It is argued that if a finite partially ordered population is given, and incomparability is taken as the relevant type of dissimilarity, then diversity comparisons between subpopulations may be conveniently based on widths namely on the maximum number of pairwise incomparable units they include. We introduce two widthbased rankings. The first one is the plain width-ranking of subposets as induced by width computation. The second one is the undominated width-ranking of subposets namely the ranking induced by the sizes of undominated subposets. Simple axiomatic characterizations of the foregoing rankings are provided.
Vannucci, S., Basili, M. (2013). Diversity as width. SOCIAL CHOICE AND WELFARE, 40(3), 913-936 [10.1007/s00355-011-0649-8].
Diversity as width
VANNUCCI, STEFANO;BASILI, MARCELLO
2013-01-01
Abstract
It is argued that if a finite partially ordered population is given, and incomparability is taken as the relevant type of dissimilarity, then diversity comparisons between subpopulations may be conveniently based on widths namely on the maximum number of pairwise incomparable units they include. We introduce two widthbased rankings. The first one is the plain width-ranking of subposets as induced by width computation. The second one is the undominated width-ranking of subposets namely the ranking induced by the sizes of undominated subposets. Simple axiomatic characterizations of the foregoing rankings are provided.
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https://hdl.handle.net/11365/21001
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