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: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Simmons, Forest
Sent: Tuesday, September 27, 2005 5:52 PM
To: [EMAIL PROTECTED]
Cc: [EMAIL PROTECTED]
Subject: [EM] RE: [Condorcet] Re: why the Schulze Method is a Better ProposalOn 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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