[EM] CRCLE ( Resolving Cycles- Ranked Pairs Doesn't Do Very Well )

[Dgamble997 at aol.com]

Hello List

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.

Ranked Pairs was generally highly recommended as a method. However, 
attempting it with various examples I found the results very disappointing. 

Take the (normal Condorcet) example:

45 A
6 B>A
5 B>C
44 C>B

A versus B      45 v 55   margin 10 winner B
A versus C      51 v 49   margin  2  winner A
B versus C      11 v 44   margin  33 winner C

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).

Am I doing Ranked Pairs right ?

Assuming I am doing it right I don't think it's very good.

I came up with a different method of resolving cycles that seems better but 
which I can't find described anywhere.

The procedure for CRCLE is as follows:

In instances of a cycle for Condorcet loser eliminate the candidate with the 
lowest maximum level of support in pairwise comparisons.



For the example:

45 A
6 B>A
5 B>C
44 C>B

A versus B      45 v 55   margin 10 winner B
A versus C      51 v 49   margin  2  winner A
B versus C      11 v 44   margin  33 winner C

A's level of support is 45 in the AB comparison and 51 in the AC comparison.
A's maximum level of support is therefore 51.

B levels of support are 55 and 11.
B's maximum level of support is 55.

C levels of support are 49 and 44.
C maximum level of support is 49.

Maximum support for A is 51.
Maximum support for B is 55.
Maximum support for C is 49.

C has the lowest maximum level of support and is eliminated as Condorcet 
loser.

Is this method of resolving cycles described/mentioned/invented by somebody 
else and if so who ?

Is this method of resolving cycles badly flawed in any way ?

David Gamble


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