This paper examines competition in the standard one-dimensional Downsian model of two-candidate elections, but where one candidate A enjoys an advantage over the other candidate D. Voters' preferences are Euclidean, but any voter will vote for candidate A over candidate D unless D is closer to her ideal point by some xed distance . The location of the median voter's ideal point is uncertain, and its distribution is commonly known by both candidates. The candidates simultaneously choose locations to maximize the probability of victory. Pure strategy equilibria often fails to exist in this model, except under special conditions about and the distribution of the median ideal point. We solve for the essentially unique symmetric mixed equilibrium, show that candidate A adopts more moderate policies than candidate D, and obtain some comparative statics results about the probability of victory and the expected distance between the two candidates' policies.

Many have observed that political candidates running for election are often purposefully expressing themselves in vague and ambiguous terms. In this paper we provide a simple formal model of this phenomenon. We model the electoral competition between two candidates as a two-stage game. In the first stage of the game two candidates simultaneously choose their ideologies, and in the second stage they simultaneously choose their level of ambiguity. Our results show that ambiguity, although disliked by voters, may be sustained in equilibrium. The introduction of ambiguity as a strategic choice variable for the candidates can also serve to explain why candidates with the same electoral objectives end up "separating," that is, assuming different ideological positions.

International audiencePeople may be surprised by noticing certain regularities that hold in existing knowledge they have had for some time. That is, they may learn without getting new factual information. We argue that this can be partly explained by computational complexity. We show that, given a database, finding a small set of variables that obtain a certain value of R^2 is computationally hard, in the sense that this term is used in computer science. We discuss some of the implications of this result and of fact-free learning in general

This paper examines competition in the standard one-dimensional Downsian model of two-candidate elections, but where one candidate A enjoys an advantage over the other candidate D. Voters' preferences are Euclidean, but any voter will vote for candidate A over candidate D unless D is closer to her ideal point by some xed distance. The location of the median voter's ideal point is uncertain, and its distribution is commonly known by both candidates. The candidates simultaneously choose locations to maximize the probability of victory. Pure strategy equilibria often fails to exist in this model, except under special conditions about and the distribution of the median ideal point. We solve for the essentially unique symmetric mixed equilibrium, show that candidate A adopts more moderate policies than candidate D, and obtain some comparative statics results about the probability of victory and the expected distance between the two candidates' policies.

We study the set of envy-free allocations for economies with indivisible objects and quasi-linear utility functions. We characterize the minimal amount of money necessary for its nonemptiness when negative distributions of money are not allowed. We also find that, when this is precisely the available amount of money, there is a unique way to combine objects and money such that these bundles may form an envy-free allocation. Based on this property, we describe a solution to the envy-free selection problem following a pseudo-egalitarian criterion. This solution coincides with the "Money Rawlsian Solution" proposed by Alkan et al. (1991).