[EM] Ranked Pairs, continued

[MIKE OSSIPOFF]

To continue what I was saying about Ranked Pairs (RP), I like
SSD, CSSD, & RP because they only drop (or decline to keep) a defeat
if it's the weakest defeat in a cycle, and that gives them compliance
with GSFC & SDSC. PC at least meets SFC.

For PC & SSD, the problem with cycles is that there might
not be any unbeaten candidate. So these methods drop weakest defeats
till they undefeat someone.

Of course for RP it's also a problem if
no one is undefeated, but RP looks at cycles more critically, and
RP regards defeats in a cycle as being contradicted, nullified.
As judged by RP, we can't really name the unbeaten candidates till
we get rid of all the cycles, by judging which defeats most deserve
to be kept.

Whereas RP gets rid of all the cycles, CSSD gets rid of all the
cycles in the Schwartz set, drops weakest Schwartz set defeats till
the current Schwartz set has no cycles--that happens when that set
has no defeats among its members.

So--two differences: Only dropping defeats in the current Schwartz
set; and dropping weakest instead of keeping strongest. I don't have
an opinion about which sounds fairer or more right.

The example
that I posted is one in which both methods only drop one defeat,
and all the candidates are in the Schwartz set. So there, the 2 methods
only differ in keep-strongest vs drop weakest. I guess the question
is whether or not a defeat is nulified by a beatpath in the opposite
direction, as opposed to honoring all defeats except for the weakest,
even if they're in cycles, contradicted by return beatpaths. The
question is, how important is a beatpath, in disagreeing with a defeat.

Of course one could just simultaneously drop every cycle's weakest
defeat, but that often undefeats unnecessarily many candidates.
Repetition of that procedure to narrow down the winner-set has been
shown to be nonmonotonic.

By starting at the top, RP minimizes the number of defeats that need
to be not kept, when making a transitive ordering, by sequentially keeping 
the strongest defeats if
they aren't contradicted by already-kept defeats.

Of course
most would like the tendency for RP's winner to pairbeat the winners
of other monotonic Condorcet versions, including SSD & CSSD, where
those winners differ.

Speaking of monotonic, though, I don't know if RP(wv) or RP(m) has
been shown to be monotonic. CSSD & PC have been demonstrated to be
monotonic.

Though RP's procedure for equal defeats isn't important in public
elections, because equal defeats are vanishingly rare in public
elections, the electoral law still must include a provision for
equal defeats. But it still isn't something that need be brought
up to complicate public RP proposals. Most likely it's something
that no one needs to bother with till the electoral law is written.

The public electoral law provision for equal defeats in the middle
of an RP count could be something like "If the defeats are even, then
treat as stronger the ones whose defeating candidate is alphabetized
earlier. If they're odd, treat as stronger the ones whose defeating
candidtate is alphabetized later." That's no worse than the drawing
of lots specified for ties in Plurality elections.

I bring all this up because 1) Someone asked about RP; and 2) Now that
IRV has been adopted in SF, there's more interest in public proposals,
because it's obvious that Approvalists & Condorcetists have been
letting themselves be left-behind promotionally.

Mike Ossipoff





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