Condocet Versions--some equivalent?

[Mike Ositoff]

I've just gotten home. I'd been meaning to send this letter.
After sending it, I'm going to check the discussion that's taken
place while I was away yesterday & today.

Markus's wording, to sequentially throw out smallest defeats till
something is unbeaten seems equivalent to plain Condorcete(EM).

If it were limited to defeats that are part of a cycle that
would be Smith//Condorcet, no? That shows that SC can be worded
other than as a compound method. Is that more publicly explainable?

Norm's method, when it speaks of _tentative_ acceptance of each
next defeat--that tentative part suggests to me that it could
be worded other than as a sequential procedure.

How about: Throw out defeats that conflict (by forming a cycle)
with stronger defeats. 

That's brief. And doesn't that also describe what Tideman
(in the definition that I recently quoted here) says to do?

All 3 of these methods do the same as Schulze, in the examples
I've tried. All 4 equivalent?

This other Tideman definition merely says that skipping a
defeat doesn't lock it out--it merely doesn't lock it in.

***

All 4 of those procedures can't deal with a subcycle example
in which one member of the subcycle is winner with respect to
all non-subcycle alternatives, but not within the subcycle.

A subycle rule or tiebreaker needed.

Without a good, & simply-stated one, SC is very much in the
running. Though it can fail Independence from Clones, it works
fine if the subcycle defeats are smaller than the large cycle
defeats. Doesn't need a tiebreaker or subcycle rule.

Mike Ossipoff