[EM] Yet Another Lottery Method

[Simmons, Forest]

This method makes use of ordinal information as well as approval information.
 
1.  Eliminate each candidate X for which there is a candidate Y such that on each of more than half of the ballots Y is approved and X is not.
 
2.  Use random ballot among the remaining candidates to choose the winner.
 
Note that if any candidate X is eliminated, then some candidate Y must have more than fifty percent approval, which makes her invulnerable to elimination.
 
This method satisfies Monotonicity, Clone Independence, Independence from Pareto Dominated Alternatives, Strong Favorite Betrayal Criterion, etc.  In fact, as near as I can tell there is no incentive for any insincere order reversal or collapse.
 
Of course, Random Ballot without step 1 satisfies all of those criteria, too, but it is a bit too promiscuous with the probability. 
 
With this new method any united majority can eliminate any dangerous candidate from consideration.  This majority defense feature has a name, but I won't try to remember what it is.
 
Forest
 
 
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