Aggregation of equivalence relations |
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Authors: | Peter C Fishburn Ariel Rubinstein |
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Institution: | (1) AT&T Bell Laboratories, 07974 Murray Hill, New Jersey, USA;(2) Department of Economics, The Hebrew University, Jerusalem, Israel |
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Abstract: | Each ofn attributes partitions a set of items into equivalence classes. Aconsistent aggregator of then partitions is defined as an aggregate partition that satisfies an independence condition and a unanimity condition. It is shown that the class of consistent aggregators is precisely the class ofconjunctive aggregators. That is, for each consistent aggregator there is a nonempty subsetN of the attributes such that two items are equivalent in the aggregate partition if and only if they are equivalent with respect to each attribute inN. |
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Keywords: | Classification aggregation consistency conjunctive aggregator |
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