[EM] RE: [Condorcet] Re: why the Schulze Method is a Better Proposal
kislanko at airmail.net
Tue Sep 27 16:10:29 PDT 2005
As a novice in the EM field but as a literate lay-person I think I can
explain the logical argument below (see below).
From: election-methods-electorama.com-bounces at electorama.com
[mailto:election-methods-electorama.com-bounces at electorama.com] On Behalf Of
Sent: Tuesday, September 27, 2005 5:52 PM
To: Condorcet at yahoogroups.com
Cc: election-methods at electorama.com
Subject: [EM] RE: [Condorcet] Re: why the Schulze Method is a Better
On Sun, 25 Sep 2005, Jeff Fisher wrote:
> Cycles (Condorcet paradoxes) still exist in DMC whether it recognizes
> them or not. To avoid discussing them would be possible but dishonest.
> DMC's tendency to hide cycles rather than acknowledge
> them head on is a liability rather than an asset.
> What does it mean to say that cycles exist in a method?
I take this to be the same as Arrow's proof that it's not possible to create
an unambiguous ordering of group preferences based upon any algorithm that
tries to do so from individual preferences. In methods that count cells in
the pairwise matrix, these are "cycles", and it doesn't hurt to call the
same phenomenon a "cycle" when the manifestation is a tie in methods that
don't use the pairwise matrix to create an ordered list. I don't know this
for sure, but it seems reasonable that any problematic list by any method
would be accompanied by a "cycle" in the pairwise matrix.
> I think of cycles as existing in a directed graph that some people might
use to represent a set of ballots or a set of voter preferences.
This is one way to visualize a cycle, but you can find the problematic
triplets of alternatives without using a graph.
> But cycles existing in a method?
"Cycles" in either the directed graph sense or the analytical sense can
always occur. The real question is how a method resolves them or makes them
easy to identify algorithmically.
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