If the millionth digit of pi is in fact odd, but the statement “millionth digit of pi is even ⇒ agent pays up” has a much shorter proof than “millionth digit of pi is even ⇒ agent doesn’t pay up”, Omega should think that the agent would pay up.
This seems equivalent to:
has a much shorter proof than “millionth digit of pi is odd”
But does that make sense? What if it were possible to have really short proofs of whether the n-th digit of pi is even or odd and it’s impossible for the agent to arrange to have a shorter proof of “millionth digit of pi is even ⇒ agent pays up”? Why should the agent be penalized for that?
Maybe the whole point of a logical coinflip is about being harder to prove than simple statements about the agent. If the coinflip were simple compared the the agent, like “1!=1”, then a CDT agent would not have precommitted to cooperate, because the agent would have figured out in advance that 1=1. So it’s not clear that a UDT agent should cooperate either.
This seems equivalent to:
But does that make sense? What if it were possible to have really short proofs of whether the n-th digit of pi is even or odd and it’s impossible for the agent to arrange to have a shorter proof of “millionth digit of pi is even ⇒ agent pays up”? Why should the agent be penalized for that?
Maybe the whole point of a logical coinflip is about being harder to prove than simple statements about the agent. If the coinflip were simple compared the the agent, like “1!=1”, then a CDT agent would not have precommitted to cooperate, because the agent would have figured out in advance that 1=1. So it’s not clear that a UDT agent should cooperate either.