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