Oh yes, interesting! And I do see the advantages of the betrayal framing.
How would you handle an opponent whose proving ability is simply too weak — one that often can’t establish that anyone cooperates? It never defects on someone it knows cooperates, so it counts as fair in your sense, but only because it’s never in a position to betray anyone in the first place. So I’d certify it and cooperate, and it would defect on me. Old-style fairness seems to fail safe here instead, since it asks whether the opponent actually cooperates rather than what they’d do if they knew.
Oh yes, interesting! And I do see the advantages of the betrayal framing.
How would you handle an opponent whose proving ability is simply too weak — one that often can’t establish that anyone cooperates? It never defects on someone it knows cooperates, so it counts as fair in your sense, but only because it’s never in a position to betray anyone in the first place. So I’d certify it and cooperate, and it would defect on me. Old-style fairness seems to fail safe here instead, since it asks whether the opponent actually cooperates rather than what they’d do if they knew.