[EM] Confirmed -- SD is not monotonic.

[Norman Petry]

Yesterday, Mike wrote:

>
>I've just received the message that I'm replying to, and so
>there hasn't yet been an opportunity to check out the SD
>nonmonotonicity example. If SD can be nonmonotonic under many-voter
>conditions, that would certainly count against it as a public
>proposal.
>

I've verified Blake's result showing that yes, SD is *not* monotonic.  Since
Blake's example doesn't have any pairties, this outcome would be possible
even in a large public election (although highly improbable, imho).

Here are the results I got for Blake's example using a variety of voting
methods:

SD:      D, then A -> NOT monotonic
SSD:     A, then G -> monotonic
Schulze: A, then G -> monotonic
Tideman: D, then G -> monotonic
IBCM:    D, then A -> NOT monotonic
PC:      D, then D -> monotonic

No surprises really (except for SD).  IBCM was already known to be
non-monotonic.  I tried to modify Blake's 9-candidate example to one having
fewer candidates but exhibiting the same problem, but was unsuccessful.
Therefore, I think that SD's violation would be extremely rare in practice,
just as its GITC violations are also very rare.  This means that although
the method is both simple and would be excellent for actual use, it would be
open to academic criticism.  As Blake said, Tideman doesn't have these
particular problems, and is also fairly simple, so I agree that it is a
better public proposal.

Norm Petry