[EM] Re: MDD,ER-Bucklin (whole)

[Chris Benham]

Kevin,
You are right,  I erred.  MDD,ER-Bucklin(Whole)  doesn't meet  
Smith(Gross),  so scrub that and replace
it with "Condorcet(Gross)".

Douglas Woodall  gives this demonstration:

49: a>b>c>d>i>j>k>e>f>g>h
31: e>f>g>h>j>k>i>a>b>c>d
20: k>i>j>a>b>c>d>e>f>g>h

>The Smith set is {i,j,k} (beating a,b,c,d by 51 to 49 and e,f,g,h by
>69 to 31).  But i beats j by 69 to 31, j beats k by 80 to 20, and k
>beats i by 51 to 49, so that every candidate has a majority-strength
>defeat.  Thus the MDD bit has no effect, and the method reduces to 
>Bucklin.  No candidate has a majority in the top three preferences, 
>and if the top four preferences are counted then A wins.  But A is 
>not in the Smith set.
>

I  don't  consider this to be a serious drawback,  and  I don't doubt 
that you are right that compliance
with any sort of  top-cycle criterion  is incompatible with  FBC.


Chris  Benham