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Vocabulary aggregation

Marco LiCalzi, M. Alperen Yasar

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.

Vocabulary aggregation

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.
Paper Structure (18 sections, 14 theorems, 15 equations, 13 figures)

This paper contains 18 sections, 14 theorems, 15 equations, 13 figures.

Table of Contents

  1. Introduction
  2. Setup
  3. An example
  4. The model
  5. Homogeneous vocabularies
  6. Axioms
  7. Main result
  8. Interval aggregation
  9. Heterogeneous vocabularies
  10. Results
  11. Majoritarian consensus
  12. Incomplete vocabularies
  13. Single-peaked vocabularies
  14. Statement about Conflict of Interest
  15. Appendix
  16. ...and 3 more sections

Key Result

Theorem 1

A separable aggregation rule for homogeneous vocabularies is strictly consistent, unanimous, anonymous, stable and continuous if and only if it is a $p$-rule.

Figures (13)

  • Figure 1: A vocabulary
  • Figure 2: Collective vocabularies under three aggregation rules
  • Figure 3: An individual interval
  • Figure 4: A partial vocabulary
  • Figure 5: A partial 2-word vocabulary and its three endpoints
  • ...and 8 more figures

Theorems & Definitions (23)

  • Example 1
  • Theorem 1
  • Theorem 2
  • proof
  • Theorem 3
  • Example 2
  • Proposition 4
  • proof
  • Proposition 5
  • proof
  • ...and 13 more