Kevin--
I'd said:
So every candidate s/he doesn't rank is treated as if it were last-ranked
on his-her ballot, with all the others ranked over that candidate.
You say:
I think this makes it too dangerous to rank among acceptable candidates.
I reply:
No, it dosn't. By the definition of an acceptable/unacceptable situation,
you'd rather maximize the probability that the winner will come from the
acceptable set than influence which acceptable candidate wins or influence
which unacceptable candidate wins.
Of course maybe you're talkiing about when it isn't an
acceptable/unacceptable situation. Hello, are we talking about the same
subject? I've been discussing strategy in an acceptable/unacceptable
situation.
But if you're talking about general ranking strategy, then I commend you for
the ambitiousness of your project. Soon you'll post your strategy solutions,
based on probabilities and utilities, for ranking under general conditions.
You continue:
I suggest this instead:
Assume everyone uses power truncation (and why wouldn't they?)
I reply:
No reason why they wouldn't, in an acceptable/unacceptable situation.
You continue:
Elect the
candidate with the lowest "MMPO+PT score," which is equal to the greater of
the candidate's MMPO score, and the number of ballots on which he is not
ranked
("disapproved," we could say).
I reply:
Proposing new methods is more popular than demonstrating their properties or
telling what makes them better.
Regarding your new method, using max(MMPO score, disapproval), I'll call it
maxMMPOd, rather than try to find something better right now. But if you
have a better designation of course I'll use that, since it's your method.
Maybe maxMMPOd is better. Maybe it's the best. I couldn't say, and in fact I
don't even know what its motivation and justification are.
You continue:
So back to this scenario:
49 A
24 B
27 C>B
With your definition, assuming everyone uses power truncation, A wins and B
does the worst, if I'm not mistaken. (I posted this earlier.)
Using the "max(MMPO score,disapproval)" wording:
The MMPO scores are A 51, B 49, C 49. Disapproval is A 51, B 49, C 73.
Taking the max of these, the scores are A 51, B 49, C 73, so that B wins
decisively.
I reply:
And so...what? You've shown that MMPOpt and maxMMPOd can give different
results. It's been demonstrated that different methods can give different
results. That's why we call them different methods.
Maybe your point is that maxMMPOd chooses, in that example, as wv does,
while MMPOpt doesn't.
MMPOpt is not wv. Under some conditions wv gives a better result than
MMPOpt. In other conditions MMPOpt gives a better result than wv.
If you want to show that maxMMPOd complies with wv's criteria better than
MMPOpt does, then showing one example won't accomplish that. You'd actually
have to demonstrate it for various specific criteria.
It would be great if maxMMPOd improves on MMPOpt. I like improvements. But
they have to be demonstrated.
Your example doesn't show MMPOpt violating CC, though of course such an
example could be written.
By the way, in other postings you say or imply that tMMWV and your other
similar methods are significantly more likely to meet CC than MMPO or MMPOpt
is. But you haven't shown that either.
In the acceptable/unacceptable situation that we're discussing, of course
equal ranking in 1st place will be pretty much universal. And, depending on
how much lesser-of-2-evils voting will continue, with rank balloting, that
too would be enough, by itself, to cause lots of equal-ranking in 1st place.
For one thing, that spoils your near-CC-compliance. For another thing it
results in a ridiculous number of ties in public elections.
Mike Ossipoff
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