2 problems
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The degree bound for unbiased non-transitive-symmetric graph voting rules
Degree-bound conjecture. There exist -regular graphs whose associated voting rules are unbiased but not transitive-symmetric whenever
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The square-root-logarithmic bound for unbiased totally asymmetric voting rules
Square-root-logarithmic bound conjecture. There exist voting rules that are unbiased, totally asymmetric, and have winning coalitions of size