[EM] TTR,MinMax, Losing Votes (TERW)

[Michael Ossipoff]

Chris's TERW, or IC-MaxMin(lv), seems to do all that he says that it
does. Well, I'd initially been skeptical of ICT too.

If the number of ballots ranking X over Y isn't greater than the
number ranking Y over X, plus the number ranking X and Y equal-top,
then I say that X doesn't beat Y. So, by my wording, TERW chooses
among the unbeaten candidates by MaxMin(lv).

Here's how I say the improved Condorcet definition of "beats":

X beats Y iff (X>Y) > (Y>X) + X=Y)T.

The losing-votes seems to avoid the chicken dilemma, while also
avoiding that split vote that Chris referred to (though it's hardly a
split-vote worthy of the name. It doesn't come close to a mutual
majority violation in ICT).

And there's appeal, and maybe some practical advantage, or resulting
criterion-compliance, in using a pairwise count method to choose among
the unbeaten candidates.

Also, I'd like to point out that ICT doesn't meaningfully fail to
choose a CW. Anyone top-ranking X and Y would prefer that someone
lower-ranked not win. That means that s/he doesn't want X or Y to beat
the other, preventing hir from being unbeaten, and giving the win to
someone lower-ranked.

So, when the equal-top ranking is interpreted in that way, the really
legitimate CW is the one based on the "beats" definition written
above. ICT passes the legitimately-defined Condorcet Criterion.

But yes, for choosing among unbeaten (as defined above) candidates,
maybe there isn't a chicken-dilemma issue, and so we're free to just
use pairwise-count to choose among the unbeaten candidates.

But, in a u/a election, in order to minimize the probability of an
unacceptable winning, wouldn't it be best to rank all of the
unacceptables, in order to do one's best to try to make them beaten,
even if by eachother?

So maybe TERW would benefit from the symmetrical-ness of Symmetrical ICT:

X beats Y iff (X>Y) + (X=Y)B > (Y>X) + (X=Y)T.

Wouldn't that bring 0-info LNHe compliance to TERW as well?

I don't know what TERW stands for. It seems to me that it would be
better to stick with Kevin's naming, and call it IC-MaxMin(lv).

I assume that if everyone or no one is beaten, then MaxMin(lv) is
applied to the whole candidate set. And that if some, but not all, are
unbeaten, then MaxMin(lv) is used to choose among the unbeaten
candidates.

What are TERW's criterion compliances. I'm assuming that it meets FBC
and CD. Doesn't it (like ICT) fail MMC when there's a cycle among the
majority-preferred candidates?

AOCBucklin has the advantage of fully passing MMC. Also, ER-Bucklin,
and presumably its AOCBucklin version too, passes Participation. It
thereby avoids that outrage that embarrasses all of the Condorcet
versions.

In Bucklin, if you rank X over Y, then X will get a vote from you
before Y does. It's difficult to find a way whereby adding such a
ballot could change the winner from X to Y.

Such an advantage is natural, for a method that's just stepwise
Approval. Another advantage resulting therefrom is the possibility of
offering AOCBucklin as an _option_ in an Approval election.  No one
can object to an option. It's your vote, and you can use it as you
wish.

Choosing between AOCBucklin and the IC versions, the choice would be
between AOCBucklin's reliable MMC compliance, and ICT's and TERW's
better defection-resistance. Is it worse for the method to be
vulnerable to people voting ridiculously insincerely to make a
possible next-level secondary chicken dilemma, or is it worse to fail
MMC in the unlikely event of a cycle among the majority-preferred
candidates?

Mike Ossipoff