Mathematics – Optimization and Control
Scientific paper
2009-12-11
Mathematics
Optimization and Control
This is part one of a revised version of arxiv:0810.2263. Version 3 is the result of certain modifications, both in the statem
Scientific paper
10.1007/s00355-011-0548-z
A method is given for quantitatively rating the social acceptance of different options which are the matter of a complete preferential vote. Completeness means that every voter expresses a comparison (a preference or a tie) about each pair of options. The proposed method is proved to have certain desirable properties, which include: the continuity of the rates with respect to the data, a decomposition property that characterizes certain situations opposite to a tie, the Condorcet-Smith principle, and a property of clone consistency. One can view this rating method as a complement for the ranking method introduced in 1997 by Markus Schulze. It is also related to certain methods of one-dimensional scaling or cluster analysis.
Camps Rosa
Mora Xavier
Saumell Laia
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