[EM] SD example--incomplete. Has error?

[Norman Petry]

Mike wrote:

>
>As I said, if SD can be nonmonotonic without pair-ties or equal defeats,
>I'd like to hear about it. But Blake, it seems to me, hasn't shown
>that. Let's have a complete example.
>

Here's an example that's equivalent to Blake's which shows all the pairwins
('AC43' means A beats C 43:0, etc.):

AC43, AE10, AG37, AH12
BA41, BD14, BF36, BG16, BI18
CB42, CE20, CG22, CI24
DA35, DC19, DE40, DH25
EB15, EF39, EG27, EI29
FA11, FC21, FD38, FH31
GD34, GF32, GH46
HB17, HC23, HE28, HI45
IA13, ID26, IF30, IG44

Note that there are no pair-ties or equal defeats.  The SD winner for the
above set of pairwins is D.  If the pairwin AG37 is replaced with AG33, then
A wins.  Therefore, since A won as a result of being downranked against G by
4 voters, SD is non-monotonic (polytonic?)

I wish this weren't so, but Blake's result is correct.  The only remaining
uncertainty is whether or not this is a *possible* pairwise matrix.  It's
somewhat difficult to work backwards from a 9-candidate example to a set of
ballots, so I haven't attempted it.


Norm