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.
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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.
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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.
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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
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DOI: https://doi.org/10.1007/978-3-319-23114-3_27
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