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