[EM] RP done right in small committees

[MIKE OSSIPOFF]

Some, including me, after listing to others, have
criticized RP for small committees by saying that
it can need tiebreaking during the middle of the
count, when it encounters 2 or more equally strongest
defeats.

But that seems to not be so. Let me write a definition
of RP, and then add a provision for equal defeats:

In order of stronger defeats first, consider each
defeat in turn as follows: Keep it if it doesn't
contradict already-kept defeats (by being in a cycle
with them--i.e. by being in a cycle consisting only
of it and some already-kept defeats).

When all defeats have been so considered, a candidate
wins if s/he has no kept defeats.

But when 2 or more defeats are equally the strongest
ones not yet considered, then, in any order, consider
each of them by keeping them if they don't cycle with
_stronger_ kept defeats. Then, when all of those
equal defeats have been so considered (I'll call that
the 1st consideration), unkeep any of those equal
defeats that cycle with defeats that were kept
at the completion of the 1st consideration. Then resume considering
next-strongest defeats as described in the main instuctions before
this paragraph.

[end of definition]

Fortunately that last paragraph isn't need in public proposals, where
equal defeats are very unlikely. Sure, some provision must be made,
as a formality, but it could be about drawing lots. It could be the
above paragraph too, but the important thing is that there'd be no
need to bother the man-in-the-street about equal defeats procedures,
since it's practically certain that there won't be any.

That certainly isn't simpler than randomly choosing
consideration order, but it avoids tiebreaking during the middle of
the count.

I don't claim to have a good public-proposal name
for RP, but a good descriptive name is:
Sequentially-Keep-Un-Nullified-Defeats.

Of course, "Ranked-Pairs" is no descriptive name
at all.

It seems to me that the difference between SKUND (RP)
and BeatpathWinner/NIN/CSSD is that SKUND considers
a nullified defeat to be unqualified to nullify
another defeat.

Obviously my way of dealing with equal defeats in
SKUND in small committees still spoils SKUND's
simplicity under those conditions. That's why I'd
be more likely to recommend NIN for small committees.

In public elections, if single-winner reform advocates
want a rank-method, and if they don't like SKUND,
I'd next offer NIN. And if they don't like that
either,
I'd next offer SD. If they don't like that either,
I'd then offer PC. If they don't like that, I'd ask
them to reconsider their requirement for rank
balloting, and to consider Approval, which wouldn't
lead to a count-rule debate.

As much as I like the advantages of the best rank methods such
as SKUND & NIN, I'd probably, in a place where there wasn't already
a desire for rank-balloting, just propose Approval, to avoid
the debate between the rank-counts, if there's any likelihood that
people would insist on comparing a wide range of rank-count
proposals, and debating which is best.

Mike Ossipoff



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