Vocabulary aggregation

TL;DR

This paper models vocabularies as partitions of a set and explores rules for aggregating individual vocabularies into a collective one, ensuring strategy-proofness under certain conditions.

Contribution

It characterizes aggregation rules for vocabularies modeled as ordered partitions, extending the theory to diverse vocabularies and preference restrictions.

Findings

Aggregation rules are strategy-proof under specific preference restrictions.

The model accommodates vocabularies with varying sizes and spans.

Characterization of aggregation rules for ordered vocabularies.

Abstract

A vocabulary is a list of words designating subsets from a grand set X. We model a vocabulary as a partition of X and study the aggregation of individual vocabularies into a collective one. We characterize aggregation rules when X is linearly ordered and each word of the vocabulary spans an order interval. We allow for individual vocabularies to differ both in the number and in the span of their words. Under a suitable restriction on agents' preferences, we show that our aggregation rules are strategy-proof.