[EM] Condorcet How?

[robert bristow-johnson]

On Mar 21, 2010, at 1:30 AM, robert bristow-johnson wrote:

> On Mar 20, 2010, at 5:04 PM, Markus Schulze wrote:
>
>> Here are the proposed statutory rules:
>>
>> http://m-schulze.webhop.net/propstat.pdf
>
> __________________
> Suppose d[V,W] is the number of valid ballots on which candidate V  
> is strictly preferred to candidate W. ...
>
> A Òpath from candidate X to candidate Y of strength zÓ is a  
> sequence of candidates C(1),...,C(n) with the following four  
> properties:
>
>  1. C(1) is identical to X.
>  2. C(n) is identical to Y.
>  3. For all i = 1,...,(nÐ1): d[C(i),C(i+1)] > d[C(i+1),C(i)].
>  4. For all i = 1,...,(nÐ1): d[C(i),C(i+1)] ³ z.
>
> p[A,B] is the maximum value such that there is a path from  
> candidate A to candidate B of that strength. If there is no path  
> from candidate A to candidate B at all, then p[A,B] : = 0.
> __________________

i just thought i would take a look at the 2009 Burlington mayoral  
election (that was far from having any Condorcet cycles, in fact it  
was super-well ordered):

    M 4064
    K 3477
     < 587>

    M 4597     K 4313
    W 3664     W 4061
     < 933>     < 252>

    M 4570     K 3944     W 3971
    S 2997     S 3576     S 3793
     <1573>     < 368>     < 178>

    M 6263     K 5515     W 5270     S 5570
    H  591     H  844     H 1310     H  721
     <5672>     <4671>     <3960>     <4849>


M, of course is the winner and p[M,K] = 587 (as i would expect), but  
what i didn't expect is that M's defeat strength over W, S, and H are  
no larger.  p[M,H] is also 587, but p[M,W] is 252 (same as p[K,W])  
and p[M,S] is 178.

or am i doing this wrong?  is it instead p[M,K]=587, p[M,W]=933, p 
[M,S]=1573 and p[M,H]=5672?  just curious.

--

r b-j                  rbj at audioimagination.com

"Imagination is more important than knowledge."