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<p>We study the structure of random ordinal Bayesian incentive compatible (OBIC) rules. We restrict attention to some special class of priors that we call “uniform-like” priors. We consider a class of priors, called <i>top uniform priors:</i> for any two alternatives <i>a</i> and <i>b</i>, a prior is top uniform if the aggregate probability (under the prior distribution) of preferences with respectively <i>a</i> and <i>b</i> at the top are the same. Over the unrestricted domain the uniform prior is a member of this class. We consider a class of random voting rules—<i>random vote share</i> rules, a generalization of plurality rule. For top uniform priors and arbitrary domains, Theorem <InternalRef RefID="FPar12">4.1</InternalRef> shows that every top monotonic and symmetric random vote share rule is OBIC. Over a domain satisfying some natural “richness” condition, we demonstrate that if a symmetric and strongly top responsive random vote share rule is OBIC with respect to some prior, then that prior must necessarily be a top uniform prior. We also provide some analogous results for <i>veto share rules</i> that are probabilistic generalizations of anti-plurality rule.</p>

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On the ordinal Bayesian incentive compatibility of vote share and veto share rules

  • 期刊论文

  • 发表日期：

    2026年6月16日

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  • Madhuparna Karmokar,
  • Dipjyoti Majumdar,
  • Souvik Roy

摘要

We study the structure of random ordinal Bayesian incentive compatible (OBIC) rules. We restrict attention to some special class of priors that we call “uniform-like” priors. We consider a class of priors, called top uniform priors: for any two alternatives a and b, a prior is top uniform if the aggregate probability (under the prior distribution) of preferences with respectively a and b at the top are the same. Over the unrestricted domain the uniform prior is a member of this class. We consider a class of random voting rules—random vote share rules, a generalization of plurality rule. For top uniform priors and arbitrary domains, Theorem 4.1 shows that every top monotonic and symmetric random vote share rule is OBIC. Over a domain satisfying some natural “richness” condition, we demonstrate that if a symmetric and strongly top responsive random vote share rule is OBIC with respect to some prior, then that prior must necessarily be a top uniform prior. We also provide some analogous results for veto share rules that are probabilistic generalizations of anti-plurality rule.