In summary, the system of logical statements that specifies the problem does not completely determine what will happen, because we can consistently extend it with another axiom that makes Omega cooperate even if you defect. IOW, you can’t go wrong by cooperating, but some correct Omegas will reward defectors as well.
I am another person who pays outright. While I acknowledge the “could even reward defectors” logical difficulty I am also comfortable asserting that not paying is an outright wrong choice. A payoff of “$1,000″ is to be preferred to a payoff of “either $1,000 or $0”.
It’s not clear to me if this problem can be “fixed”.
It would seem to merely require more precise wording in the problem statement. At the crudest level you simply add the clause “if it is logically coherent to so refrain Omega will not give you $1,000”.
I am another person who pays outright. While I acknowledge the “could even reward defectors” logical difficulty I am also comfortable asserting that not paying is an outright wrong choice. A payoff of “$1,000″ is to be preferred to a payoff of “either $1,000 or $0”.
It would seem to merely require more precise wording in the problem statement. At the crudest level you simply add the clause “if it is logically coherent to so refrain Omega will not give you $1,000”.