[EM] methods based on cycle proof conditions

[Chris Benham]

I.  BDR or "Bucklin Done Right:" 
>
>Use 4 levels, say, zero through three.  First eliminate all candidates defeated 
>pairwise with a defeat ratio of 3 to 1.  Then collapse the top two levels, and 
>eliminate all candidates that suffer a defeat ratio of 2 to 1.  If any 
>candidates are left, among these elect the one with the greatest number of 
>positive ratings. 
>  
>
><snip> 

This seems to be even more Approvalish than normal Bucklin. 

65: A3, B2 
35: B3, A0 

(I assume that zero indicates least preferred) 

Forest's "BDR" method elects A, failing Majority Favourite. 

In response to the above, Abd Lomax-Smith wrote (3 June 2010):

<snip>

Now, who would use BDR with only two candidates? It's like using 
>Range with only two candidates. Why would you care about "majority 
>favorite" if you decide to use raw range. I wonder why the A faction 
>even bothered to vote with that pattern of utilities ("ratings"). 
>That's what is completely unrealistic about this kind of analysis.
><snip>

I was content to simply prove that the method simply fails Majority Favourite, but to appease 
Abd  here is a similar example with three candidates:

60: A3, B1, C0
35: B3, A0, C1
05: C3, A2, C0

A is the big majority favourite and the big voted  "raw range" winner, and yet  B wins.

Chris Benham