comput. Sci. 150 1 1 55
2. Alon, N., Spencer, J.: The Probabilistic Method, 2nd edn. Wiley-Interscience, New York (2000)
3. Black, D.: The Theory of Committees and Elections. Cambridge University Press, Cambridge (1958)
4. Brown, D.: A probabilistic analysis of a greedy algorithm arising from computational biology. In: Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 206-207. ACM, New York (2001)
5. A. Bogdanov L. Trevisan 2006 On worst-case to average-case reductions for NP problems SIAM J. Comput. 36 4 1119 1159 (Pubitemid 47246879)
6. J. Bartholdi III C. Tovey M. Trick 1989 Voting schemes for which it can be difficult to tell who won the election Soc. Choice Welf. 6 2 157 165
7. J. Cai T. Gundermann J. Hartmanis L. Hemachandra V. Sewelson K. Wagner G. Wechsung 1988 The boolean hierarchy I: structural properties SIAM J. Comput. 17 6 1232 1252
8. H. Chernoff 1952 A measure of the asymptotic efficiency for tests of a hypothesis based on the sum of observations Ann. Math. Stat. 23 4 493 509
9. L. Chang J. Korsh 1976 Canonical coin changing and greedy solutions J. ACM 23 3 418 422
10. Cormen, T., Leiserson, C., Rivest, R., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press/McGraw-Hill, Cambridge/New York (2001)
11. Conitzer, V., Sandholm, T.: Nonexistence of voting rules that are usually hard to manipulate. In: Proceedings of the 21st National Conference on Artificial Intelligence, pp. 627-634. AAAI Press, Menlo Park (2006) (Pubitemid 44705353)
12. de Borda, J.: Mémoire sur les élections au scrutin. Hist. Acad. Roy. Sci. Ann. 1781 (1784)
13. de Caritat, M.J.A.N.: Marquis de Condorcet. Essai sur l'application de l'analyse à la probabilité des décisions rendues à la pluralité des voix (1785). Facsimile reprint of original published in Paris, 1972, by the Imprimerie Royale
14. Dodgson, C.: A method of taking votes on more than two issues. Pamphlet printed by the Clarendon Press, Oxford, and headed "not yet published" (see the discussions in McLean and Urken (1995) and Black (1958), both of which reprint this paper) (1876)
15. Downey, R.: Parameterized complexity for the skeptic. In: Proceedings of the 18th Annual IEEE Conference on Computational Complexity, pp. 147-168. IEEE Computer Society, Los Alamitos (2003)
16. Downey, R., Fellows, M.: Parameterized Complexity. Springer, Berlin (1999)
17. Erdélyi, G., Hemaspaandra, L., Rothe, J., Spakowski, H.: On approximating optimal weighted lobbying, and frequency of correctness versus average-case polynomial time. Technical Report TR-914, Department of Computer Science, University of Rochester, Rochester, NY (March 2007)
18. Faliszewski, P., Hemaspaandra, E., Hemaspaandra, L.: The complexity of bribery in elections. In: Proceedings of the 21st National Conference on Artificial Intelligence, pp. 641-646. AAAI Press, Menlo Park (2006a) (Pubitemid 44705355)
19. Faliszewski, P., Hemaspaandra, E., Hemaspaandra, L.: How hard is bribery in elections? Technical Report TR-895, Department of Computer Science, University of Rochester, Rochester, NY, April 2006. Revised (September 2006b)
20. Faliszewski, P., Hemaspaandra, E., Hemaspaandra, L., Rothe, J.: Llull and Copeland voting broadly resist bribery and control. In: Proceedings of the 22nd National Conference on Artificial Intelligence, pp. 724-730. AAAI Press, Menlo Park (2007) (Pubitemid 350149656)
21. Goldberg, A., Marchetti-Spaccamela, A.: On finding the exact solution of a zero-one knapsack problem. In: Proceedings of the 16th ACM Symposium on Theory of Computing, pp. 359-368. ACM, New York (1984)
22. G. Hägele F. Pukelsheim 2001 The electoral writings of Ramon Llull Stud. Lulliana 41 97 3 38
23. L. Hemachandra 1989 The strong exponential hierarchy collapses J. Comput. Syst. Sci. 39 3 299 322
24. Hemaspaandra, E., Hemaspaandra, L.: Computational politics: electoral systems. In: Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science. Lecture Notes in Computer Science, vol. 1893, pp. 64-83. Springer, Berlin (2000)
25. E. Hemaspaandra L. Hemaspaandra J. Rothe 1997 Exact analysis of Dodgson elections: Lewis Carroll's 1876 voting system is complete for parallel access to NP J. ACM 44 6 806 825 (Pubitemid 127628552)
26. E. Hemaspaandra H. Spakowski J. Vogel 2005 The complexity of Kemeny elections Theor. Comput. Sci. 349 3 382 391
27. Homan, C., Hemaspaandra, L.: Guarantees for the success frequency of an algorithm for finding Dodgson-election winners. In: Proceedings of the 31st International Symposium on Mathematical Foundations of Computer Science. Lecture Notes in Computer Science, vol. 4162, pp. 528-539. Springer, Berlin (2006) (Pubitemid 44577943)
28. Impagliazzo, R.: A personal view of average-case complexity. In: Proceedings of the 10th Structure in Complexity Theory Conference, pp. 134-147. IEEE Computer Society, Los Alamitos (1995)
29. J. Kadin 1988 The polynomial time hierarchy collapses if the boolean hierarchy collapses SIAM J. Comput. 17 6 1263 1282 Erratum appears in the same journal 20(2), 404
30. Kaporis, A., Kirousis, L., Lalas, E.: The probabilistic analysis of a greedy satisfiability algorithm. In: Proceedings of the 10th Annual European Symposium on Algorithms. Lecture Notes in Computer Science, vol. 2461, pp. 574-585. Springer, Berlin (2002)
31. H. Lenstra Jr. 1983 Integer programming with a fixed number of variables Math. Oper. Res. 8 4 538 548
32. L. Levin 1986 Average case complete problems SIAM J. Comput. 15 1 285 286 (Pubitemid 16477196)
33. McCabe-Dansted, J., Pritchard, G., Slinko, A.: Approximability of Dodgson's rule. In: Endriss, U., Lang, J. (eds.) Proceedings of the 1st International Workshop on Computational Social Choice, pp. 331-344. Universiteit van Amsterdam (2006). Available online at staff.science.uva.nl/∼ulle/ COMSOC-2006/proceedings.html
34. McLean, I., Urken, A.: Classics of Social Choice. University of Michigan Press, Ann Arbor (1995)
35. E. Nanson 1882 Methods of election Trans. Proc. Roy. Soc. Vic. 19 197 240
36. Niedermeier, R.: Invitation to fixed-parameter algorithms. Habilitation thesis, University of Tübingen (2002)
37. A. Procaccia J. Rosenschein 2007 Junta distributions and the average-case complexity of manipulating elections J. Artif. Intell. Res. 28 157 181 (Pubitemid 46790302)
38. Protasi, M., Talamo, M.: A new probabilistic model for the study of algorithmic properties of random graph problems. In: Proceedings of the 4th Conference on Fundamentals of Computation Theory. Lecture Notes in Computer Science, vol. 158, pp. 360-367. Springer, Berlin (1983)
39. Papadimitriou, C., Zachos, S.: Two remarks on the power of counting. In: Proceedings of the 6th GI Conference on Theoretical Computer Science. Lecture Notes in Computer Science, vol. 145, pp. 269-276. Springer, Berlin (1983)
40. G. Raffaelli M. Marsili 2005 Statistical mechanics model for the emergence of consensus Phys. Rev. E 72 1 016114
41. J. Rothe H. Spakowski J. Vogel 2003 Exact complexity of the winner problem for Young elections Theory Comput. Syst. 36 4 375 386 (Pubitemid 36913064)
42. Sankoff, D., Kruskal, J. (eds.): Time Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Computation. Addison-Wesley, Reading (1983)
43. P. Slavik 1997 A tight analysis of the greedy algorithm for set cover J. Algorithms 25 2 237 254 (Pubitemid 127451763)
44. D. Spielman S. Teng 2004 Smoothed analysis: Why the simplex algorithm usually takes polynomial time J. ACM 51 3 385 463
45. p -completeness: A classical approach for new results. In: Proceedings of the 20th Conference on Foundations of Software Technology and Theoretical Computer Science. Lecture Notes in Computer Science, vol. 1974, pp. 348-360. Springer, Berlin (2000) (Pubitemid 33209793)
46. Spakowski, H., Vogel, J.: The complexity of Kemeny's voting system. In: Proceedings of the Workshop Argentino de Informática Teórica. Anales Jornadas Argentinas de Informática e Investigación Operativa, vol. 30, pp. 157-168. SADIO (2001)
47. T. Tideman 1987 Independence of clones as a criterion for voting rules Soc. Choice Welf. 4 3 185 206
48. Trevisan, L.: Lecture notes on computational complexity. www.cs.berkeley.edu/~luca/notes/complexitynotes02.pdf (Lecture 12) (2002)
49. K. Wagner 1987 More complicated questions about maxima and minima, and some closures of NP Theor. Comput. Sci. 51 1-2 53 80 (Pubitemid 18499449)
50. K. Wagner 1990 Bounded query classes SIAM J. Comput. 19 5 833 846
51. Wang, J.: Average-case computational complexity theory. In: Hemaspaandra, L., Selman, A. (eds.) Complexity Theory Retrospective II, pp. 295-328. Springer, Berlin (1997a)
52. Wang, J.: Average-case intractable NP problems. In: Du, D., Ko, K. (eds.) Advances in Languages, Algorithms, and Complexity, pp. 313-378. Kluwer Academic, Dordrecht (1997b)