Éditeur(s) : HAL CCSD Editions Dalloz
Résumé : International audience
For a given voting situation, the Strong Borda Paradox occurs when a Condorcet loser exists and is elected. A Condorcet loser is a candidate that loses all his pairwise comparisons. In three-candidate elections, we use an analytical approach to find out, the range of all the scoring rules that can exhibit the Strong Borda Paradox under some well-known preference restrictions and we describe all the scenarios with respect to the rank of the Condorcet loser in the collective rankings. Using the parameterized Barvinok’s algorithm, we provide a simplified representation of the likelihood of the Strong Borda Paradox for the Plurality rule and the Antiplurality rule (given the size of the electorate) with the impartial and anonymous culture condition for each type of restriction.
ISSN: 0373-2630

hal-01631180
https://hal.univ-antilles.fr/hal-01631180
DOI : 10.3917/redp.273.0375

Éditeur(s) : HAL CCSD Institute of Electrical and Electronics Engineers
Résumé : International audience
Tailoring nearest neighbors algorithms to boosting is an important problem. Recent papers study an approach, UNN, which provably minimizes particular convex surrogates under weak assumptions. However, numerical issues make it necessary to experimentally tweak parts of the UNN algorithm, at the possible expense of the algorithm's convergence and performance. In this paper, we propose a lightweight alternative algorithm optimizing proper scoring rules from a very broad set, and establish formal convergence rates under the boosting framework that surprisingly compete with those known for UNN. It is an adaptive Newton-Raphson algorithm, which belongs to the same lineage as the popular Gentle Adaboost. To the best of our knowledge, no such boosting-compliant convergence rates were previously known for these algorithms. We provide experiments on a dozen domains, including the challenging Caltech and SUN computer vision databases. They display that GNNB significantly outperforms UNN, both in terms of convergence rate and quality of the solution obtained, and GNNB provides a simple and efficient contender to techniques that can be used on very large domains, like stochastic gradient descent -- for which little is known to date. Experiments include a divide-and-conquer improvement of GNNB which exploits the link with proper scoring rules optimization.
ISSN: 0162-8828

hal-00958809
https://hal.archives-ouvertes.fr/hal-00958809
https://hal.archives-ouvertes.fr/hal-00958809/document
https://hal.archives-ouvertes.fr/hal-00958809/file/PAMI.pdf
DOI : 10.1109/TPAMI.2014.2307877