Classification Aggregation without Unanimity
This work addresses foundational issues in social choice theory for classification tasks, providing an impossibility result that is incremental but extends coverage to cases with two categories.
The paper tackles the problem of classification aggregation, showing that any citizen sovereign and independent aggregation function is essentially a dictatorship, which implies an earlier result by Maniquet and Mongin (2016) and relates to Arrow's impossibility theorem in preference aggregation.
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.