IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-05395413.html

Learning How to Vote with Principles: Axiomatic Insights Into the Collective Decisions of Neural Networks

Author

Listed:
  • Levin Hornischer

    (LMU - Ludwig Maximilian University [Munich] = Ludwig Maximilians Universität München)

  • Zoi Terzopoulou

    (GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - UL2 - Université Lumière - Lyon 2 - UJM - Université Jean Monnet - Saint-Étienne - EM - EMLyon Business School - CNRS - Centre National de la Recherche Scientifique)

Abstract

Can neural networks be applied in voting theory, while satisfying the need for transparency in collective decisions? We propose axiomatic deep voting: a framework to build and evaluate neural networks that aggregate preferences, using the wellestablished axiomatic method of voting theory. Our findings are: (1) Neural networks, despite being highly accurate, often fail to align with the core axioms of voting rules, revealing a disconnect between mimicking outcomes and reasoning. ( 2) Training with axiom-specific data does not enhance alignment with those axioms. (3) By solely optimizing axiom satisfaction, neural networks can synthesize new voting rules that often surpass and substantially differ from existing ones. This offers insights for both fields: For AI, important concepts like bias and value-alignment are studied in a mathematically rigorous way; for voting theory, new areas of the space of voting rules are explored.

Suggested Citation

  • Levin Hornischer & Zoi Terzopoulou, 2025. "Learning How to Vote with Principles: Axiomatic Insights Into the Collective Decisions of Neural Networks," Post-Print hal-05395413, HAL.
    • Handle: RePEc:hal:journl:hal-05395413
    DOI: 10.1613/jair.1.18890
    Note: View the original document on HAL open archive server: https://hal.science/hal-05395413v1
    as

    Download full text from publisher

    File URL: https://hal.science/hal-05395413v1/document
    Download Restriction: no
    File URL: https://libkey.io/10.1613/jair.1.18890?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Shmuel Nitzan, 1985. "The vulnerability of point-voting schemes to preference variation and strategic manipulation," Public Choice, Springer, vol. 47(2), pages 349-370, January.
    2. Wesley H. Holliday & Eric Pacuit, 2020. "Split Cycle: A New Condorcet Consistent Voting Method Independent of Clones and Immune to Spoilers," Papers 2004.02350, arXiv.org, revised Nov 2023.
    3. Pierre Favardin & Dominique Lepelley & Jérôme Serais, 2002. "original papers : Borda rule, Copeland method and strategic manipulation," Review of Economic Design, Springer;Society for Economic Design, vol. 7(2), pages 213-228.
    4. Wesley H. Holliday & Eric Pacuit, 2023. "Split Cycle: a new Condorcet-consistent voting method independent of clones and immune to spoilers," Public Choice, Springer, vol. 197(1), pages 1-62, October.
    5. Pierre Favardin & Dominique Lepelley, 2006. "Some Further Results on the Manipulability of Social Choice Rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(3), pages 485-509, June.
    6. Burka, Dávid & Puppe, Clemens & Szepesváry, László & Tasnádi, Attila, 2022. "Voting: A machine learning approach," European Journal of Operational Research, Elsevier, vol. 299(3), pages 1003-1017.
    7. Raphael Koster & Jan Balaguer & Andrea Tacchetti & Ari Weinstein & Tina Zhu & Oliver Hauser & Duncan Williams & Lucy Campbell-Gillingham & Phoebe Thacker & Matthew Botvinick & Christopher Summerfield, 2022. "Human-centred mechanism design with Democratic AI," Nature Human Behaviour, Nature, vol. 6(10), pages 1398-1407, October.
      • Raphael Koster & Jan Balaguer & Andrea Tacchetti & Ari Weinstein & Tina Zhu & Oliver Hauser & Duncan Williams & Lucy Campbell-Gillingham & Phoebe Thacker & Matthew Botvinick & Christopher Summerfield, 2022. "Human-centered mechanism design with Democratic AI," Papers 2201.11441, arXiv.org.
    8. Robert Powers, 2007. "The Number of Times an Anonymous Rule Violates Independence in the 3 × 3 Case," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(3), pages 363-373, April.
    9. Jean-François Laslier, 2011. "And the loser is... Plurality Voting," Working Papers hal-00609810, HAL.
    10. Pierre Favardin & Dominique Lepelley & Jérôme Serais, 2002. "Borda rule, Copeland method and strategic manipulation," Post-Print halshs-00069522, HAL.
    11. William Thomson, 2001. "On the axiomatic method and its recent applications to game theory and resource allocation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(2), pages 327-386.
    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. James Green-Armytage & T. Tideman & Rafael Cosman, 2016. "Statistical evaluation of voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 183-212, January.
    2. Mostapha Diss, 2015. "Strategic manipulability of self-selective social choice rules," Annals of Operations Research, Springer, vol. 229(1), pages 347-376, June.
    3. Green-Armytage, James, 2011. "Strategic voting and nomination," MPRA Paper 32200, University Library of Munich, Germany.
    4. Krzysztof Kontek & Honorata Sosnowska, 2020. "Specific Tastes or Cliques of Jurors? How to Reduce the Level of Manipulation in Group Decisions?," Group Decision and Negotiation, Springer, vol. 29(6), pages 1057-1084, December.
    5. Diss, Mostapha & Tsvelikhovskiy, Boris, 2021. "Manipulable outcomes within the class of scoring voting rules," Mathematical Social Sciences, Elsevier, vol. 111(C), pages 11-18.
    6. Dominique Lepelley & Ahmed Louichi & Hatem Smaoui, 2008. "On Ehrhart polynomials and probability calculations in voting theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(3), pages 363-383, April.
    7. Bednay, Dezső & Moskalenko, Anna & Tasnádi, Attila, 2019. "Dictatorship versus manipulability," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 72-76.
    8. James Green-Armytage, 2014. "Strategic voting and nomination," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(1), pages 111-138, January.
    9. Haris Aziz & Alexander Lam, 2021. "Obvious Manipulability of Voting Rules," Papers 2111.01983, arXiv.org, revised Jun 2022.
    10. Aleskerov, Fuad & Karabekyan, Daniel & Sanver, M. Remzi & Yakuba, Vyacheslav, 2012. "On the manipulability of voting rules: The case of 4 and 5 alternatives," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 67-73.
    11. Holliday, Wesley H., 2024. "An impossibility theorem concerning positive involvement in voting," Economics Letters, Elsevier, vol. 236(C).
    12. Jean-François Laslier, 2016. "Heuristic Voting Under the Alternative Vote: The Efficiency of “Sour Grapes” Behavior," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 33(1), pages 57-76, August.
    13. Yeawon Yoo & Adolfo R. Escobedo, 2021. "A New Binary Programming Formulation and Social Choice Property for Kemeny Rank Aggregation," Decision Analysis, INFORMS, vol. 18(4), pages 296-320, December.
    14. Wesley H. Holliday & Eric Pacuit, 2023. "Stable Voting," Constitutional Political Economy, Springer, vol. 34(3), pages 421-433, September.
    15. Pietro Battiston & Marco Magnani & Dimitri Paolini & Luca Rossi, 2025. "Country Music: Positional Voting and Strategic Behavior," Discussion Papers 2025/322, Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy.
    16. Rahimdel, Mohammad Javad & Noferesti, Hossein, 2020. "Investment preferences of Iran's mineral extraction sector with a focus on the productivity of the energy consumption, water and labor force," Resources Policy, Elsevier, vol. 67(C).
    17. Jalil Heidary Dahooie & Ali Husseinzadeh Kashan & Zahra Shoaei Naeini & Amir Salar Vanaki & Edmundas Kazimieras Zavadskas & Zenonas Turskis, 2022. "A Hybrid Multi-Criteria-Decision-Making Aggregation Method and Geographic Information System for Selecting Optimal Solar Power Plants in Iran," Energies, MDPI, vol. 15(8), pages 1-20, April.
    18. Marie-Louise Lackner & Martin Lackner, 2017. "On the likelihood of single-peaked preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(4), pages 717-745, April.
    19. repec:hal:pseose:halshs-01168670 is not listed on IDEAS
    20. Cervone, Davide P. & Dai, Ronghua & Gnoutcheff, Daniel & Lanterman, Grant & Mackenzie, Andrew & Morse, Ari & Srivastava, Nikhil & Zwicker, William S., 2012. "Voting with rubber bands, weights, and strings," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 11-27.
    21. Wesley H. Holliday & Eric Pacuit, 2026. "An extension of May’s Theorem to three alternatives: axiomatizing Minimax voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 66(2), pages 395-422, March.

    More about this item

    Keywords

    ;
    ;

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:hal:journl:hal-05395413. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.