[EM] Let MMPO solve its ties. It elects A in the example. The simplest is the best.

[MIKE OSSIPOFF]

As I said, let MMPO solve its ties. If MMPO has a tie, solve the tie by MMPO (with only the tied candidates in the count).
 
That's what I'll mean when I say "MMPO".
 
In the MMPO example that was posted, which was:
 
9999 ballots: A
1 ballot:        A=C
9999 ballots: B
 
MMPO, as I've defined it here, chooses A, the Condorcet winner.
 
Ways of stating MMPO:
 
Elect the candidate over whom fewest people have ranked the same other candidate.
 
Or
 
Elect the candidate who, compared to the other candidates, doesn't have anyone ranked over him by as many people.
 
Now I'd like to mention another example, sometimes used as an Approval "bad-example". I mention it
because I'm going to tell how various rank methods do in that example. Myself, I don't consider it bad 
really, because Approval isn't claimed to be perfect, just very good. Here's the example:
 
100 voters:
 
Sincere preferences:
 
40: C
35: ABC
25: BAC
 
In fact, the A voters and B voters quite despise C.
 
The A voters co-operate to defeat C, and so they approve A and B.
 
The B voters only approve B.
 
Maybe the B voters are intentionally taking advantage of the co-operativeness of the A voters.
Or maybe they just have much stronger feelings about the choice between A and B.
 
A wins, because of his voters' defection.
 
If that example looks bad, remember that the important thing about Approval is that it lets everyone 
vote for their favorite, and voters' support for candidates isn't concealed as it is in Plurality. This election 
gives the A voters better information, not only about the candidates' support, but about the B voters, who 
won't be able to expect approval from A voters again--at least not in the subsequent election.
 
The A voters did the right thing, because approving B gave them a better result than they'd get
if they hadn't done so.
 
_Scientific American_ described a computer simulation experiment in which many different strategy
programs competed, in pairs, in the nonzero-sum cooperation/defection game known as "prisoner's dilemma".
Each pair of strategy programs played the game  over and over, many times. Each strategy's total number
of points from all of its games, with all of the other candidates, is summed.
 
Some strategies did much better than others. The best, of the ones tested, was called "Tit-For-Tat". It simply
copied the other player's play in the previous game.  A series of Approval elections is a similar nonzero-sum game of 
co-operation and betrayal. 
 
Later, an even better strategy was found for that game in that simulation. I don't remember what it was, but it
could be looked up. Those strategies will be of interest in Approval elections with co-operation/defection.
 
Anyway, how do some other methods do in that example?:
 
Some methods that fail in that example:
 
Condorcet (including wv(including Beatpath, Ranked-Pairs, PC, etc.)), Bucklin, MDDA, MAMPO
 
Some FBC-complying methods that don't fail in that example:
 
MMPO, DMC (both its original and enhanced versions)
 
The simplest is the best.
 
When I do public polling, I'll just include Approval and MMPO in the poll.  ...with RV kept in reserve in case
people reject the better methods.
 
 
  		 	   		  
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