A differential evolution algorithm for finding the median ranking under the Kemeny axiomatic approach
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Rank (graph theory)
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We consider axiomatic characterization of social choice functions when there exist a fixed number of voters. Our particular interest is in social choice functions that reflect, to some extent, positional information in voters' preference rankings as well as orders between two alternatives. More specifically, we look for social choice functions that satisfy Neutrality, Positive Responsiveness, and Invariance for Average-Position Preserving Reversals. It turns out that there exists one and only one social choice function satisfying the three axioms, namely, Borda rule.
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In [She82], it is shown that four basic functional properties are enough to characterize plain Kolmogorov complexity, hence obtaining an axiomatic characterization of this notion. In this paper, we try to extend this work, both by looking at alternative axiomatic systems for plain complexity and by considering potential axiomatic systems for other types of complexity. First we show that the axiomatic system given by Shen cannot be weakened (at least in any natural way). We then give an analogue of Shen's axiomatic system for conditional complexity. In a the second part of the paper, we look at prefix-free complexity and try to construct an axiomatic system for it. We show however that the natural analogues of Shen's axiomatic systems fails to characterize prefix-free complexity.
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In [6], it is shown that four of its basic functional properties are enough to characterize plain Kolmogorov complexity, hence obtaining an axiomatic characterization of this notion. In this paper, we try to extend this work, both by looking at alternative axiomatic systems for plain complexity and by considering potential axiomatic systems for other types of complexity. First we show that the axiomatic system given by Shen cannot be weakened (at least in any natural way). We then give an analogue of Shen's axiomatic system for conditional complexity. In the second part of the paper, we look at prefix-free complexity and try to construct an axiomatic system for it. We show however that the natural analogues of Shen's axiomatic systems fail to characterize prefix-free complexity.
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In [She82], it is shown that four basic functional properties are enough to characterize plain Kolmogorov complexity, hence obtaining an axiomatic characterization of this notion. In this paper, we try to extend this work, both by looking at alternative axiomatic systems for plain complexity and by considering potential axiomatic systems for other types of complexity. First we show that the axiomatic system given by Shen cannot be weakened (at least in any natural way). We then give an analogue of Shen's axiomatic system for conditional complexity. In a the second part of the paper, we look at prefix-free complexity and try to construct an axiomatic system for it. We show however that the natural analogues of Shen's axiomatic systems fails to characterize prefix-free complexity.
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The main goal of "Naive Axiomatic Mengenlehre" (NAM) is to find a more or less adequately explicit criterion that precisely formalizes the intuitive notion of a "normal set". NAM is mainly a construction procedure for building several formal systems NAMix, each of which can turn out to be an adequate codification of the contentual naive set theory. ("i" is a natural number which enumerates the used "normality" condition, and "x" is a letter which points to the variants of the used axioms.) Parallel to NAM, the Naive Axiomatic Class Theory NACT is constructed as a system of systems too.
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Axiomatic method is of great importance in formulating legal theories,the reason of which lies in that it can enhance the comprehensiveness of the theories and result in the theories better-knit and more convincing and developing quickly.Thus axiomatic method is often adopted by people while writing law works or compiling codes.But still some issues should be noted while we are doing our work:the fewer the axiomatic method is,the better;the axiomatic method chosen should be of prima facie rationale;truth is self-evident,etc.
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