[EM] Score Cover Sort

Forest Simmons forest.simmons21 at gmail.com
Sun Jul 17 17:37:32 PDT 2022


Remember that candidate X "defeats" candidate Y iff X is ranked or rated
ahead of Y on more ballots than Y is ranked or rated ahead of X.

Additionally candidate X "covers" candidate Y iff candidate X not only
defeats Y, but also any candidate that does defeat X also defeats Y.

For each candidate, make a 3"×5" card with its name, score, list of
candidates it covers, and a list of any other candidates defeated by it.

First sort the cards by score.

Then while any candidate X covers some candidate Y above it (in the card
deck) reinsert the highest such X card immediately above the highest
candidate Y that it covers.

Elect the candidate that finishes at the top of the deck.

This is the simplest monotone, clone free finish order that I know of that
always elects an uncovered candidate.

Since it respects the score as far as possible while monotonically electing
an uncovered candidate, it is probably the highest Voter Satisfaction
Efficiency, monotone method that always elects an uncovered candidate.

And think of the dissatisfaction that inevitably results when a method can
elect a covered candidate!

-Forest
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