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steven0461 comments on 3 Levels of Rationality Verification - Less Wrong
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Good idea. It could work online if there's enough trust between participants.
As an addendum, I think the whole thing could still work pretty well even if everyone is explicitly allowed to use the web (or any other data store) for research.
Bets that can be settled with immediately available information won't be very useful in that context, of course; but you could still bet on near future events. Speed research would be a valuable skill in this variant. Nevertheless, if you have any significant domain specific knowledge useful for making a short-term prediction, that should give you an advantage over someone speed-researching the topic before deciding if they want to make a specific bet on it against you.
The real problem is that access to the internet (or any nontrivial subset) also allows you to do realtime communication with other humans, so you might convince/hire a master rationalist to offer you advice during the test, which would be an extremely effective way to cheat.
A fairly simple windows application could nearly eliminate the problem of research during the test - if it were timed. Each round being timed would allow little time to bypass the lockdowns that can be imposed through a windows API. Each time the test is given, a new version of the test software would be released Even the fastest hacker would be locked into taking the test!