Smallest Tournaments Not Realizable by 23-Majority Voting

  title={Smallest Tournaments Not Realizable by 23-Majority Voting},
  author={Dylan Shepardson and Craig A. Tovey},
Define the predictability number α(G) of a tournament T to be the largest supermajority threshhold 1 2 < α ≤ 1 for which T could represent the pairwise voting outcomes from some population of voter preference orders. We establish that the predictability number always exists and is rational. Only acyclic tournaments have predictability 1; the Condorcet voting paradox tournament has predictability 2 3 ; Gilboa (4) found a tournament on 54 alternatives (i.e. vertices) that has predictability less… CONTINUE READING

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