Sprucing up

From electowiki

Sprucing up refers to a procedure for ensuring that a voting method satisfies the Condorcet Criterion and Independence of clones. It was described by Forest Simmons on the election-methods mailing list. See his original description ("Sprucing up MMPO and other methods" from Forest Simmons on 2004-12-21) for more information.

When an otherwise good method fails Clone Independence and/or the Condorcet Criterion, perhaps it can be rescued by the following general "spruce up:"

1. Eliminate covered candidates until each remaining candidate has a short (length one or two) beat path to each of the other remaining candidates.

2. Collapse all proper "beat clone sets."

3. Apply the rescue worthy method, say MMPO, to the resulting set of ballots.

4. If the winner in step 3 is one of the original candidates, then we are done.

5. Otherwise, the winner is one of the collapsed clone sets. In this case we (recursively) use this "spruce up" on the clone set to find a winner.

Sprucing up a method might lead it to fail summability or monotonicity as a consequence of eliminating candidates in step one.