[EM] Simpson-Kramer

[MIKE OSSIPOFF]

Dear Markus--

You say:

however, at least when each voter casts a complete ranking
of all candidates then the Simpson-Kramer method is identical
to what you call "Plain Condorcet".

I reply:

Not good enough. The fact that Simpson-Kramer can sometimes give the same 
result as PC doesn't mean that Simpson-Kramer is PC.

You continue:

This cannot be said about
Condorcet's proposals (who, by the way, doesn't discuss partial
individual rankings either).

I reply:

Condorcet proposed that when there's no CW ("consistent opinion", or words 
to that effect, in some translations) then we should ignore the proposition 
(pairwise defeat) that has the least support. And do so till there is a 
consistent opinion.

That sounds like PC.

Norm posted a quote that showed that Condorcet discussed partial rankings.

But thanks for showing that you can't deny the things that I said in my 
previous "Simpson-Kramer" posting, meaning that you admit that 
Simpson-Kramer is not PC, and that PC is not Simpson-Kramer.

Since we agree that MinMax is Simpson-Kramer (to deny it would be to deny 
the authority of your authors), then we agree that MinMax must not be PC. 
That's because if Simpson-Kramer isn't PC, and if MinMax can only be one 
thing, and if MinMax is Simpson-Kramer, then MinMax can't also be PC.

You continue:

So after all, you didn't give any
justification why you call this method "Plain Condorcet(wv)"
and not "Simpson-Kramer(wv)".

I reply:

But why would I call PC "Simpson-Kramer(wv)" when Simpson-Kramer elects the 
candidate whose greatest pairwise vote against him in a pairwise-comparison 
(not necessarily a pairwise defeat of his) is less than anyone else's 
greatest pairwise vote against them in a pairwise comparison?

You continue:

By the way: Most of the terminology (e.g. "Copeland set",

I reply:

I don't often mention the Copeland set.

You continue:

..."Smith set", "Schwartz set")
that is used in this mailing list
comes from a paper by Fishburn ("Condorcet Social Choice
Functions", SIAM Journal on Applied Mathematics, vol. 33,
pp. 469--489). Also Fishburn presumes that each voter casts
a complete ranking of all candidates. He writes on page 470
of his paper:

>It will be assumed throughout that all voters have linear
>preference orders on the candidates or alternatives so that
>individual indifference between distinct candidates does not
>arise.

So if you really wanted to be consistent you wouldn't use
Fishburn's terminology either.

I reply:

I've posted definitions of the Smith set and the Schwartz set. Is it really 
necessary for me to post them again for you? I don't depend on Fishburn's 
definitions. Let me know if there's a term that I use that I haven't defined 
and which needs a definition.

Fishburn refers, by the name "Condorcet", to the method which I call PC.

If Fishburn's assumption that you quoted means that Fishburn's method 
definitions, including his Condorcet definition, don't apply unless everyone 
ranks all the candidates--no problem. I've defined PC without any such 
assumption. You're welcome, then, to refer to PC if you want to name a 
method defined without the assumption that everyone votes a complete 
ranking.

Condorcet also proposed a method that Tideman reasonably interpreted as what 
we call Ranked-Pairs, except that Tideman measures defeats by margins.

Condorcet's RP and PC methods have in common the fact that circular ties are 
solved by successively dropping weakest defeats or keeping  ("locking-in") 
strongest defeats. Other Condorcet versions describable in that way, such as 
Smith//PC, SD, SSD, or CSSD are less literal interpretations of Condorcet's 
PC wording. It may well be that if Condorcet actually conducted a 
defeat-dropping Condorcet election, he'd use SD, SSD or Smith//PC instead of 
PC.

Anyway, I justify calling SD, SSD, and Smith//PC Condorcet for that reason, 
and because they solve circular ties by successively dropping weakest 
defeats. I call CSSD, and therefore BeatpathWinner, Condorcet by extensiion 
from SSD.

Mike Ossipoff


Markus Schulze

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