<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD><TITLE>[Condorcet] Re: why the Schulze Method is a Better Proposal</TITLE>
<META http-equiv=Content-Type content="text/html; charset=us-ascii">
<META content="MSHTML 6.00.2900.2722" name=GENERATOR></HEAD>
<BODY>
<DIV dir=ltr align=left><SPAN class=421315822-27092005><FONT face=Arial
color=#0000ff size=2>As a novice in the EM field but as a literate lay-person I
think I can explain the logical argument below (see
below).</FONT></SPAN></DIV><BR>
<BLOCKQUOTE dir=ltr
style="PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #0000ff 2px solid; MARGIN-RIGHT: 0px">
<DIV class=OutlookMessageHeader lang=en-us dir=ltr align=left>
<HR tabIndex=-1>
<FONT face=Tahoma size=2><B>From:</B>
election-methods-electorama.com-bounces@electorama.com
[mailto:election-methods-electorama.com-bounces@electorama.com] <B>On Behalf
Of </B>Simmons, Forest <BR><B>Sent:</B> Tuesday, September 27, 2005 5:52
PM<BR><B>To:</B> Condorcet@yahoogroups.com<BR><B>Cc:</B>
election-methods@electorama.com<BR><B>Subject:</B> [EM] RE: [Condorcet] Re:
why the Schulze Method is a Better Proposal<BR></FONT><BR></DIV>
<DIV></DIV>
<DIV id=idOWAReplyText44143 dir=ltr>
<DIV dir=ltr><FONT size=2>On Sun, 25 Sep 2005, Jeff Fisher
wrote:<BR>><BR>> Cycles (Condorcet paradoxes) still exist in DMC whether
it recognizes<BR>> them or not. To avoid discussing them would be possible
but dishonest.<BR>><BR>> DMC's tendency to hide cycles rather than
acknowledge<BR>> them head on is a liability rather than an
asset.<BR><BR><SPAN class=421315822-27092005><FONT face=Arial
color=#0000ff> <FONT face="Times New Roman"
color=#000000>></FONT> </FONT></SPAN>What does it mean to say that
cycles exist in a method?<SPAN class=421315822-27092005><FONT face=Arial
color=#0000ff> </FONT></SPAN></FONT></DIV>
<DIV dir=ltr><FONT size=2><SPAN class=421315822-27092005><FONT face=Arial
color=#0000ff>I take this</FONT> <FONT face=Arial color=#0000ff>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.</FONT></SPAN></FONT></DIV>
<DIV dir=ltr><FONT face=Arial color=#0000ff size=2><SPAN
class=421315822-27092005></SPAN></FONT> </DIV>
<DIV dir=ltr><FONT size=2><SPAN class=421315822-27092005><FONT face=Arial
color=#0000ff> > </FONT></SPAN>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.<SPAN class=421315822-27092005><FONT face=Arial
color=#0000ff> </FONT></SPAN></FONT></DIV>
<DIV dir=ltr><FONT size=2><SPAN class=421315822-27092005><FONT face=Arial
color=#0000ff>This is one way</FONT> <FONT face=Arial color=#0000ff>to
visualize a cycle, but you can find the problematic triplets of alternatives
without using a graph.</FONT></SPAN></FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2><SPAN class=421315822-27092005><FONT face=Arial
color=#0000ff> > </FONT></SPAN>But cycles existing in a
method?<SPAN class=421315822-27092005><FONT face=Arial
color=#0000ff> </FONT></SPAN></FONT></DIV>
<DIV dir=ltr><FONT size=2><SPAN class=421315822-27092005><FONT face=Arial
color=#0000ff>"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.</FONT></SPAN></FONT></DIV>
<DIV dir=ltr><FONT size=2><SPAN
class=421315822-27092005></SPAN></FONT> </DIV>
<DIV dir=ltr><FONT size=2><SPAN
class=421315822-27092005> </SPAN></FONT></DIV></DIV></BLOCKQUOTE></BODY></HTML>