Abstract
It is well known that standard game-theoretic approaches to voting mechanisms lead to a multitude of Nash Equilibria (NE), many of which are counter-intuitive. We focus on truth-biased voters, a model recently proposed to avoid such issues. The model introduces an incentive for voters to be truthful when their vote is not pivotal. This is a powerful refinement, and recent simulations reveal that the surviving equilibria tend to have desirable properties.
However, truth-bias has been studied only within the context of plurality, which is an extreme example of k-approval rules with \(k=1\). We undertake an equilibrium analysis of the complete range of k-approval. Our analysis begins with the veto rule, the other extreme point of k-approval, where each ballot approves all candidates but one. We identify several crucial properties of pure NE for truth-biased veto. These properties show a clear distinction from the setting of truth-biased plurality. We proceed by establishing that deciding on the existence of NE in truth-biased veto is an NP-hard problem. We also characterise a tight (in a certain sense) subclass of instances for which the existence of a NE can be decided in poly-time. Finally, we study analogous questions for general k-approval rules.
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
Notes
- 1.
Unlike regular, non-truth-biased voting games, with truth-bias there are scenarios where there is no Nash equilibrium at all. This has also been shown for plurality.
References
Branzei, S., Caragiannis, I., Morgenstern, J., Procaccia, A.D.: How bad is selfish voting? In: AAAI (2013)
Desmedt, Y., Elkind, E.: Equilibria of plurality voting with abstentions. In: ACM EC, pp. 347–356 (2010)
Dutta, B., Laslier, J.F.: Costless honesty in voting. In: 10th International Meeting of the Society for Social Choice and Welfare, Moscow (2010)
Dutta, B., Sen, A.: Nash implementation with partially honest individuals. Games Econ. Behav. 74(1), 154–169 (2012)
Farquharson, R.: Theory of Voting. Yale University Press, New Haven (1969)
Garey, M.R., Johnson, D.S.: Computers and intractability: a guide to the theory of NP-completeness. Series of Books in the Mathematical Sciences. W. H. Freeman, New York (1979)
Gibbard, A.: Manipulation of voting schemes. Econometrica 41(4), 587–602 (1973)
Laffont, J.J.: Incentives and the allocation of public goods. In: Handbook of Public Economics, vol. 2, chap. 10, pp. 537–569. Elsevier (1987)
Laslier, J.F., Weibull, J.W.: A strategy-proof condorcet jury theorem. Scand. J. Econ. (2012)
Lev, O., Rosenschein, J.S.: Convergence of iterative voting. In: AAMAS, pp. 611–618 (2012)
Meir, R., Polukarov, M., Rosenschein, J.S., Jennings, N.R.: Convergence to equilibria of plurality voting. In: AAAI, pp. 823–828 (2010)
Messner, M., Polborn, M.K.: Miscounts, duverger’s law and duverger’s hypothesis. Technical Report 380, Innocenzo Gasparini Institute for Economic Research, Bocconi University (2011)
Myerson, R.B., Weber, R.J.: A theory of voting equilibria. Am. Polit. Sci. Rev. 87(1), 102–114 (1993)
Obraztsova, S., Markakis, E., Thompson, D.R.M.: Plurality voting with truth-biased agents. In: Vöcking, B. (ed.) SAGT 2013. LNCS, vol. 8146, pp. 26–37. Springer, Heidelberg (2013)
Rabinovich, Z., Obraztsova, S., Lev, O., Markakis, E., Rosenschein, J.S.: Analysis of equilibria in iterative voting schemes. In: Proceedings of the 29th AAAI Conference on Artificial Intelligence (AAAI), pp. 1007–1013. Austin, Texas January 2015
Satterthwaite, M.A.: Strategy-proofness and arrow’s conditions: existence and correspondence theorems for voting procedures and social welfare functions. J. Econ. Theor. 10(2), 187–217 (1975)
Thompson, D.R.M., Lev, O., Leyton-Brown, K., Rosenschein, J.S.: Empirical aspects of plurality election equilibria. In: AAMAS (2013)
Xia, L., Conitzer, V.: Stackelberg voting games: computational aspects and paradoxes. In: AAAI, pp. 805–810 (2010)
Acknowledgements
This research was supported in part by Israel Science Foundation grant #1227/12, Israel Ministry of Science and Technology grant #3-6797, and by Microsoft Research through its PhD Scholarship Programme. It has also been supported by the EU (European Social Fund) and Greek national funds through the Operational Program “Education and Lifelong Learning" of the National Strategic Reference Framework (NSRF) - Research Funding Program: THALES. The work of S. Obraztsova was partially supported by ERC grant #337122 under the EU FP7/2007–2013 and RFFI grant 14-01-00156-a.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Obraztsova, S., Lev, O., Markakis, E., Rabinovich, Z., Rosenschein, J.S. (2015). Beyond Plurality: Truth-Bias in Binary Scoring Rules. In: Walsh, T. (eds) Algorithmic Decision Theory. ADT 2015. Lecture Notes in Computer Science(), vol 9346. Springer, Cham. https://doi.org/10.1007/978-3-319-23114-3_27
Download citation
DOI: https://doi.org/10.1007/978-3-319-23114-3_27
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-23113-6
Online ISBN: 978-3-319-23114-3
eBook Packages: Computer ScienceComputer Science (R0)