[EM] Condorcet How?
robert bristow-johnson
rbj at audioimagination.com
Sun Mar 21 18:04:35 PDT 2010
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."
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