Given a set B of ballots and a way of constructing "lotteries" from ballot sets ...
Create a lottery L(B) and incorporate this lottery into the ballot set B to get a new ballot set B' that has this lottery L included as an artificial candidate in the appropriate rank or with the appropriate rating on each ballot.
Cross off of each ballot in B' all of those candidates that are beaten pairwise by L.
If L is the only remaining candidate, then use the lottery L to pick the winning option from the original candidates.
Else If all candidates beat the lottery, then elect the candidate that beats the lottery by the greatest margin.
Else If the number of remaining candidates is strictly between zero and the original number of candidates, then restrict the ballots of B to this remaining set and apply the method recursively to pick a winner.
Forest
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