There are precious few methods besides regular Approval that have been proposed which satisfy the FBC. Demorep's ACMA and ACLA and other versions of Approval Completed Condorcet are among the few seriously proposed methods that satisfy this important property. Another variation that seems to satisfy the FBC is this: Of the two candidates with the most approval, take the one that is preferred over the other by the greater margin of voters. This can be thought of as an instant runoff where the two candidates that qualify for the second (i.e. final) round are picked by Approval. Forest
