Actually, what is the worst that could happen? It's not [the structure of the universe is destabilized by the breakdown of causality], because that would have already happened if it were going to.
The obvious one would be [Eliezer loses $20,000], except that would only occur in the event that it were possible to violate causality, in which case he would presumably arrange to prevent his past self from making the bet in the first place, yeah? So really, it's a win-win.
Unless one of the people betting against him is doing so because ve received a mysterious parchment on which was written, in ver own hand, "MESS WITH TIME."
If there are ways to violate causality they are likely restrictive enough that we can't use them to violate causality prior to when we knew about the methods (roughly). This is true for most proposed causality violating mechanisms. For example, you might be able to violate causality with a wormhole, but you can't do it to any point in spacetime prior to the existence of the wormhole.
In general, if there are causality violating mechanisms we should expect that they can't violate causality so severely as to make the past become radically altered since we j...
http://www.nature.com/news/2011/110922/full/news.2011.554.html
http://arxiv.org/abs/1109.4897v1
http://usersguidetotheuniverse.com/?p=2169
http://news.ycombinator.com/item?id=3027056
Perhaps the end of the era of the light cone and beginning of the era of the neutrino cone? I'd be curious to see your probability estimates for whether this theory pans out. Or other crackpot hypotheses to explain the results.