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JGWeissman comments on Eight Short Studies On Excuses - Less Wrong
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Sounds like a weak precomittment. Schelling includes the theory of excuses in his work, and they are a key part of bargaining, since pre-commitments that can be averted without appearing to weaken the bargainer's position will be.
IOW, once a breach has been made it will be in both parties' interests not to have the threat carried out, and any "wiggle room" in the precommitment will be exploited. Because of this, bargainers are well-advised to make the circumstances that will trigger their threat as unambiguous and externally verifiable as possible.
I don't see any way to do this with your model precommitment, unless the agent(s) you're bargaining with and any third parties observing have access to your source code.
It can be weak on its own, if I am not predictable. But if I combine it with more specific precomittments, then other agents who plan to exploit a one time excuse, where part of convincing me not to carry through the threat, is that I can precommit never to allow that excuse again, can predict that I will wish I had precommitted from the beginning to never allow that excuse at all, and therefore act as if I had made that precommittment, and still cary through the punishment, so they should not provoke the punishment planning to offer that excuse.
This greatly strengthens any specific precommittment I make, by preventing the exploitation of one time excuses. If an agent wants to offer me an excuse, they will need to be able to convince me that I should always allow that excuse.
In the grieving student example, I am willing to allow the excuse for the same reasons that I am willing to explicitly ammend the precommittment to allow an exception in those circumstances.
I see--as an anti-single-exception rule that makes sense to me, as long as it's communicable clearly. The term "wishing" seemed insufficiently constrained and precise to me, at first.