This isn't in reply to any subjct-line. This was something that I've
intended to post for a few days, a continuation of what I was saying about
MMPO. Obviously any method's criterion-failures should be addressed, and
MMPO is no exception.
MMPO can fail ICC, by means of a fratricidal majority cycle. But candidates
in a clone-set are presumably rather similar. So how come, in that ICC
failure scenario, they can muster more votes against eachother than
againsts their genuine opponent?
Likewise with MMC. That majority prefer eachother's candidates to all the
others. And yet they contribute to greater vote totals against eachother
than against someone they all like less?
Condorcet Loser? It must be a peculiarly popular Condorcet loser who has the
fewest people who prefer someone else to him. Not only is it unlikely for a
Condorcet Loser, but suppose one did. It would be unaesthetic to elect a
Condorcet loser, but how disastrous would it really be to elect a candidate
over whom fewest people prefer someone else? Would Hitler, Bush, or David
Duke win MMPO? Do some people worry too much?
In one of the Internet presidential polls, the person who conducted the
poll, in addition to finding the winner, also determined the Condorcet
loset. Yes, it was Bush. Was Bush the MMPO winner? The guy almost surely
didn't do an MMPO count. Would you care to make a little wager?
What odds would someone have to offer to you, to get you to bet that Bush
was the MMPO winner, though he was Condorcet loser? 100 to 1? Not unless
you're an incredible sucker. 1000 to 1? Say someone offered you a million
dollars, in the event that it turns out that Bush, the Condorcet loser in
that poll, was the MMPO winner, and all you had to had to put up was 1000
dollars. Would you accept the bet, as an easy million, or would it be more
like a very overpriced lottery ticket, and a reliable way to give away 1000
dollars?
If you answered "B", you'd be right. If I had the startup capital, the
million to cover the initial bets, and a steady supply of suckers who'd take
those odds, I could make a steady and dependable income with bets like that.
Twice recently on EM, I told the story of "The Three Silllies". The Sillies
would no doubt be very worried about these MMPO risks.
Enhancements for MMPO:
I suggested AERLO, to gain some criterion compliances. When I defined AERLO,
and wrote the part about cycles, for pairwise-count methods, I was writing
it for wv. For MMPO, I'd remove the stipulation that it must be a circular
tie containing above-line and below-line candidates. Maybe I'd leave in
something that says that there must be a cycle that has some above-line
candidates.
For ATLO, I'd leave the wording as-is.
As I said, AERLO brings compliance with SDSC and Strong FBC.
Collapsing cycles also brings SDSC compliance. And compliance with ICC, MMC
and GSFC.
It seems to me that cycle-collapsing caused PC (That's MM(wv)) to be
nonmonotonic. I don't know if it would cause nonmonotonicity with MMPO.
When I proposed the "subcycle rule", some years ago, I discussed two ways of
doing it: From the inside out, and from the outside in. You (Forest) suggest
an outside-in procedure that treats a cycle as a single candidate, and then,
if the winner is a cycle, that cycle is solved.
That outside-in approach seems that it would minimize execution-time, and
it's probably what I'd suggest too.
Most likely, just as with wv, ATLO would avoid a co-operation-defection
problem.
As I said, I'd propose the unenhanced method first, for simplicity, and then
offer the enhancements in subsequent initiatives.
So why discuss the enhancements now? Because they give us an idea how
improvable the various proposals are.
So, because enhancments are important for that reason, I'm going to keep
trying to look up the definition of sprucing-up. I once found a definition,
but it referred to terms that were defined elsewhere. So it would be
necessary to find a number of postings, with the definitions of the terms
used in that definition.
It seems to me that the first step of sprucing-up was to eliminate every
candidate who isn't in a certain selection set. The set of candidates who
could win without violating BC? And then was that followed immediately by
the collapsing of beat-clone-sets? A two-part procedure?Anyway, I guess I'll
keep looking. But Forest, could you post the full complete definition when
you get a chance to?
Mike Ossipoff
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