<HTML><FONT FACE=arial,helvetica><FONT SIZE=2 FAMILY="SANSSERIF" FACE="Arial" LANG="0">Hello List<BR>
<BR>
Before I came up with CRCLE ( Cardinal Rating Condorcet Loser Elimination ) I'd never paid much attention to the various methods of resolving Condorcet cycles. CRCLE is considerably more prone to developing cycles than plain Condorcet so I looked at various websites promoting Condorcet to find a good cycle resolution method.<BR>
<BR>
Ranked Pairs was generally highly recommended as a method. However, attempting it with various examples I found the results very disappointing. <BR>
<BR>
Take the (normal Condorcet) example:<BR>
<BR>
45 A<BR>
6 B>A<BR>
5 B>C<BR>
44 C>B<BR>
<BR>
A versus B 45 v 55 margin 10 winner B<BR>
A versus C 51 v 49 margin 2 winner A<BR>
B versus C 11 v 44 margin 33 winner C<BR>
<BR>
C's defeat of B is locked first followed by B's defeat of A. This gives C>B>A. Under Ranked Pairs C the least supported candidate is the winner. Under CRCLE ( using RP as an elimination method) assuming utilities for all candidates close to 1.00 A is eliminated as Condorcet loser and C wins against B ( 44 v 11).<BR>
<BR>
Am I doing Ranked Pairs right ?<BR>
<BR>
Assuming I am doing it right I don't think it's very good.<BR>
<BR>
I came up with a different method of resolving cycles that seems better but which I can't find described anywhere.<BR>
<BR>
The procedure for CRCLE is as follows:<BR>
<BR>
In instances of a cycle for Condorcet loser eliminate the candidate with the lowest maximum level of support in pairwise comparisons.<BR>
<BR>
<BR>
<BR>
For the example:<BR>
<BR>
45 A<BR>
6 B>A<BR>
5 B>C<BR>
44 C>B<BR>
<BR>
A versus B 45 v 55 margin 10 winner B<BR>
A versus C 51 v 49 margin 2 winner A<BR>
B versus C 11 v 44 margin 33 winner C<BR>
<BR>
A's level of support is 45 in the AB comparison and 51 in the AC comparison.<BR>
A's maximum level of support is therefore 51.<BR>
<BR>
B levels of support are 55 and 11.<BR>
B's maximum level of support is 55.<BR>
<BR>
C levels of support are 49 and 44.<BR>
C maximum level of support is 49.<BR>
<BR>
Maximum support for A is 51.<BR>
Maximum support for B is 55.<BR>
Maximum support for C is 49.<BR>
<BR>
C has the lowest maximum level of support and is eliminated as Condorcet loser.<BR>
<BR>
Is this method of resolving cycles described/mentioned/invented by somebody else and if so who ?<BR>
<BR>
Is this method of resolving cycles badly flawed in any way ?<BR>
<BR>
David Gamble<BR>
<BR>
<BR>
</FONT></HTML>