[EM] A small group method that satisfies the FBC

[Simmons, Forest]

Random ballot satisfies the Strong FBC, but it is too promiscuous with the probability for most situations.
 
Here's a small group method that  is much more frugal with the probability while still satisfying the FBC, if not the Strong FBC.
 
1. List the alternatives in order of approval on the black board at the front of the room.
 
2.  Have everybody that approves the top alternative stand up.
 
3.  Go down the list one alternative at a time, adding supporters until at least 50% of the voters are standing.
 
4.  Erase all of the alternatives below this level.
 
5.  Have everybody sit down, and then have a randomly chosen voter choose the winner from among the alternatives that remain on the black board.
 
Comments:  
 
The method can be adapted to large elections by making use of ordinal ballots with approval cutoffs.
 
The fifty percent quota could be replaced by a higher quota Q in a situation where the "tyranny of the 50+ majority" was a problem.  
 
 Here's my suggestion for Rwanda.  Nominally set Q at 66.7%.  Then in each election that a two-thirds majority wants Q lowered to 50%, go ahead and lower it for that election.
 
Forest
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