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Condorcet's theory of voting

H. P. Young (1990)

Mathématiques et Sciences Humaines

Condorcet believed that the purpose of voting is to make a choice that is “best” for society. According to his view, there is one choice that is objectively best, another that is second-best, and so forth. Unfortunately, voters sometimes make mistakes ; they misperceive what is best. In designing a voting rule, therefore, the objective should be to choose the alternative that is most likely to be best. Condorcet solved this problem using a form of maximum likelihood estimation. The procedure that...

Confidence regions in nonlinear regression models

Rastislav Potocký, Van Ban To (1992)

Applications of Mathematics

New curvature measures for nonlinear regression models are developed and methods of their computing are given. Using these measures, more accurate confidence regions for parameters than those based on linear or quadratic approximations are obtained.

Confidence regions of minimal area for the scale-location parameter and their applications

A. Czarnowska, A. V. Nagaev (2001)

Applicationes Mathematicae

The area of a confidence region is suggested as a quality exponent of parameter estimation. It is shown that under very mild restrictions imposed on the underlying scale-location family there exists an optimal confidence region. Explicit formulae as well as numerical results concerning the normal, exponential and uniform families are presented. The question how to estimate the quantile function is also discussed.

Congruences and ideals in lattice effect algebras as basic algebras

Sylvia Pulmannová, Elena Vinceková (2009)

Kybernetika

Effect basic algebras (which correspond to lattice ordered effect algebras) are studied. Their ideals are characterized (in the language of basic algebras) and one-to-one correspondence between ideals and congruences is shown. Conditions under which the quotients are OMLs or MV-algebras are found.

Consensus clustering with differential evolution

Miroslav Sabo (2014)

Kybernetika

Consensus clustering algorithms are used to improve properties of traditional clustering methods, especially their accuracy and robustness. In this article, we introduce our approach that is based on a refinement of the set of initial partitions and uses differential evolution algorithm in order to find the most valid solution. Properties of the algorithm are demonstrated on four benchmark datasets.

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