I wonder why people call it a debate. IMHO the two candidates were holding monologues on certain issues and often they even didn't try to answer the questions of the moderator. Unfortunately the moderator didn't interfere when the candidates went off-topic. IMO Cheney did this more than Edwards, he even refused to do a rebuttal several times or he said that he had not enough time to do a rebuttal (which is almost the same for me, although I know that a rebuttal time of 30 seconds isn't much). For that reason and because Edwards argued his points much better I think Edwards won this monologue contest.