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Displaying similar documents to “Fair majorities in proportional voting”

Different approaches to weighted voting systems based on preferential positions

Robert Bystrický (2012)

Kybernetika

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Voting systems produce an aggregated result of the individual preferences of the voters. In many cases the aggregated collective preference – the result of the voting procedure – mirrors much more than anything else the characteristics of the voting systems. Preferential voting systems work most of the time with equidistant differences between the adjacent preferences of an individual voter. They produce, as voting systems usually do, some paradoxical results under special circumstances....

Measuring consistency and inconsistency of pair comparison systems

Jaroslav Ramík, Milan Vlach (2013)

Kybernetika

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In this paper we deal with mathematical modeling of real processes that are based on preference relations in the sense that, for every pair of distinct alternatives, the processes are linked to a value of preference degree of one alternative over the other one. The use of preference relations is usual in decision making, psychology, economics, knowledge acquisition techniques for knowledge-based systems, social choice and many other social sciences. For designing useful mathematical...

Approximate dynamic programming based on high dimensional model representation

Miroslav Pištěk (2013)

Kybernetika

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This article introduces an algorithm for implicit High Dimensional Model Representation (HDMR) of the Bellman equation. This approximation technique reduces memory demands of the algorithm considerably. Moreover, we show that HDMR enables fast approximate minimization which is essential for evaluation of the Bellman function. In each time step, the problem of parametrized HDMR minimization is relaxed into trust region problems, all sharing the same matrix. Finding its eigenvalue decomposition,...

A fast Lagrangian heuristic for large-scale capacitated lot-size problems with restricted cost structures

Kjetil K. Haugen, Guillaume Lanquepin-Chesnais, Asmund Olstad (2012)

Kybernetika

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In this paper, we demonstrate the computational consequences of making a simple assumption on production cost structures in capacitated lot-size problems. Our results indicate that our cost assumption of increased productivity over time has dramatic effects on the problem sizes which are solvable. Our experiments indicate that problems with more than 1000 products in more than 1000 time periods may be solved within reasonable time. The Lagrangian decomposition algorithm we use does of...