Abstract
We investigate how robust are results of committee elections to small changes in the input preference orders, depending on the voting rules used. We find that for typical rules the effect of making a single swap of adjacent candidates in a single preference order is either that (1) at most one committee member can be replaced, or (2) it is possible that the whole committee can be replaced. We also show that the problem of computing the smallest number of swaps that lead to changing the election outcome is typically \({\mathrm {NP}}\)-hard, but there are natural \({\mathrm {FPT}}\) algorithms. Finally, for a number of rules we assess experimentally the average number of random swaps necessary to change the election result.
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Notes
- 1.
Indeed, the formal definition is more complex due to taking care of ties.
- 2.
We also construct somewhat artificial rules with robustness levels between 1 and k.
- 3.
We found STV to be computationally too intensive for our experiments, so we used a simplified variant where all internal ties are broken lexicographically. We omit NED for similar reasons (but we expect the results to be similar as for k-Copeland).
References
Aziz, H., Elkind, E., Faliszewski, P., Lackner, M., Skowron, P.: The Condorcet principle for multiwinner elections: from shortlisting to proportionality. arXiv preprint arXiv:1701.08023 (2017)
Barberà, S., Coelho, D.: How to choose a non-controversial list with \(k\) names. Soc. Choice Welf. 31(1), 79–96 (2008)
Betzler, N., Slinko, A., Uhlmann, J.: On the computation of fully proportional representation. J. Artif. Intell. Res. 47, 475–519 (2013)
Blom, M., Stuckey, P., Teague, V.: Towards computing victory margins in STV elections. arXiv preprint arXiv:1703.03511 (2017)
Bredereck, R., Faliszewski, P., Kaczmarczyk, A., Niedermeier, R., Skowron, P., Talmon, N.: Robustness among multiwinner voting rules. arXiv preprint arXiv:1707.01417 (2017)
Caragiannis, I., Hemaspaandra, E., Hemaspaandra, L.: Dodgson’s rule and Young’s rule. In: Brandt, F., Conitzer, V., Endriss, U., Lang, J., Procaccia, A.D. (eds.) Handbook of Computational Social Choice. Cambridge University Press, Cambridge (2016)
Cary, D.: Estimating the margin of victory for instant-runoff voting. Presented at EVT/WOTE-2011, August 2011
Chamberlin, B., Courant, P.: Representative deliberations and representative decisions: proportional representation and the Borda rule. Am. Polit. Sci. Rev. 77(3), 718–733 (1983)
Coelho, D.: Understanding, evaluating and selecting voting rules through games and axioms. Ph.D. thesis, Universitat Autònoma de Barcelona (2004)
Conitzer, V., Rognlie, M., Xia, L.: Preference functions that score rankings and maximum likelihood estimation. In: Proceedings of IJCAI-2009, pp. 109–115, July 2009
Cygan, M., Fomin, F.V., Kowalik, Ł., Lokshtanov, D., Marx, D., Pilipczuk, M., Pilipczuk, M., Saurabh, S.: Parameterized Algorithms. Springer, Heidelberg (2015)
Elkind, E., Faliszewski, P., Skowron, P., Slinko, A.: Properties of multiwinner voting rules. Social Choice Welf. 48(3), 599–632 (2017)
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). doi:10.1007/978-3-642-04645-2_27
Faliszewski, P., Skowron, P., Slinko, A., Talmon, N.: Committee scoring rules: axiomatic classification and hierarchy. In: Proceedings of IJCAI-2016, pp. 250–256 (2016)
Gehrlein, W.: The Condorcet criterion and committee selection. Math. Soc. Sci. 10(3), 199–209 (1985)
Kaczmarczyk, A., Faliszewski, P.: Algorithms for destructive shift bribery. In: Proceedings of AAMAS-2016, pp. 305–313 (2016)
Kamwa, E.: On stable voting rules for selecting committees. J. Math. Econ. 70, 36–44 (2017)
Lenstra Jr., H.: Integer programming with a fixed number of variables. Math. Oper. Res. 8(4), 538–548 (1983)
Lu, T., Boutilier, C.: Budgeted social choice: from consensus to personalized decision making. In: Proceedings of IJCAI-2011, pp. 280–286 (2011)
Magrino, T., Rivest, R., Shen, E., Wagner, D.: Computing the margin of victory in IRV elections. Presented at EVT/WOTE-2011, August 2011
Mattei, N., Walsh, T.: Preflib: a library for preferences. In: Proceedings of the 3rd International Conference on Algorithmic Decision Theory, pp. 259–270 (2013)
McGarvey, D.: A theorem on the construction of voting paradoxes. Econometrica 21(4), 608–610 (1953)
Procaccia, A., Rosenschein, J., Zohar, A.: On the complexity of achieving proportional representation. Soc. Choice Welf. 30(3), 353–362 (2008)
Sekar, S. Sikdar., Xia, L.: Condorcet consistent bundling with social choice. In: Proceedings of AAMAS-2017, May 2017
Shiryaev, D., Yu, L., Elkind, E.: On elections with robust winners. In: Proceedings of AAMAS-2013, pp. 415–422 (2013)
Xia, L.: Computing the margin of victory for various voting rules. In: Proceedings of EC-2012, pp. 982–999, June 2012
Acknowledgments
We are grateful to anonymous SAGT reviewers for their useful comments. R. Bredereck was supported by the DFG fellowship BR 5207/2. P. Faliszewski was supported by the NCN, Poland, under project 2016/21/B/ST6/01509. A. Kaczmarczyk was supported by the DFG project AFFA (BR 5207/1 and NI 369/15). P. Skowron was supported by a Humboldt Fellowship. N. Talmon was supported by an I-CORE ALGO fellowship.
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Bredereck, R., Faliszewski, P., Kaczmarczyk, A., Niedermeier, R., Skowron, P., Talmon, N. (2017). Robustness Among Multiwinner Voting Rules. In: Bilò, V., Flammini, M. (eds) Algorithmic Game Theory. SAGT 2017. Lecture Notes in Computer Science(), vol 10504. Springer, Cham. https://doi.org/10.1007/978-3-319-66700-3_7
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