THE COMPLEXITY OF MANIPULATING κ-APPROVAL ELECTIONS

Andrew Lin

Abstract

An important problem in computational social choice theory is the complexity of undesirable behavior among agents, such as control, manipulation, and bribery in election systems, which are tempting at the individual level but disastrous for the agents as a whole. Creating election systems where the determination of such strategies is difficult is thus an important goal. An interesting set of elections is that of scoring protocols. Previous work in this area has demonstrated the complexity of misuse in cases involving a fixed number of candidates, and of specific election systems on unbounded number of candidates such as Borda. In contrast, we take the first step in generalizing the results of computational complexity of election misuse to cases of infinitely many scoring protocols on an unbounded number of candidates. We demonstrate the worst-case complexity of various problems in this area, by showing they are either polynomial-time computable, NP-hard, or polynomial-time equivalent to another problem of interest. We also demonstrate a surprising connection between manipulation in election systems and some graph theory problems.

References

  1. Anstee, R. (1987). A polynomial algorithm for bmatchings: an alternative approach. Information Processing Letters, pages 554-559.
  2. Bartholdi, J., Tovey, C., and Trick, M. (1989). The computational difficulty of manipulating an election. Social Choice and Welfare, pages 227-241.
  3. Bartholdi, J., Tovey, C., and Trick, M. (1992). How hard is it to control an election? Mathematical and Computer Modelling, pages 27-40.
  4. Brams, S. and Herschbach, D. (2001). The science of elections. In Science, page 1449.
  5. Brelsford, E., Faliszewski, P., Hemaspaandra, E., Schnoor, H., and Schnoor, I. (2008). Approximability of manipulating elections. In Proceedings of the Twenty-Third AAAI Conference on Artificial Intelligence, pages 44- 49.
  6. Conitzer, V., Lang, J., and Sandholm, T. (2002). When are elections with few candidates hard to manipulate? Journal of the ACM, Volume 54, Issue 3, Article 14, pages 1-33.
  7. Cunningham, W. and III, A. M. (1978). A primal algorithm for optimum matching. Polyhedral Combinatorics, Mathematical Programming Study 8, pages 50-72.
  8. Duggan, J. and Schwartz, T. (2000). Strategic manipulability without resoluteness or shared beliefs: Gibbardsatterthwaite generalized. Social Choice and Welfare, pages 85-93.
  9. Faliszewski, P., Hemaspaandra, E., and Hemaspaandra, L. (2006). How hard is bribery in elections. Journal of AI Research, Volume 35, pages 485-532.
  10. Faliszewski, P., Hemaspaandra, E., and Schnoor, H. (2008). Copeland voting: Ties matter. In Proceedings of the 7th International Conference on Autonomous Agents and Multiagent Systems, pages 983-990.
  11. Friedgut, E., Kalai, G., and Nisan, N. (2008). Elections can be manipulated often. In Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science, pages 243-249.
  12. Gabow, H. (1983). An efficient reduction technique for degree-constrained subgraph and bidirected network flow problems. In Proceedings of the Fifteenth Annual ACM Symposium on Theory of Computation, pages 448-456.
  13. Garey, M. and Johnson, D. (1979). Computers and intractability: A guide to the theory of NPcompleteness. W.H. Freeman and Company.
  14. Gibbard, A. (1973). Manipulation of voting schemes: a general result. Econometrica, pages 587-601.
  15. Hemaspaandra, E. and Hemaspaandra, L. (2007). Dichotomy for voting systems. Journal of Computer and System Sciences, pages 73-83.
  16. Hemaspaandra, E., Hemaspaandra, L., and Rothe, J. (2007). Anyone but him: The complexity of precluding an alternative. Artificial Intelligence, pages 255-285.
  17. Karp, R. (1972). Reducibility among combinatorial problems. Complexity of Computer Computations, pages 85-103.
  18. Lin, A. (2010). The complexity of manipulating k-approval elections,arxiv:1005.4159.
  19. Procaccia, A. (2009). Personal communication.
  20. Pulleyblank, W. (1973). Faces of matching polyhedra. Ph.D. Thesis, Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario.
  21. Russell, N. (2007). Complexity of control of Borda count elections. Rochester Institute of Technology.
  22. Satterthwaite, M. (1975). Vote elicitation: Strategyproofness and arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions. Journal of Economic Theory 10 (April 1975), pages 187-217.
  23. Schrijver, A. (2003). Combinatorial optimization. Springer.
  24. Walsh, T. (2009). Where are the really hard manipulation problems? the phase transition in manipulating the veto rule. In International Joint Conference on Artificial intelligence, pages 324-329.
Download


Paper Citation


in Harvard Style

Lin A. (2011). THE COMPLEXITY OF MANIPULATING κ-APPROVAL ELECTIONS . In Proceedings of the 3rd International Conference on Agents and Artificial Intelligence - Volume 2: ICAART, ISBN 978-989-8425-41-6, pages 212-218. DOI: 10.5220/0003168802120218


in Bibtex Style

@conference{icaart11,
author={Andrew Lin},
title={THE COMPLEXITY OF MANIPULATING κ-APPROVAL ELECTIONS},
booktitle={Proceedings of the 3rd International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,},
year={2011},
pages={212-218},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003168802120218},
isbn={978-989-8425-41-6},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 3rd International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,
TI - THE COMPLEXITY OF MANIPULATING κ-APPROVAL ELECTIONS
SN - 978-989-8425-41-6
AU - Lin A.
PY - 2011
SP - 212
EP - 218
DO - 10.5220/0003168802120218