Some chance for consensus: voting methods for which consensus is an equilibrium

@article{Heitzig2012SomeCF,
  title={Some chance for consensus: voting methods for which consensus is an equilibrium},
  author={Jobst Heitzig and Forest W. Simmons},
  journal={Social Choice and Welfare},
  year={2012},
  volume={38},
  pages={43-57}
}
We introduce the following basic voting method: voters submit both a “consensus” and a “fall-back” ballot. If all “consensus” ballots name the same option, it wins; otherwise, a randomly drawn “fall-back” ballot decides. If there is one potential consensus option that everyone prefers to the benchmark lottery which picks the favorite of a randomly drawn voter, then naming that option on all “consensus” ballots builds a very strong form of correlated equilibrium. Unlike common consensus… 
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