IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2603.12958.html

Vocabulary aggregation

Author

Listed:
  • 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.

Suggested Citation

  • Marco LiCalzi & M. Alperen Yasar, 2026. "Vocabulary aggregation," Papers 2603.12958, arXiv.org.
    • Handle: RePEc:arx:papers:2603.12958
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2603.12958
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Chambers, Christopher P., 2007. "Ordinal aggregation and quantiles," Journal of Economic Theory, Elsevier, vol. 137(1), pages 416-431, November.
    2. Hugh Ward & Albert Weale, 2010. "Is Rule by Majorities Special?," Political Studies, Political Studies Association, vol. 58(1), pages 26-46, February.
    3. William Thomson, 2018. "On the terminology of economic design: a critical assessment and some proposals," Review of Economic Design, Springer;Society for Economic Design, vol. 22(1), pages 67-99, June.
    4. Mihir Bhattacharya & Ojasvi Khare, 2024. "Strategy-proof interval-social choice correspondences over extended single-peaked domains," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(3), pages 893-911, September.
    5. Bettina Klaus & Panos Protopapas, 2020. "On strategy-proofness and single-peakedness: median-voting over intervals," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(4), pages 1059-1080, December.
    6. Ovchinnikov, Sergei, 1996. "Means on ordered sets," Mathematical Social Sciences, Elsevier, vol. 32(1), pages 39-56, August.
    7. Wilson, Robert, 1975. "On the theory of aggregation," Journal of Economic Theory, Elsevier, vol. 10(1), pages 89-99, February.
    8. Block, Veronica, 2010. "Efficient and strategy-proof voting over connected coalitions: A possibility result," Economics Letters, Elsevier, vol. 108(1), pages 1-3, July.
    9. Edurne Falcó & Madhuparna Karmokar & Souvik Roy & Ton Storcken, 2020. "On update monotone, continuous, and consistent collective evaluation rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(4), pages 759-776, December.
    10. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2009. "Aggregation functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445120, HAL.
    11. Yves Sprumont, 1995. "Strategyproof Collective Choice in Economic and Political Environments," Canadian Journal of Economics, Canadian Economics Association, vol. 28(1), pages 68-107, February.
    12. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    13. Mishra, Debasis & Roy, Souvik, 2012. "Strategy-proof partitioning," Games and Economic Behavior, Elsevier, vol. 76(1), pages 285-300.
    14. Kim C. Border & J. S. Jordan, 1983. "Straightforward Elections, Unanimity and Phantom Voters," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(1), pages 153-170.
    15. Rubinstein, Ariel & Fishburn, Peter C., 1986. "Algebraic aggregation theory," Journal of Economic Theory, Elsevier, vol. 38(1), pages 63-77, February.
    16. Peter Fishburn & Ariel Rubinstein, 1986. "Aggregation of equivalence relations," Journal of Classification, Springer;The Classification Society, vol. 3(1), pages 61-65, March.
    17. Pierre Barthelemy, Jean & Monjardet, Bernard, 1981. "The median procedure in cluster analysis and social choice theory," Mathematical Social Sciences, Elsevier, vol. 1(3), pages 235-267, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chatterji, Shurojit & Zeng, Huaxia, 2018. "On random social choice functions with the tops-only property," Games and Economic Behavior, Elsevier, vol. 109(C), pages 413-435.
    2. Olivier Hudry & Bernard Monjardet, 2010. "Consensus theories: An oriented survey," Documents de travail du Centre d'Economie de la Sorbonne 10057, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    3. Adrian Fernandez-Perez & Marta Gómez-Puig & Simón Sosvilla-Rivero, 2025. "Hot Property: A Spatial Analysis of Temperature and Housing Prices in Spain," IREA Working Papers 202516, University of Barcelona, Research Institute of Applied Economics.
    4. Ernesto Savaglio & Stefano Vannucci, 2019. "Strategy-proof aggregation rules and single peakedness in bounded distributive lattices," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(2), pages 295-327, February.
    5. Régis Renault & Alain Trannoy, 2011. "Assessing the extent of strategic manipulation: the average vote example," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 2(4), pages 497-513, December.
    6. Hans Gersbach & Kremena Valkanova, 2024. "Voting with Random Proposers: Two Rounds May Suffice," Papers 2410.20476, arXiv.org, revised Oct 2025.
    7. John A. Weymark, 2008. "Strategy‐Proofness and the Tops‐Only Property," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 10(1), pages 7-26, February.
    8. Le Breton, Michel & Weymark, John A., 1999. "Strategy-proof social choice with continuous separable preferences," Journal of Mathematical Economics, Elsevier, vol. 32(1), pages 47-85, August.
    9. Shurojit Chatterji & Huaxia Zeng, 2023. "Decomposability and Strategy-proofness in Multidimensional Models," Papers 2303.10889, arXiv.org, revised Nov 2023.
    10. Tobias Rachidi, 2021. "Optimal Voting Mechanisms on Generalized Single-Peaked Domains," CRC TR 224 Discussion Paper Series crctr224_2020_214v2, University of Bonn and University of Mannheim, Germany.
    11. BOSSERT, Walter & WEYMARK, J.A., 2006. "Social Choice: Recent Developments," Cahiers de recherche 2006-01, Universite de Montreal, Departement de sciences economiques.
    12. Dolors Berga & Bernardo Moreno, 2009. "Strategic requirements with indifference: single-peaked versus single-plateaued preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(2), pages 275-298, February.
    13. John Weymark, 2011. "A unified approach to strategy-proofness for single-peaked preferences," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 2(4), pages 529-550, December.
    14. Bonifacio, Agustín G. & Massó, Jordi, 2021. "Corrigendum to "On strategy-proofness and semilattice single-peakedness" [Games Econ. Behav. 124 (2020) 219–238]," Games and Economic Behavior, Elsevier, vol. 130(C), pages 684-689.
    15. Jordi Massó & Shurojit Chatterji, 2015. "On Strategy-proofness and the Salience of Single-peakedness," UFAE and IAE Working Papers 952.15, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    16. Tobias Rachidi, 2020. "Optimal Voting Mechanisms on Generalized Single-Peaked Domains," CRC TR 224 Discussion Paper Series crctr224_2020_214, University of Bonn and University of Mannheim, Germany.
    17. Nehring, Klaus & Puppe, Clemens, 2010. "Abstract Arrowian aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 467-494, March.
    18. Barbera, S. & Masso, J. & Serizawa, S., 1998. "Strategy-Proof Voting on Compact Ranges," Games and Economic Behavior, Elsevier, vol. 25(2), pages 272-291, November.
    19. Chatterji, Shurojit & Zeng, Huaxia, 2019. "Random mechanism design on multidimensional domains," Journal of Economic Theory, Elsevier, vol. 182(C), pages 25-105.
    20. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations with abstentions," Journal of Economic Theory, Elsevier, vol. 145(2), pages 544-561, March.

    More about this item

    JEL classification:

    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • Z13 - Other Special Topics - - Cultural Economics - - - Economic Sociology; Economic Anthropology; Language; Social and Economic Stratification

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2603.12958. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.