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Exploring the No-Show Paradox for Condorcet Extensions

In: Evaluating Voting Systems with Probability Models

Author

Listed:
  • Felix Brandt

    (Technische Universität München)

  • Johannes Hofbauer

    (Technische Universität München)

  • Martin Strobel

    (National University of Singapore)

Abstract

An important and surprising phenomenon in voting theory is the No-Show Paradox (NSP), which occurs if a voter is better off by abstaining from an election. While it is known that certain voting rules suffer from this paradox in principle, the extent to which it is of practical concern is not well understood. We aim at filling this gap by analyzing the likelihood of the NSP for six Condorcet extensions (Black’s rule, Baldwin’s rule, Nanson’s rule, Max-Min, Tideman’s rule, and Copeland’s rule) under various preference models using Ehrhart theory as well as extensive computer simulations. We find that, for few alternatives, the probability of the NSP is rather small (less than 4% for four alternatives and all considered preference models, except for Copeland’s rule). As the number of alternatives increases, the NSP becomes much more likely and which rule is most susceptible to abstention strongly depends on the underlying distribution of preferences.

Suggested Citation

  • Felix Brandt & Johannes Hofbauer & Martin Strobel, 2021. "Exploring the No-Show Paradox for Condorcet Extensions," Studies in Choice and Welfare, in: Mostapha Diss & Vincent Merlin (ed.), Evaluating Voting Systems with Probability Models, pages 251-273, Springer.
    • Handle: RePEc:spr:stcchp:978-3-030-48598-6_11
    DOI: 10.1007/978-3-030-48598-6_11
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    Cited by:

    1. Eric Kamwa & Vincent Merlin & Faty Mbaye Top, 2023. "Scoring Run-off Rules, Single-peaked Preferences and Paradoxes of Variable Electorate," Working Papers hal-03143741, HAL.
    2. David McCune & Jennifer Wilson, 2023. "Ranked-choice voting and the spoiler effect," Public Choice, Springer, vol. 196(1), pages 19-50, July.
    3. Lirong Xia, 2021. "The Smoothed Satisfaction of Voting Axioms," Papers 2106.01947, arXiv.org.

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