Candidate stability and voting correspondences

For each set of candidates at state and each profile of voters' preferences over running candidates a voting corresponsence selects a set of candidates. following Dutta, Jackson and Le Breton (Econometrica 2001) a voting correspondence is candidate stable if a candidate never benefits from withdrawing unilateraly her candidacy. If candidates cannot vote and compare sets of candidates according to their expected utility conditional on some prior probability assessment only dictatorial voting correspondences are candidate stable and unanimous. If the assessments are restricted to be uniform, rules that select the set of best candidates of tww fixed voters are also allowed. We also analyze other domains of preferences fitting extreme attitudes towards risk in which positive results are obtained

CANDIDATE STABILITY AND VOTING CORRESPONDENCES

For each set of candidates at state and each profile of voters' preferences over running candidates a voting corresponsence selects a set of candidates. following Dutta, Jackson and Le Breton (Econometrica 2001) a voting correspondence is candidate stable if a candidate never benefits from withdrawing unilateraly her candidacy. If candidates cannot vote and compare sets of candidates according to their expected utility conditional on some prior probability assessment only dictatorial voting correspondences are candidate stable and unanimous. If the assessments are restricted to be uniform, rules that select the set of best candidates of tww fixed voters are also allowed. We also analyze other domains of preferences fitting extreme attitudes towards risk in which positive results are obtainedVoting Correspondence ; Candidate Stability ; Preferences over Sets

Candidate Stability and Voting Correspondences

We study the incentives of candidates to enter or to exit elections in order to strategically affect the outcome of a voting correspondence. We extend the results of Dutta, Jackson and Le Breton (2000), who only considered single-valued voting procedures by admitting that the outcomes of voting may consist of sets of candidates. We show that, if candidates form their preferences over sets according to Expected Utility Theory and Bayesian updating, every unanimous and non dictatorial voting correspondence violates candidate stability. When candidates are restricted to use even chance prior distributions, only dictatorial or bidictatorial rules are unanimous and candidate stable. We also analyze the implications of using other extension criteria to define candidate stability that open the door to positive results.Candidate Stability, Voting Correspondence, Extension Criterion

Split Cycle: A New Condorcet Consistent Voting Method Independent of Clones and Immune to Spoilers

We propose a Condorcet consistent voting method that we call Split Cycle. Split Cycle belongs to the small family of known voting methods that significantly narrow the choice of winners in the presence of majority cycles while also satisfying independence of clones. In this family, only Split Cycle satisfies a new criterion we call immunity to spoilers, which concerns adding candidates to elections, as well as the known criteria of positive involvement and negative involvement, which concern adding voters to elections. Thus, in contrast to other clone-independent methods, Split Cycle mitigates both "spoiler effects" and "strong no show paradoxes."Comment: 71 pages, 15 figures. Added a new explanation of Split Cycle in Section 1, updated the caption to Figure 2, the discussion in Section 3.3, and Remark 4.11, and strengthened Proposition 6.20 to Theorem 6.20 to cover single-voter resolvability in addition to asymptotic resolvability. Thanks to Nicolaus Tideman for helpful discussio

Split Cycle: A New Condorcet Consistent Voting Method Independent of Clones and Immune to Spoilers

We introduce a new Condorcet consistent voting method, called Split Cycle. Split Cycle belongs to the small family of known voting methods satisfying independence of clones and the Pareto principle. Unlike other methods in this family, Split Cycle satisfies a new criterion we call immunity to spoilers, which concerns adding candidates to elections, as well as the known criteria of positive involvement and negative involvement, which concern adding voters to elections. Thus, relative to other clone-independent Paretian methods, Split Cycle mitigates “spoiler effects” and “strong no show paradoxes.

A Unifying Impossibility Theorem

This paper considers social choice correspondences assigning a choice set to each non-empty subset of social alternatives. We impose three requirements on these correspondences: unanimity, independence of preferences over infeasible alternatives and choice consistency with respect to choices out of all possible alternatives. With more than three social alternatives and the universal preference domain, any social choice correspondence that satisfies our requirements is serially dictatorial. A number of known impossibility theorems — including Arrow’s Impossibility Theorem, the Muller-Satterthwaite Theorem and the impossibility theorem under strategic candidacy — follow as corollaries. Our new proof highlights the common logical underpinnings behind these theorems.

An Epipolar Line from a Single Pixel

Computing the epipolar geometry from feature points between cameras with very different viewpoints is often error prone, as an object's appearance can vary greatly between images. For such cases, it has been shown that using motion extracted from video can achieve much better results than using a static image. This paper extends these earlier works based on the scene dynamics. In this paper we propose a new method to compute the epipolar geometry from a video stream, by exploiting the following observation: For a pixel p in Image A, all pixels corresponding to p in Image B are on the same epipolar line. Equivalently, the image of the line going through camera A's center and p is an epipolar line in B. Therefore, when cameras A and B are synchronized, the momentary images of two objects projecting to the same pixel, p, in camera A at times t1 and t2, lie on an epipolar line in camera B. Based on this observation we achieve fast and precise computation of epipolar lines. Calibrating cameras based on our method of finding epipolar lines is much faster and more robust than previous methods.Comment: WACV 201