I want to emphasize that I don't want to seem contentious or defensive about the matter of the Schwartz set approach vs the beatpath approach. I asked for advantages that the beatpath approach has, and I got some answers about that. That's what I was asking for, and I'm glad to have those answers. Though I don't think the beatpath approach's advantages outweigh the proposability advantage of the Schwartz approach, I certainly recognize that those beatpath advantages are valid. But I must add that both approaches need to specify what happens when there's a final tie. Of course the Schwartz set approach is the one that needs to specify what happens when there are several defeats that are equal and weakest, during the middle of the count. But "drop them all" isn't complicated. Fewer details to specify, and greater calculation efficiency certainly do count for the beatpath approach. The efficiency difference suggests that the Schwartz set approach, even though it is more plausible & obvious, is also doing things in a more roundabout way. Anyway, though I still feel that the Schwartz set approach would be more convincing to members of the public, I don't deny the beatpath advantages that I've heard, and I'm interested in any more that can be posted. Mike Ossipoff _________________________________________________________________ Get your FREE download of MSN Explorer at http://explorer.msn.com
