Abstract
The Gibbard-Satterthwaite theorem states that no unanimous and non-dictatorial voting rule is strategyproof. We revisit voting rules and consider a weaker notion of strategyproofness called not obvious manipulability that was proposed by Troyan and Morrill (2020). We identify several classes of voting rules that satisfy this notion. We also show that several voting rules including k-approval fail to satisfy this property. We characterize conditions under which voting rules are obviously manipulable. One of our insights is that certain rules are obviously manipulable when the number of alternatives is relatively large compared to the number of voters. In contrast to the Gibbard-Satterthwaite theorem, many of the rules we examined are not obviously manipulable. This reflects the relatively easier satisfiability of the notion and the zero information assumption of not obvious manipulability, as opposed to the perfect information assumption of strategyproofness. We also present algorithmic results for computing obvious manipulations and report on experiments.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Arrow, K.: A difficulty in the concept of social welfare. J. Polit. Econ. 58, 328–346 (1950)
Black, D.: Borda, condorcet and laplace. In: The Theory of Committees and Elections, chap. 18, pp. 156–162. Springer, Dordrecht (1986). https://doi.org/10.1007/978-94-009-4225-7_18
Carroll, G.: A quantitative approach to incentives : application to voting rules (2011)
Chisholm, H.: Vote and voting. In: Encyclopaedia Britannica, p. 216 (1911)
Conitzer, V., Walsh, T.: Barriers to manipulation in voting. In: Brandt, F., Conitzer, V., Endriss, U., Lang, J., Procaccia, A.D. (eds.) Handbook of Computational Social Choice, chap. 6. Cambridge University Press (2016)
Conitzer, V., Walsh, T., Xia, L.: Dominating manipulations in voting with partial information. In: Proceedings of the 25th AAAI Conference (2011)
Faliszewski, P., Procaccia, A.D.: AI’s war on manipulation: are we winning? AI Mag. 31, 53–64 (2010)
Favardin, P., Lepelley, D., Serais, J.: Borda rule, copeland method and strategic manipulation. Rev. Econ. Des. 7(2), 213–228 (2002). https://doi.org/10.1007/s100580200073
Fraenkel, J., Grofman, B.: The Borda count and its real-world alternatives: comparing scoring rules in Nauru and Slovenia. Aust. J. Polit. Sci. 49(2), 186–205 (2014)
Gibbard, A.: Manipulation of voting schemes: a general result. Econometrica 41(4), 587–601 (1973)
Li, S.: Obviously strategy-proof mechanisms. Am. Econ. Rev. 107, 3257–3287 (2017)
Meir, R.: Strategic voting. Synth. Lect. Artif. Intell. Mach. Learn. 13, 1–167 (2018)
Niou, E.: Strategic voting under plurality and runoff rules. J. Theor. Polit. 13(2), 209–227 (2001)
Nitzan, S.: The vulnerability of point-voting schemes to preference variation and strategic manipulation. Public Choice 47, 349–370 (1985). https://doi.org/10.1007/BF00127531
Ortega, J.: Obvious manipulations in cake-cutting. CoRR abs/1908.02988 (2019)
Peleg, B.: A note on manipulability of large voting schemes. Theor. Decis. 11(4), 401–412 (1979). https://doi.org/10.1007/BF00139450
Reilly, B.: Social choice in the south seas: electoral innovation and the Borda count in the Pacific Island countries. Int. Polit. Sci. Rev. 23(4), 355–372 (2002)
Satterthwaite, M.A.: Strategy-proofness and arrow’s conditions: existence and correspondence theorems for voting procedures and social welfare functions. J. Econ. Theor. 10, 187–217 (1975)
Slinko, A., White, S.: Non-dictatorial social choice rules are safely manipulable. In: COMSOC 2008, pp. 403–413 (2008)
Slinko, A., White, S.: Is it ever safe to vote strategically? Soc. Choice Welfare 43, 403–427 (2014)
Taylor, A.D.: Social Choice and the Mathematics of Manipulation. Cambridge University Press, Cambridge (2005)
Tideman, N.: The single transferable vote. J. Econ. Perspect. 9(1), 27–38 (1995)
Troyan, P., Morrill, T.: Obvious manipulations. J. Econ. Theor. 185, 104970 (2020)
Wilson, M.C., Reyhani, R.: The probability of safe manipulation. In: COMSOC 2010 (2010)
Xia, L., Zuckerman, M., Procaccia, A.D., Conitzer, V., Rosenschein, J.S.: Complexity of unweighted coalitional manipulation under some common voting rules. In: Proceedings of the 21st IJCAI, pp. 348–353 (2009)
Zuckerman, M., Procaccia, A.D., Rosenschein, J.S.: Algorithms for the coalitional manipulation problem. Artif. Intell. 173(2), 392–412 (2009)
Acknowledgments
The authors thanks Anton Baychkov, Barton Lee and the anonymous reviewers of ADT 2021 for useful feedback.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Aziz, H., Lam, A. (2021). Obvious Manipulability of Voting Rules. In: Fotakis, D., RÃos Insua, D. (eds) Algorithmic Decision Theory. ADT 2021. Lecture Notes in Computer Science(), vol 13023. Springer, Cham. https://doi.org/10.1007/978-3-030-87756-9_12
Download citation
DOI: https://doi.org/10.1007/978-3-030-87756-9_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-87755-2
Online ISBN: 978-3-030-87756-9
eBook Packages: Computer ScienceComputer Science (R0)