[EM] New MN court affidavits by those defending non-Monotonic voting methods & IRV/STV

[Kristofer Munsterhjelm]

Kathy Dopp wrote:
>> From: Greg <greg at somervilleirv.org>
>> 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.