I don't know the answer to the problem as you stated it. I did, however, recently work for a state Senate campaign and asked alot of questions. One thing they told me was that negative advertising only puts doubt in the mind of the unaligned voters regarding the opponent rather than winning any voter's support.
As an example, here in Michigan, Dick Posthumus was trailing Jennifer Granholm in the polls by quite a bit. The Posthumus campaign ran no positive Posthumus ads for quite some time, instead running negative ads about Granholm in the hopes of getting unaligned voters to abandon her. Once the polls showed that alot of unaligned voters had become undecided again, the Posthumus campaign started in on the positive Posthumus ads to win those undecided voters over. In the end the results were close. I know that doesn't help solve the problem as you worded it, but perhaps the payoffs are different from what your example assumed. So any candidate trailing in the polls will run negative ads to make the unaligned voters become undecided again. Once that is accomplished, all candidates must begin competition all over again for those votes. With three viable candidates, I suppose the two trailing ones must play a game of brinkmanship, waiting for the other to go negative, and cash in on the newly dislodged voters. -jsh __________________________________________________ Do you Yahoo!? Yahoo! Mail Plus - Powerful. Affordable. Sign up now. http://mailplus.yahoo.com