MIKE OSSIPOFF nkklrp at hotmail.com
Sat Jan 14 10:43:55 PST 2012

ied-at-Top-Pairwise-Beats-All, Top Ratings. 

In keeping with Kevin's naming, and reflecting its relation to ICA, it could be called 
Improved Condorcet-Top (ICT).

I'll use that because it's shorter.

One thing that I like about the tied-at-top methods is that they elect A in the ABE,
meaning that one-sided coalition support is sufficient to defeat C, but without giving
the election away to B.

Of course the election of A violates the Plurality Criterion, but that's fine with me.
To me, the _practical_ advantage described in the previous paragraph is worth more than
the non-practical, aesthetic, Plurality Criterion.

ICT has burial strategy. In the ABE, the B voters can make B win by burying A, by middle-
rating C but not A. Then A doesn't have any indifference on his side, in hir comparison
with C.

But B still beats C, because B>C is still greater than C>B. For the same reason, C
still doesn't  beat everyone.

And B still beats A, because
B>A + B=A  is greater than A>B. 

So B is now the only beats-all candidate. B wins.

As currently defined, ICT elects C in Kevin's MMPO bad-example.

No one is indifferent between A and B.

So, since A=B is zero, then A>B + A=B is no greater than B>A. 

Likewise vice-versa, of course, since A & B are symmetrically-related.

Therefore, neither beats the other.

Maybe that can be fixed, by defining "beat" in the opposite way, so that x beats y
if x>y is greater than y>x + x=y, and then saying that the winning set is the set
of unbeaten candidates.

In summary, ICT does three things that some find unacceptable:

1. Plurality Criterion violation
2. Successful burial strategy
3. Noncompliance in Kevin's MMPO bad-example.

#1 and #2 aren't a problem to me. #2 could be, but I don't know what burial-deterrence
ICT has.

With the sole exception of MMT, the conditional methods meet Mono-Add-Plump.

They probably meet the Plurality Criterion too, because of their close relation to
Approval. If B defects, those methods elect C, in compliance with the Plurality Criterion.

Burial strategy has no meaning in the conditional methods. As I've been saying, they're
a completely new kind of method, with a new kind of strategy, a milder strategy.

Mike Ossipoff
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