28,052 research outputs found

    Condorcet Methods - When, Why and How?

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    Geometric representations of 3-candidate profiles are used to investigate properties of preferential election methods. The representation visualizes both the possibility to win by agenda manipulation, i.e. introducing a third and chanceless candidate in a 2-candidate race, and the possibility to win a 3-candidate election through different kinds of strategic voting. Here the focus is on the "burying" strategy in single-winner elections, where the win is obtained by ranking a main competitor artificially low. Condorcet methods are compared with the major alternatives (Borda Count, Approval Voting, Instant Runoff Voting). Various Condorcet methods are studied, and one method is proposed that minimizes the number of noncyclic profiles where burying is possible.Preferential election methods; agenda manipulation; strategic voting

    Social choice on complex objects: A geometric approach

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    Marengo and Pasquali (2008) present a model of object construction in majority voting and show that, in general, by appropriate changes of such bundles, different social outcomes may be obtained. In this paper we extend and generalize this approach by providing a geometric model of individual preferences and social aggregation based on hyperplanes and their arrangements. As an application of this model we give a necessary condition for existence of a local social optimum. Moreover we address the question if a social decision rule depends also upon the number of voting agents. More precisely: are there social decision rules that can be obtained by an odd (even) number of voting agent which cannot be obtained by only three (two) voting agent? The answer is negative. Indeed three (or two) voting agent can produce all possible social decision rules.Social choice; object construction power; agenda power; intransitive cycles; arrangements; graph theory.

    Cumulative object categorization in clutter

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    In this paper we present an approach based on scene- or part-graphs for geometrically categorizing touching and occluded objects. We use additive RGBD feature descriptors and hashing of graph configuration parameters for describing the spatial arrangement of constituent parts. The presented experiments quantify that this method outperforms our earlier part-voting and sliding window classification. We evaluated our approach on cluttered scenes, and by using a 3D dataset containing over 15000 Kinect scans of over 100 objects which were grouped into general geometric categories. Additionally, color, geometric, and combined features were compared for categorization tasks

    A Minimalist Approach to Type-Agnostic Detection of Quadrics in Point Clouds

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    This paper proposes a segmentation-free, automatic and efficient procedure to detect general geometric quadric forms in point clouds, where clutter and occlusions are inevitable. Our everyday world is dominated by man-made objects which are designed using 3D primitives (such as planes, cones, spheres, cylinders, etc.). These objects are also omnipresent in industrial environments. This gives rise to the possibility of abstracting 3D scenes through primitives, thereby positions these geometric forms as an integral part of perception and high level 3D scene understanding. As opposed to state-of-the-art, where a tailored algorithm treats each primitive type separately, we propose to encapsulate all types in a single robust detection procedure. At the center of our approach lies a closed form 3D quadric fit, operating in both primal & dual spaces and requiring as low as 4 oriented-points. Around this fit, we design a novel, local null-space voting strategy to reduce the 4-point case to 3. Voting is coupled with the famous RANSAC and makes our algorithm orders of magnitude faster than its conventional counterparts. This is the first method capable of performing a generic cross-type multi-object primitive detection in difficult scenes. Results on synthetic and real datasets support the validity of our method.Comment: Accepted for publication at CVPR 201

    Geometric vulnerability of democratic institutions against lobbying: a sociophysics approach

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    An alternative voting scheme is proposed to fill the democratic gap between a president elected democratically via universal suffrage (deterministic outcome, the actual majority decides), and a president elected by one person randomly selected from the population (probabilistic outcome depending on respective supports). Moving from one voting agent to a group of r randomly selected voting agents reduces the probabilistic character of the outcome. Building r such groups, each one electing its president, to constitute a group of the groups with the r local presidents electing a higher-level president, does reduce further the outcome probabilistic aspect. Repeating the process n times leads to a n-level bottom-up pyramidal structure. The hierarchy top president is still elected with a probability but the distance from a deterministic outcome reduces quickly with increasing n. At a critical value n_{c,r} the outcome turns deterministic recovering the same result a universal suffrage would yield. The scheme yields several social advantages like the distribution of local power to the competing minority making the structure more resilient, yet preserving the presidency allocation to the actual majority. An area is produced around fifty percent for which the president is elected with an almost equiprobability slightly biased in favor of the actual majority. However, our results reveal the existence of a severe geometric vulnerability to lobbying. A tiny lobbying group is able to kill the democratic balance by seizing the presidency democratically. It is sufficient to complete a correlated distribution of a few agents at the hierarchy bottom. Moreover, at the present stage, identifying an actual killing distribution is not feasible, which sheds a disturbing light on the devastating effect geometric lobbying can have on democratic hierarchical institutions.Comment: 52 pages, 22 figures, to appear in Mathematical Models and Methods in Applied Science