DanielLC comments on Open Thread, Apr. 20 - Apr. 26, 2015 - Less Wrong Discussion
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I'd say that the main point is that the doctor pays a cost to help you, where a blackmailer would pay a cost to hurt you. If you never pay, the blackmailer has no incentive to hurt you and you'd be fine, but the doctor would have no incentive to help you and you'd die.