IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2602.04494.html

Anchor-proofness in Voting

Author

Listed:
  • Federico Fioravanti
  • Zoi Terzopoulou

Abstract

This work contributes to a foundational question in economic theory: how do individual-level cognitive biases interact with collective choice mechanisms? We study a setting where voters hold intrinsic preference rankings over a set of alternatives but cast approval ballots to determine the collective outcome. The ballots are shaped by an anchoring bias: alternatives are presented sequentially by a social planner, and a voter approves an alternative if and only if it is acceptable and strictly preferred to all alternatives previously encountered. We first analyze which approval-based voting rules are anchor-proof, in the sense that they always select the same winner regardless of the presentation order. We show that this requirement is extremely demanding: only very restrictive rules satisfy it. We then turn to the potential influence of the social planner. On the upside, when the planner has no information about the voters' intrinsic preferences, she cannot manipulate the outcome.

Suggested Citation

  • Federico Fioravanti & Zoi Terzopoulou, 2026. "Anchor-proofness in Voting," Papers 2602.04494, arXiv.org, revised Feb 2026.
    • Handle: RePEc:arx:papers:2602.04494
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2602.04494
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Gori, Michele, 2021. "Manipulation of social choice functions under incomplete information," Games and Economic Behavior, Elsevier, vol. 129(C), pages 350-369.
    2. Sekiguchi, Yohei, 2012. "A characterization of the plurality rule," Economics Letters, Elsevier, vol. 116(3), pages 330-332.
    3. Barberà, Salvador & Gerber, Anke, 2017. "Sequential voting and agenda manipulation," Theoretical Economics, Econometric Society, vol. 12(1), January.
    4. Ulle Endriss, 2013. "Sincerity and manipulation under approval voting," Theory and Decision, Springer, vol. 74(3), pages 335-355, March.
    5. Kahneman, Daniel & Knetsch, Jack L & Thaler, Richard H, 1986. "Fairness and the Assumptions of Economics," The Journal of Business, University of Chicago Press, vol. 59(4), pages 285-300, October.
    6. Raluca M. Ursu, 2018. "The Power of Rankings: Quantifying the Effect of Rankings on Online Consumer Search and Purchase Decisions," Marketing Science, INFORMS, vol. 37(4), pages 530-552, August.
    7. Zoi Terzopoulou & Jérôme Lang & William S. Zwicker, 2026. "Approval compatible voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 66(1), pages 1-26, February.
    8. Jean-François Bonnefon, 2010. "Behavioral evidence for framing effects in the resolution of the doctrinal paradox," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(4), pages 631-641, April.
    9. Yuliya A. Veselova, 2020. "Does Incomplete Information Reduce Manipulability?," Group Decision and Negotiation, Springer, vol. 29(3), pages 523-548, June.
    10. Antoinette Baujard & Herrade Igersheim, 2011. "Framed-field Experiment on Approval Voting and Evaluation Voting. Some Teachings to Reform the French Presidential Electoral System," Studies in Public Choice, in: Bernard Dolez & Bernard Grofman & Annie Laurent (ed.), In Situ and Laboratory Experiments on Electoral Law Reform, chapter 0, pages 69-89, Springer.
    11. Michel Regenwetter & Ilia Tsetlin, 2004. "Approval voting and positional voting methods: Inference, relationship, examples," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 22(3), pages 539-566, June.
    12. Florian Brandl & Dominik Peters, 2022. "Approval voting under dichotomous preferences: A catalogue of characterizations," Post-Print hal-03816040, HAL.
    13. Yohei Sekiguchi, 2012. "A Characterization of the Plurality Rule," CIRJE F-Series CIRJE-F-833, CIRJE, Faculty of Economics, University of Tokyo.
    14. Brandl, Florian & Peters, Dominik, 2022. "Approval voting under dichotomous preferences: A catalogue of characterizations," Journal of Economic Theory, Elsevier, vol. 205(C).
    15. Pedro Bordalo & Nicola Gennaioli & Andrei Shleifer, 2012. "Salience Theory of Choice Under Risk," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 127(3), pages 1243-1285.
    16. Bernard Grofman & Michel Regenwetter, 1998. "Choosing subsets: a size-independent probabilistic model and the quest for a social welfare ordering," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(3), pages 423-443.
    17. Steven J. Brams & M. Remzi Sanver, 2009. "Voting Systems that Combine Approval and Preference," Studies in Choice and Welfare, in: Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), The Mathematics of Preference, Choice and Order, pages 215-237, Springer.
    18. Gershkov, Alex & Moldovanu, Benny & Shi, Xianwen, 2019. "Voting on multiple issues: what to put on the ballot?," Theoretical Economics, Econometric Society, vol. 14(2), May.
    19. Andreas Kleiner & Benny Moldovanu, 2017. "Content-Based Agendas and Qualified Majorities in Sequential Voting," American Economic Review, American Economic Association, vol. 107(6), pages 1477-1506, June.
    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. Salvatore Barbaro & Anna-Sophie Kurella, 2025. "Dichotomous Preferences: Concepts, Measurement, and Evidence," Working Papers 2506, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    2. Patrick Lederer, 2025. "Robust Voting Rules on the Interval Domain," Papers 2509.04874, arXiv.org.
    3. Hiroki Saitoh, 2022. "Characterization of tie-breaking plurality rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(1), pages 139-173, July.
    4. Z. Emel Öztürk, 2020. "Consistency of scoring rules: a reinvestigation of composition-consistency," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(3), pages 801-831, September.
    5. Lederer, Patrick, 2024. "Bivariate scoring rules: Unifying the characterizations of positional scoring rules and Kemeny's rule," Journal of Economic Theory, Elsevier, vol. 218(C).
    6. Walter Bossert & Kotaro Suzumura, 2017. "The greatest unhappiness of the least number," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 49(3), pages 637-655, December.
    7. Chris Dong & Patrick Lederer, 2023. "Refined Characterizations of Approval-based Committee Scoring Rules," Papers 2312.08799, arXiv.org, revised Mar 2024.
    8. Gershkov, Alex & Moldovanu, Benny & Shi, Xianwen, 2020. "Monotonic norms and orthogonal issues in multidimensional voting," Journal of Economic Theory, Elsevier, vol. 189(C).
    9. 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.
    10. Aziz, Haris & Lederer, Patrick & Lu, Xinhang & Suzuki, Mashbat & Vollen, Jeremy, 2025. "Approximately fair and population consistent budget division via simple payment schemes," Games and Economic Behavior, Elsevier, vol. 154(C), pages 208-225.
    11. Federico Fioravanti & Ulle Endriss, 2024. "Voting with Partial Orders: The Plurality and Anti-Plurality Classes," Working Papers 329, Red Nacional de Investigadores en Economía (RedNIE).
    12. Jac C. Heckelman, 2021. "Characterizing plurality using the majoritarian condition: a new proof and implications for other scoring rules," Public Choice, Springer, vol. 189(3), pages 335-346, December.
    13. 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.
    14. Chris Dong & Patrick Lederer, 2023. "Characterizations of Sequential Valuation Rules," Papers 2302.11890, arXiv.org.
    15. Z. Emel Ozturk, 2017. "A composition-consistency characterization of the plurality rule," Working Papers 2017_04, Business School - Economics, University of Glasgow.
    16. Bardal, Tuva & Endriss, Ulle, 2025. "Axiomatic analysis of approval-based scoring rules," Games and Economic Behavior, Elsevier, vol. 153(C), pages 345-358.
    17. Barberà, Salvador & Bossert, Walter, 2023. "Opinion aggregation: Borda and Condorcet revisited," Journal of Economic Theory, Elsevier, vol. 210(C).
    18. Gershkov, Alex & Kleiner, Andreas & Moldovanu, Benny & Shi, Xianwen, 2023. "Voting with interdependent values: The Condorcet winner," Games and Economic Behavior, Elsevier, vol. 142(C), pages 193-208.
    19. Wesley H. Holliday & Eric Pacuit, 2023. "An extension of May's Theorem to three alternatives: axiomatizing Minimax voting," Papers 2312.14256, arXiv.org, revised Apr 2025.
    20. Salvador Barberà & Walter Bossert & Kotaro Suzumura, 2021. "Daunou’s voting rule and the lexicographic assignment of priorities," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(2), pages 259-289, February.

    More about this item

    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:arx:papers:2602.04494. 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.