The mugging part is helpful in that is frames the thought experiment as a decision problem, which allows abstracting it from most theoretical frameworks (such as ways of assigning a prior or flavors of utilitarianism) and avoids related disputes about definitions. In a decision problem, a common understanding of probability or utility doesn’t have to be presupposed, instead each solution is free to apply whatever tools and additional assumptions seem appropriate.
The mugging part is helpful in that is frames the thought experiment as a decision problem, which allows abstracting it from most theoretical frameworks (such as ways of assigning a prior or flavors of utilitarianism) and avoids related disputes about definitions. In a decision problem, a common understanding of probability or utility doesn’t have to be presupposed, instead each solution is free to apply whatever tools and additional assumptions seem appropriate.