>BENTHAM. Fair enough. But, even so, I worry that giving you the money would set a bad precedent, encouraging copycats to run similar schemes.

>MUGGER. Don't. This transaction will be our little secret. You have my word.

Fun thought experiment! I think the easiest way for utilitarians to respond is to zero in on this section.

1. In reality, giving into muggings like this will pretty much unavoidably encourage copycats. Naive act utilitarianism, funnily enough, does better in practice than in theory here.
2. In a world where Bentham's muggers exist and really do have a strict mugger-victim confidentiality agreement: The utilitarian thing to do would be to precommit to saying no to all muggings, tell a bunch of people about your precommittment, and then encourage all other utilitarians to do the same. If the Bentham's muggers know in advance that you're going to say no, they won't try to mug you in the first place.

The scenario seems like it's inspired by Newcomb's problem. A utilitarian who one-boxes in Newcomb's problem--i.e. who endorses a decision theory that tells them to one-box and to accept point 2 above--won't have any issues with muggers.