Kathy Dopp wrote:
From: Greg <[EMAIL PROTECTED]>
Subject: Re: [EM] New MN court affidavits by those defending
non-Monotonic voting methods & IRV/STV
As you acknowledge, IRV does not satisfy monotonicity when there are
three (or more) candidates.
True. IRV does not, but plurality does.
Top-two runoff is equivalent to IRV when
there are three candidates.
Greg,
Your statement above is provably false and very simply so. IRV and
top-two runoff are nowhere even close to "equivalent". Read my
affidavit from a month ago or my paper on the flaws of IRV or any of
Abd'ul's emails, or just think about it for a while.
If you consider top two runoff a single election that takes ranked
ballots (people's preference orderings), and first votes for the
first-ranked and then (on the second round) for whoever ranks highest of
the candidates remaining in the race, then TTR is nonmonotonic.
Abd seems to show that TTR cannot be reduced in such a mechanical
manner, by that states that, when using TTR, used to elect candidates
that weren't plurality winners, no longer elects them under IRV. Thus,
the deliberation period between the first and second rounds are of
importance. I don't think that makes TTR monotonic, though.
What we'd need to show to have TTR nonmonotonic even with deliberation
is for A and B to be winners if you vote in a "strategic" manner, but,
if you raise your honest favorites, C and D win, both of which you think
are worse than A and B. Can this be done? (Other list members, anyone? :-)
Anyway, the point is that your nonmonotonicity argument against IRV
could be used by others to argue that TTR is a virtual single-round
method (of the form I described above), and thus that it too is
nonmonotonic, and thus that either nonmonotonicity is too strict, or
that TTR must be reverted to Plurality.
If you face this, I think you should argue that TTR is a two-round
mechanism and thus the deliberation gets around the problem (unless the
A,B->C,D example is possible, in which case you have a problem). Or you
might say that getting rid of TTR is a price you'll have to pay, and
that getting Condorcet later might just be worth that price. Beware that
you might look like a Plurality defender if you do so, though;
especially so since TTR seems to give better results than Plurality, and
probably better results than IRV too.
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