Multiwinner Candidacy Games (original) (raw)

Real Candidacy Games: A New Model for Strategic Candidacy

2017

We introduce Real Candidacy Games (RCGs)---a novel strategic candidacy model, where candidates have a continuous range of positions that affect their attractiveness for voters. We also allow candidates to have their own non-trivial preferences over the candidate set. We study RCGs with restricted and unrestricted positioning strategies to establish conditions for Nash Equilibrium (NE) existence. That is, we investigate under what voting rules and tie-breaking schemes, a stable candidate positioning exists. While for several voting rule classes (e.g., Condorcet-Consistent) we obtain positive results, we also show that for some scoring rules there are examples without a NE for an arbitrarily large number of voters.

Electoral competition with an arbitrary number of participants

2011

In this Thesis, we extend "Hotelling's Electoral Competition Game" to fit a political framework. We assume a sequential choice of postition by the players, who represent candidates in an election, an exit choice, and an incumbent effect – that is, only one player can adopt a specific policy on the policy spectrum. We then find that the subgame-perfect Nash-equilibrium in this game seems to be consistent with many findings in politics nowadays and in the past, for example Duverger's Law or results for the behavior of candidates in the US primary elections. A conjecture exists about the subgame-perfect Nash-equilibrium in this game for N players, and two Theorems concerning this conjecture were formulated and proven in this Thesis.

Strategic Candidacy Games with Lazy Candidates

2015

In strategic candidacy games, both voters and candidates have preferences over the set of candidates, and candidates may strategically withdraw from the election in order to manipulate the outcome according to their preferences. In this work, we extend the standard model of strategic candidacy games by observing that candidates may find it costly to run an electoral campaign and may therefore prefer to withdraw if their presence has no effect on the election outcome. We study the Nash equilibria and outcomes of natural best-response dynamics in the resulting class of games, both from a normative and from a computational perspective, and compare them with the Nash equilibria of the standard model.

Voting Equilibria in Multi-candidate Elections

Journal of Public Economic Theory, 2009

We consider a general plurality voting game with multiple candidates, where voter preferences over candidates are exogenously given. In particular, we allow for arbitrary voter indifferences, as may arise in voting subgames of citizencandidate or locational models of elections. We prove that the voting game admits pure strategy equilibria in undominated strategies. The proof is constructive: we exhibit an algorithm, the "best winning deviation" algorithm, that produces such an equilibrium in finite time. A byproduct of the algorithm is a simple story for how voters might learn to coordinate on such an equilibrium.

The complexity of strategic behavior in multi-winner elections

2008

Although recent years have seen a surge of interest in the computational aspects of social choice, no specific attention has previously been devoted to elections with multiple winners, e.g., elections of an assembly or committee. In this paper, we characterize the worst-case complexity of manipulation and control in the context of four prominent multiwinner voting systems, under different formulations of the strategic agent's goal.

Strategic Candidacy and Voting Procedures

Econometrica, 2001

We study the impact of considering the incentives of candidates to strategically affect the outcome of a voting procedure. First we show that every non-dictatorial voting procedure that satisfies unanimity, is open to strategic entry or exit by candidates: there necessarily exists some candidate can affect the outcome by entering or exiting the election, even when they do not win the election. Given that strategic candidacy always matters, we analyze the impact of strategic candidacy effects. We show that the equilibrium set of outcomes of the well-known voting by successive elimination procedure expands in a well-defined way when strategic candidacy is accounted for.

Strategic candidacy for multivalued voting procedures

Journal of Economic Theory, 2004

Dutta et al. (Econometrica 69 (2001) 1013) (Dutta, Jackson, and Le Breton-DJLeB) initiate the study of manipulation of voting procedures by a candidate who withdraws from the election. A voting procedure is candidate stable if this is never possible. We extend the DJLeB framework by allowing: (a) the outcome of the procedure to be a set of candidates; (b) some or all of the voters to have weak preference orderings of the candidates. When there are at least three candidates, any strongly candidate stable voting selection satisfying a weak unanimity condition is characterized by a serial dictatorship. This result generalizes Theorem 4 of DJLeB. r

A broader picture of the complexity of strategic behavior in multi-winner elections

2008

Recent work by Procaccia, Rosenschein and Zohar [14] established some results regarding the complexity of manipulation and control in elections with multiple winners, such as elections of an assembly or committee; that work provided an initial understanding of the topic. In this paper, we paint a more complete picture of the topic, investigating four prominent multi-winner voting rules. First, we characterize the complexity of manipulation and control in these voting rules under various kinds of formalizations of the manipulator's goal. Second, we extend the results about complexity of control to various well-known types of control. This work enhances our comprehension of which multi-winner voting rules should be employed in various settings.

On Coalitional Manipulation for Multiwinner Elections: Shortlisting

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence

Shortlisting of candidates—selecting a group of “best” candidates—is a special case of multiwinner elections. We provide the first in-depth study of the computational complexity of strategic voting for shortlisting based on the most natural and simple voting rule in this scenario, l-Bloc (every voter approves l candidates). In particular, we investigate the influence of several tie-breaking mechanisms (e.g. pessimistic versus optimistic) and group evaluation functions (e.g. egalitarian versus utilitarian) and conclude that in an egalitarian setting strategic voting may indeed be computationally intractable regardless of the tie-breaking rule. We provide a fairly comprehensive picture of the computational complexity landscape of this neglected scenario.