Abstract
We consider the aggregation of classifications of objects that are graded in a single dimension into categories that are ranked. Grading is a sufficient domain restriction to avoid dictatorship. In contrast to other results, it is possible to use a majority-based aggregator when objects can be located in any number of categories. The aggregator locates an object below a boundary between specified categories just if a majority do so. In contrast, preponderance aggregators that are directly based on locations of objects can locate a higher graded object in a lower ranked category. Any aggregator that satisfies other independence conditions relating to the locations of objects or positions of boundaries must be dictatorial.
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