Classification Aggregation without Unanimity

TL;DR

This paper proves that any classification aggregation function that is citizen sovereign and independent must be a dictatorship, extending existing impossibility results to cases with two categories and analyzing all such functions for two categories and objects.

Contribution

It extends the impossibility of classification aggregation functions to the two-category case and provides a complete characterization of independent and unanimous functions in that setting.

Findings

Every citizen sovereign and independent classification aggregation function is a dictatorship.

The impossibility extends to the two-category case except when there are only two objects.

All independent and unanimous classification aggregation functions for two categories and two objects are identified.

Abstract

A classification is a surjective mapping from a set of objects to a set of categories. A classification aggregation function aggregates every vector of classifications into a single one. We show that every citizen sovereign and independent classification aggregation function is essentially a dictatorship. This impossibility implies an earlier result of Maniquet and Mongin (2016), who show that every unanimous and independent classification aggregation function is a dictatorship. The relationship between the two impossibilities is reminiscent to the relationship between Wilson's and Arrow's impossibilities in preference aggregation. Moreover, while the Maniquet-Mongin impossibility rests on the existence of at least three categories, we propose an alternative proof technique that covers the case of two categories, except when the number of objects is also two. We also identify all independent and unanimous classification aggregation functions for the case of two categories and two objects.