thomblake comments on Problem of Optimal False Information - Less Wrong
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Comments (113)
You can subtly change that example to eliminate that problem. Instead of actually missing the train, you just leave later and so run into someone who gives you a ride, and then you never go back and check when the train was.
The example fails the "that you would normally reject outright" criterion though, unless I already have well established knowledge of the actual train scheduling times.