Most of tonight's blogging time has been spent playing defense (see previous post), so I'd like to quickly sketch another problem for the Chronological Ordering Principle.
It concerns a case that Brian e-mailed me. Call it the Advance Coin Flip.
(Advance Coin Flip) The angel offers you the St. Petersburg in a sealed envelope, as in the Extra Coin Flip. He also remarks, "God flipped a fair coin this morning, before S/He ran the St. Petersburg, but S/He didn't tell me what it was. Anyway, you can take this deal: If the coin came up heads, you gain 3 utils, but if it came up tails, you lose 1--in either case, over and above what's in the envelope." Do you take the extra deal?
It seems obvious that you should take it--at least as obvious as that you should take the Extra Coin Flip. It doesn't matter that the coin was flipped before the St. Petersburg was run. Except--for the Chronological Ordering Principle, it matters a great deal, since the COP only works when the finite process takes place after the infinite process.
Obviously, what's going on here is that the two processes are independent, so it doesn't matter which is done when. If the infinite process is run first, it has to be independent of the outcome of the finite process--that's how the COP works. But it would be nice to have a characterization of this independence that didn't rest on quirks of chronology.
Maybe I'll ask for one for my birthday.
Posted by Matt Weiner at January 27, 2004 07:01 PM