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Vote Delegation and Misbehavior

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  • Hans Gersbach
  • Akaki Mamageishvili
  • Manvir Schneider

Abstract

We study vote delegation with "well-behaving" and "misbehaving" agents and compare it with conventional voting. Typical examples for vote delegation are validation or governance tasks on blockchains. There is a majority of well-behaving agents, but they may abstain or delegate their vote to other agents since voting is costly. Misbehaving agents always vote. We compare conventional voting allowing for abstention with vote delegation. Preferences of voters are private information and a positive outcome is achieved if well-behaving agents win. We illustrate that vote delegation leads to quite different outcomes than conventional voting with abstention. In particular, we obtain three insights: First, if the number of misbehaving voters, denoted by f , is high, both voting methods fail to deliver a positive outcome. Second, if f takes an intermediate value, conventional voting delivers a positive outcome, while vote delegation fails with probability one. Third, if f is low, delegation delivers a positive outcome with higher probability than conventional voting. Finally, our results characterize worst-case outcomes that can happen in a liquid democracy.

Suggested Citation

  • Hans Gersbach & Akaki Mamageishvili & Manvir Schneider, 2021. "Vote Delegation and Misbehavior," Papers 2102.08823, arXiv.org, revised May 2021.
    • Handle: RePEc:arx:papers:2102.08823
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    1. John Ledyard, 1984. "The pure theory of large two-candidate elections," Public Choice, Springer, vol. 44(1), pages 7-41, January.
    2. Gersbach, Hans & Mamageishvili, Akaki & Tejada, Oriol, 2019. "The Effect of Handicaps on Turnout for Large Electorates: An Application to Assessment Voting," CEPR Discussion Papers 13921, C.E.P.R. Discussion Papers.
    3. Roger B. Myerson, 1998. "Population uncertainty and Poisson games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(3), pages 375-392.
    4. Alessandra Casella & Thomas Palfrey, 2019. "Trading Votes for Votes. A Dynamic Theory," Econometrica, Econometric Society, vol. 87(2), pages 631-652, March.
    5. Thomas Palfrey & Howard Rosenthal, 1983. "A strategic calculus of voting," Public Choice, Springer, vol. 41(1), pages 7-53, January.
    6. Stefanos Leonardos & Daniël Reijsbergen & Georgios Piliouras, 2020. "Weighted voting on the blockchain: Improving consensus in proof of stake protocols," International Journal of Network Management, John Wiley & Sons, vol. 30(5), September.
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