Well-written! However, I have two primary disagreements with the author here.

1. Bentham begins as an act utilitarian, requiring that he maximize utility, such that none of the potential alternative actions could be more effective. I would argue that, in the first scenario, the maximally effective course of action for Bentham would be to make his best effort to convince the mugger to abandon deontology--and ideally all his scheming efforts.
    
2. Partially related, I'm not even convinced that giving the mugger the money is the maximally effective action in the first case. I would assume, in most circumstances like this, that if one were to agree to the mugger's demands, he would continue his scheme into the future. The author sort of engages with this point when Bentham asks, "Won't this encourage copycats?" and the man responds, "No, it'll be our secret." However, we aren't concerned with other copycats; we're concerned with that specific mugger continuing his scheme. Reasonably so, since that's exactly what happens when Bentham gives him the money. In reality, both choices Bentham can make eventually end with the mugger cutting at least one finger off. Either he refuses himself, and the mugger cuts it off immediately, or he gives over the money, and the mugger gets multiple cut off later, having been emboldened by his previous success. Therefore, Bentham should not give over the money, as even if the mugger cuts off one finger in the moment, the failure of his scheme could discourage him from ever trying again, which ultimately saves more of his fingers.