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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References
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Fishburn, P.C., Rubinstein, A. Aggregation of equivalence relations. Journal of Classification 3, 61–65 (1986). https://doi.org/10.1007/BF01896812
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DOI: https://doi.org/10.1007/BF01896812