In the case of a Pascal’s mugging, when someone is threatening you, you should consider that giving in may encourage this behaviour further, allowing more threats and more threats followed through on, and the kind of person threatening you this way may use these resources for harm, anyway.
In the case of Pascal’s wager, there are multiple possible deities, each of which might punish or reward you or others (infinitely) based on your behaviour. It may turn out to be the case that you should take your chances with one or multiple of them, and that you should spend a lot of time and resources finding out which. This could end up being a case of unresolvable moral cluelessness, and that choosing any of the deities isn’t robustly good, nor is choosing none of them isn’t robustly bad, and you’ll never be able to get past this uncertainty. Then, you may have multiple permissible options (according to the maximality rule, say), but given a particular choice (or non-choice), there could still be things that appear to you to be robustly better than other things, e.g. donating to charity X instead of charity Y, or not torturing kittens for fun instead of torturing kittens for fun. This doesn’t mean anything goes.
Just a note on the Pascal’s Mugging case: I do think the case can probably be overcome by appealing to some aspect of the strategic interaction between different agents. But I don’t think it comes out of the worry that they’ll continue mugging you over and over. Suppose you (morally) value losing $5 to the mugger at −5 and losing nothing at 0 (on some cardinal scale). And you value losing every dollar you ever earn in your life at −5,000,000. And suppose you have credence (or, alternatively, evidential probability) of p that the mugger can and will generate any among of moral value or disvalue they claim they will. Then, as long as they claim they’ll bring about an outcome worse than −5,000,000/p if you don’t give them $5, or they claim they’ll bring about an outcome better than +5,000,000/p if you do, then EV theory says you should hand it over. And likewise for any other fanatical theory, if the payoff is just scaled far enough up or down.
In the case of a Pascal’s mugging, when someone is threatening you, you should consider that giving in may encourage this behaviour further, allowing more threats and more threats followed through on, and the kind of person threatening you this way may use these resources for harm, anyway.
In the case of Pascal’s wager, there are multiple possible deities, each of which might punish or reward you or others (infinitely) based on your behaviour. It may turn out to be the case that you should take your chances with one or multiple of them, and that you should spend a lot of time and resources finding out which. This could end up being a case of unresolvable moral cluelessness, and that choosing any of the deities isn’t robustly good, nor is choosing none of them isn’t robustly bad, and you’ll never be able to get past this uncertainty. Then, you may have multiple permissible options (according to the maximality rule, say), but given a particular choice (or non-choice), there could still be things that appear to you to be robustly better than other things, e.g. donating to charity X instead of charity Y, or not torturing kittens for fun instead of torturing kittens for fun. This doesn’t mean anything goes.
Just a note on the Pascal’s Mugging case: I do think the case can probably be overcome by appealing to some aspect of the strategic interaction between different agents. But I don’t think it comes out of the worry that they’ll continue mugging you over and over. Suppose you (morally) value losing $5 to the mugger at −5 and losing nothing at 0 (on some cardinal scale). And you value losing every dollar you ever earn in your life at −5,000,000. And suppose you have credence (or, alternatively, evidential probability) of p that the mugger can and will generate any among of moral value or disvalue they claim they will. Then, as long as they claim they’ll bring about an outcome worse than −5,000,000/p if you don’t give them $5, or they claim they’ll bring about an outcome better than +5,000,000/p if you do, then EV theory says you should hand it over. And likewise for any other fanatical theory, if the payoff is just scaled far enough up or down.