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<TITLE>Equivalent defeat strength for Approval Sorted Margins / Approval Margins</TITLE>
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<DIV dir=ltr><FONT face=Arial color=#000000 size=2>Ted,</FONT></DIV>
<DIV dir=ltr><FONT face=Arial size=2></FONT> </DIV>
<DIV dir=ltr><FONT face=Arial size=2>I've been working on that, but the answer
is not yet clear.</FONT></DIV>
<DIV dir=ltr><FONT face=Arial size=2></FONT> </DIV>
<DIV dir=ltr><FONT face=Arial size=2>Part of the problem is that only pairs that
are currently adjacent in the list are considered for swapping (the equivalent
of firming up the defeat ).</FONT></DIV></DIV>
<DIV dir=ltr> </DIV>
<DIV dir=ltr>So if at some time the current list order is
A>B>C>D>E>F, and (A,B) is the out-of-order adjacent pair with the
smallest approval difference (a-b), while the approval difference (b-d) is even
smaller, the B>A defeat would be set in stone before (or ultimately
instead of?) the D>B defeat.</DIV>
<DIV dir=ltr> </DIV>
<DIV dir=ltr>Whether this ultimately causes a problem, I do not know.<BR></DIV>
<DIV dir=ltr>Forest</DIV>
<DIV dir=ltr> </DIV>
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<DIV dir=ltr><FONT face=Tahoma size=2><B>From:</B> Monkey Puzzle
[mailto:araucaria.araucana@gmail.com]<BR><B>Sent:</B> Tue 4/5/2005 10:50
AM<BR><B>To:</B> Simmons, Forest; Jobst Heitzig; Chris Benham;
election-methods-electorama.com@electorama.com<BR><B>Subject:</B> Equivalent
defeat strength for Approval Sorted Margins / Approval
Margins<BR></FONT><BR></DIV>
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<P><FONT size=2>Forest, Jobst, Chris:<BR><BR>As earlier shown by Jobst, Pairwise
(bubble) Sorted Approval finds the<BR>same social ordering as Ranked Pairs,
Beatpath or River, when defeat<BR>strength is determined by the total approval
of the winning pairwise<BR>candidate.<BR><BR>Is it possible to find a similar
equivalence for Approval Sorted<BR>Margins? In other words, is ASM
equivalent to Ranked Pairs (and/or<BR>Beatpath and/or River) when defeat
strength is measured by the margin<BR>of approval?<BR><BR>Ted<BR>--<BR>araucaria
dot araucana at gmail dot com<BR></FONT></P></DIV>
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