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Strategic Voting and Strategic Candidacy

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Advances in Collective Decision Making

Part of the book series: Studies in Choice and Welfare ((WELFARE))

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Abstract

Models of strategic candidacy analyze the incentives of candidates to run in an election. Most work on this topic assumes that strategizing only takes place among candidates, whereas voters vote truthfully. In this article, we extend the analysis to also include strategic behavior on the part of the voters. We also study cases where only candidates or only voters are strategic. We consider a setting in which both voters and candidates have single-peaked preferences and the voting rule is majority-consistent, and we analyze the type of strategic behavior that is required in order to guarantee desirable voting outcomes.

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Notes

  1. 1.

    Manipulating the result of an election by not participating in the voting process is reminiscent of the “no-show paradox” (Fishburn & Brams, 1983; Moulin, 1988), which is concerned with voters’ participation incentives.

  2. 2.

    When the number of voters is even, a Condorcet winner is not guaranteed to exist even if preferences are single-peaked. However, in this case there will always be at least one weak Condorcet winner. The results in Sect. 5 extend to the setting with an even number of voters, with the role of the Condorcet winner taken over by one of the weak Condorcet winners, namely the one in whose favor the tie is broken.

  3. 3.

    For results without this assumption, see, e.g., Dutta et al. (2001, 2002).

  4. 4.

    This assumption is common in the literature on strategic candidacy, where it is often referred to as self-preference (Dutta et al., 2001, 2002) or self-supporting candidate preferences (Lang et al., 2013; Obraztsova et al., 2015, 2020; Polukarov et al., 2015). Without it, scenarios can arise where no candidate has an incentive to run.

  5. 5.

    If \(C(s)=\emptyset \), define \(o_f(s)= \top \). We assume that each candidate prefers herself to the outcome \(\top \). This assumption ensures that at least one candidate will run whenever candidates act strategically.

  6. 6.

    Subgame-perfect equilibria are guaranteed to exist if one allows for mixed strategies and extends the preferences of players to the set of all probability distributions over \(C \cup \{\top \}\) in an appropriate way.

  7. 7.

    If the order is not part of the input, it can be computed in polynomial time (Bartholdi & Trick, 1986; Escoffier et al., 2008).

  8. 8.

    We often simplify examples with single-peaked preference profiles by specifying the peak distribution only. This piece of information is clearly sufficient to identify both the Condorcet winner and, in the absence of ties, the plurality winner.

  9. 9.

    In particular, note that Theorem 1 does not make any assumptions on the preferences of candidates (other than self-supportedness).

  10. 10.

    Sertel and Sanver (2004) prove a similar result in the (standard) setting where all candidates are assumed to run. A further strengthening of part (ii) of Theorem 1 was pointed out to us by François Durand: instead of requiring that voters play a strong V-equilibrium for every subset of running candidates, it is sufficient to require voters to play a strong V-equilibrium only in those subgames that actually allow strong V-equilibria (and to not make any assumptions on voter behavior otherwise).

  11. 11.

    Veto does not only violate majority-consistency, but also the weaker property defined after Theorem 1.

  12. 12.

    Note that the voter v with \({\text {top}}(R_v)=a\) plays a weakly dominated strategy, because c is her least preferred alternative. This can be avoided by introducing a fourth candidate d with \(c \mathrel {\triangleleft } d\) and \(V_R(d)=\emptyset \).

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Acknowledgements

A previous version of this article has appeared in the Proceedings of the 29th AAAI Conference on Artificial Intelligence (Brill & Conitzer, 2015). We would like to thank John Duggan, François Durand, Alexander Mayer, and the anonymous reviewers for helpful comments. This work was supported by NSF and ARO under grants CCF-1101659, IIS-0953756, CCF-1337215, W911NF-12-1-0550, and W911NF-11-1-0332, by the Deutsche Forschungsgemeinschaft under grant BR 4744/2-1, and by a Feodor Lynen research fellowship of the Alexander von Humboldt Foundation.

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Brill, M., Conitzer, V. (2023). Strategic Voting and Strategic Candidacy. In: Kurz, S., Maaser, N., Mayer, A. (eds) Advances in Collective Decision Making. Studies in Choice and Welfare. Springer, Cham. https://doi.org/10.1007/978-3-031-21696-1_5

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