Ambiguity in electoral competition.

L'article propose une théorie de la compétition électorale ambigüe. Une plate-forme est ambigüe si les votants peuvent l'interpréter de différentes manières. Une telle plate-forme met plus ou moins de poids sur sur les différentes options possibles de sorte qu'elle est plus ou moins facilement interprétée comme une politique ou une autre. On fait l'hypothèse que les partis politiques peuvent contrôler exactement leurs plate-formes mais ne peuvent pas cibler celles-ci vers les votants individuellement. Chaque électeur vote d'après son interprétation des plate-formes des partis mais est averse à l'ambiguité. On montre que ce jeu de compétition électorale n'a pas d'équilibre de Nash. Cependant ses stratégies max-min sont les stratégies optimales du jeu Downsien en stratégies mixtes. De plus, si les partis se comportent de manière suffisament prudente par rapport à l'aversion pour l'ambiguité des électeurs, ces mêmes stratégies forment un équilibre.Compétition électorale;Ambigüité;Comportement prudent;Jeux à somme nulle

On beta-Plurality Points in Spatial Voting Games

Let $V$ be a set of $n$ points in $\mathbb{R}^d$, called voters. A point $p\in \mathbb{R}^d$ is a plurality point for $V$ when the following holds: for every $q\in\mathbb{R}^d$ the number of voters closer to $p$ than to $q$ is at least the number of voters closer to $q$ than to $p$. Thus, in a vote where each $v\in V$ votes for the nearest proposal (and voters for which the proposals are at equal distance abstain), proposal $p$ will not lose against any alternative proposal $q$. For most voter sets a plurality point does not exist. We therefore introduce the concept of $\beta$-plurality points, which are defined similarly to regular plurality points except that the distance of each voter to $p$ (but not to $q$) is scaled by a factor $\beta$, for some constant $0<\beta\leq 1$. We investigate the existence and computation of $\beta$-plurality points, and obtain the following. * Define \beta^*_d := \sup \{ \beta : \text{any finite multiset V$in$\mathbb{R}^d$admits a$\beta-plurality point} \}. We prove that $\beta^*_2 = \sqrt{3}/2$, and that $1/\sqrt{d} \leq \beta^*_d \leq \sqrt{3}/2$ for all $d\geq 3$. * Define \beta(p, V) := \sup \{ \beta : \text{p$is a$\beta$-plurality point for$V}\}. Given a voter set $V \in \mathbb{R}^2$, we provide an algorithm that runs in $O(n \log n)$ time and computes a point $p$ such that $\beta(p, V) \geq \beta^*_2$. Moreover, for $d\geq 2$ we can compute a point $p$ with $\beta(p,V) \geq 1/\sqrt{d}$ in $O(n)$ time. * Define \beta(V) := \sup \{ \beta : \text{V$admits a$\beta-plurality point}\}. We present an algorithm that, given a voter set $V$ in $\mathbb{R}^d$, computes an $(1-\varepsilon)\cdot \beta(V)$ plurality point in time $O(\frac{n^2}{\varepsilon^{3d-2}} \cdot \log \frac{n}{\varepsilon^{d-1}} \cdot \log^2 \frac {1}{\varepsilon})$.Comment: 21 pages, 10 figures, SoCG'2

Voting Equilibria in Multi-candidate Elections

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 indierences, as may arise in voting subgames of citizen-candidate 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 Spatial Analysis of Elections and Committees: Four Decades of Research

It has been more than thirty five years since the publication of Downs's (1957) seminal volume on elections and spatial theory and more than forty since Black and Newing (1951) offered their analysis of majority rule and committees. Thus, in response to the question "What have we accomplished since then?" it is not unreasonable to suppose that the appropriate answer would be "a great deal." Unfortunately, reality admits of only a more ambiguous response

Formal Models of Elections and Political Bargaining

The key theoretical idea in this paper is that activist groups contribute resources to their favored parties in response to policy concessions from the parties. These resources are then used by a party to enhance the leader’s valence — the electoral perception of the quality of the party leader. The equilibrium result is that parties, in order to maximize vote share, will balance a centripetal electoral force against a centrifugal activist effect. Under proportional electoral rule, there need be no pressure for activist groups to coalesce, leading to multiple political parties. Under plurality rule, however, small parties face the possibility of extinction. An activist group linked to a small party in such a polity has little expectation of influencing government policy. The paper illustrates these ideas by considering recent elections in Turkey, Britain and the United States, as well as a number of European polities.Election, plurality rule, proportional representation, activist groups

Party Formation and Coalitional Bargaining in a Model of Proportional Representation

We study a game theoretic model of a parliamentary democracy under proportional representation where `citizen candidates' form parties, voting occurs and governments are formed. We study the coalition governments that emerge as functions of the parties' seat shares, the size of the rents from holding office and their ideologies. We show that governments may be minimal winning, minority or surplus. Moreover, coalitions may be `disconnected'. We then look at how the coalition formation game affects the incentives for party formation. Our model explains the diverse electoral outcomes seen under proportional representation and integrates models of political entry with models of coalitional bargaining.Proportional representation, Party formation, Coalitions

Combinatorial Voting

We study elections that simultaneously decide multiple issues, where voters have independent private values over bundles of issues. The innovation is in considering nonseparable preferences, where issues may be complements or substitutes. Voters face a political exposure problem: the optimal vote for a particular issue will depend on the resolution of the other issues. Moreover, the probabilities that the other issues will pass should be conditioned on being pivotal. We prove that equilibrium exists when distributions over values have full support or when issues are complements. We then study large elections with two issues. There exists a nonempty open set of distributions where the probability of either issue passing fails to converge to either 1 or 0 for all limit equilibria. Thus, the outcomes of large elections are not generically predictable with independent private values, despite the fact that there is no aggregate uncertainty regarding fundamentals. While the Condorcet winner is not necessarily the outcome of a multi-issue election, we provide sufficient conditions that guarantee the implementation of the Condorcet winner. © 2012 The Econometric Society

Campaign Rhetoric and the Hide-and-Seek Game

. . .