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Brief Announcement: Liquid Democracy Under Vote Correlation: On the Fallacies of Averaging and the Excluded Middle

Authors Seth Gilbert, Stefan Schmid , Santiago Schnell, Jakub Svoboda , Michelle X. Yeo

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Subject Classification

ACM Subject Classification
  • Security and privacy → Distributed systems security
  • Applied computing
  • Theory of computation → Graph algorithms analysis
Keywords
  • Liquid democracy
  • Voting
  • Delegation
  • Mechanism design
  • Distributed algorithms

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Abstract

Liquid democracy permits voters either to vote directly or to delegate their votes to others. Existing algorithmic analyses usually assign each voter a single scalar competence parameter, representing an independent probability of voting for the ground truth. This representation is inadequate when delegation is fixed before later public information changes different voters' reliability in different ways. In this work, we study a minimal common-signal model of this realistic phenomenon. Delegation occurs before a public binary signal is realised, while voting occurs afterwards. Conditional on the signal, sink votes are independent and each voter has a signal-specific competence; marginally, correctness events are correlated through the common signal. We show that delegation based on average competence is not a safe scalarisation. We then present three novel delegation mechanisms for this setting. We analyse and show the precise conditions under which our mechanisms inherit delegation desiderata, as well as outline the tradeoffs between these mechanisms.

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Seth Gilbert, Stefan Schmid, Santiago Schnell, Jakub Svoboda, and Michelle X. Yeo. Brief Announcement: Liquid Democracy Under Vote Correlation: On the Fallacies of Averaging and the Excluded Middle. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 64:1-64:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.DISC.2026.64

Author Details

Seth Gilbert
  • National University of Singapore, Singapore
Stefan Schmid
  • TU Berlin, Germany
Santiago Schnell
  • Dartmouth College, Hanover, NH, USA
Jakub Svoboda
  • Dartmouth College, Hanover, NH, USA
Michelle X. Yeo
  • Aarhus University, Denmark
  • Nanyang Technological University, Singapore

Funding

Supported by the German Federal Ministry for Research, Technology and Space (BMFTR), BeeFAIRChain (grant 03DPC0114A), 2026-2027. S.S. and J.S. were supported by Dartmouth College.

References

  1. Krishnendu Chatterjee, Seth Gilbert, Stefan Schmid, Jakub Svoboda, and Michelle Yeo. When is liquid democracy possible?: On the manipulation of variance. In PODC, pages 241-251. ACM, 2025. URL: https://doi.org/10.1145/3732772.3733544.
  2. Krishnendu Chatterjee, Seth Gilbert, Stefan Schmid, Jakub Svoboda, and Michelle Yeo. Liquid democracy with two opposing factions. IACR Cryptol. ePrint Arch., 2026:375, 2026. URL: https://eprint.iacr.org/2026/375.
  3. Rainer Feichtinger, Robin Fritsch, Yann Vonlanthen, and Roger Wattenhofer. The hidden shortcomings of (d)aos - an empirical study of on-chain governance. CoRR, abs/2302.12125, 2023. URL: https://doi.org/10.48550/arXiv.2302.12125.
  4. Robin Fritsch, Marino Müller, and Roger Wattenhofer. Analyzing voting power in decentralized governance: Who controls daos? Blockchain: Research and Applications, 5(3):100208, 2024. URL: https://doi.org/10.1016/j.bcra.2024.100208.
  5. Seth Gilbert, Stefan Schmid, Santiago Schnell, Jakub Svoboda, and Michelle Yeo. Liquid democracy under vote correlation: On the fallacies of averaging and the excluded middle, 2026. URL: https://arxiv.org/abs/2608.16738.
  6. Andrew B. Hall and Sho Miyazaki. What Happens When Anyone Can Be Your Representative? Studying the Use of Liquid Democracy for High-Stakes Decisions in Online Platforms. Research Papers 4220, Stanford University, Graduate School of Business, October 2024. URL: https://ideas.repec.org/p/ecl/stabus/4220.html.
  7. Daniel Halpern, Joseph Y. Halpern, Ali Jadbabaie, Elchanan Mossel, Ariel D. Procaccia, and Manon Revel. In defense of liquid democracy. In Proceedings of the 24th ACM Conference on Economics and Computation, EC '23, page 852, New York, NY, USA, 2023. Association for Computing Machinery. URL: https://doi.org/10.1145/3580507.3597817.
  8. Anson Kahng, Simon Mackenzie, and Ariel D. Procaccia. Liquid democracy: An algorithmic perspective. J. Artif. Intell. Res., 70:1223-1252, 2021. URL: https://doi.org/10.1613/JAIR.1.12261.
  9. Christoph Carl Kling, Jérôme Kunegis, Heinrich Hartmann, Markus Strohmaier, and Steffen Staab. Voting behaviour and power in online democracy: A study of liquidfeedback in germany’s pirate party. In ICWSM, pages 208-217. AAAI Press, 2015. URL: http://www.aaai.org/ocs/index.php/ICWSM/ICWSM15/paper/view/10566.
  10. Alois Paulin. An overview of ten years of liquid democracy research. In Proceedings of the 21st Annual International Conference on Digital Government Research, dg.o '20, pages 116-121, New York, NY, USA, 2020. Association for Computing Machinery. URL: https://doi.org/10.1145/3396956.3396963.
  11. Stefan Schmid and Dmitry Shestakov. Invited paper: Blockchain governance and liquid democracy - quantifying decentralization in gitcoin and internet computer. In Proceedings of the 2024 Workshop on Advanced Tools, Programming Languages, and PLatforms for Implementing and Evaluating Algorithms for Distributed Systems, ApPLIED'24, pages 1-7, New York, NY, USA, 2024. Association for Computing Machinery. URL: https://doi.org/10.1145/3663338.3663678.
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