Condocet Versions--some equivalent?

[Norman Petry]

Mike,

You wrote:

>
>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 subcycle  rule or tiebreaker needed.
>

Since one of the 4 methods you're referring to is Schulze, I'll take it up
from that point of view.  I assume the problem you're referring to here is
what occurs when there's no Condorcet winner among the beat-path wins.  If
so, in describing what Markus then referred to as Tideman (what we're now
calling the Schulze method), he proposed the following ("Re: Condorcet
sub-cycle rule", 3 Oct 1997):

>If there is no unique candidate, who defeats every other
>candidate via a beat path, then the Schwartz set of
>the beat-path-defeats is calculated, those candidates,
>who are not in this Schwartz set, are eliminated and
>the algorithm is re-started with the remaining candidates.

How does this compare with your approach?  I've been meaning to write to
Markus for more information on the merits of this particular tiebreaker, so
if this is the problem you're addressing with your subcycle rule, I'm very
interested!

An example of the problem would be helpful.


Norm Petry



-----Original Message-----
From: Mike Ositoff <ntk at netcom.com>
To: election-methods-list at eskimo.com <election-methods-list at eskimo.com>
Cc: ntk at netcom.com <ntk at netcom.com>
Date: August 5, 1998 6:49 PM
Subject: Condocet Versions--some equivalent?


>
>
>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
>