Pascal's mugging refers to a thought experiment in decision theory, a finite analogue of Pascal's wager. The situation is dramatized by a mugger:
A rational agent chooses those actions with outcomes that, after being weighted by their probabilities, have a greater utility - in other words, those actions with greater expected utility. If an agent's utilities over outcomes can potentially grow much faster than the probability of those outcomes diminishes, then it will be dominated by tiny probabilities of hugely important outcomes; speculations about low-probability-high-stakes scenarios will come to dominate his moral decision making. A common method an agent could use to assign prior probabilities to outcomes is Solomonoff induction, which gives a prior inversely proportional to the length of the outcome's description. Some outcomes can have a very short description but correspond to an event with enormous utility (i.e.: saving 3^^^^3 lives), hence they would have non-negligible prior probabilities but a huge utility. The agent would always have to take those kinds of actions with far-fetched results, that have low but non-negligible probabilities but extremely high returns.
This is seen as an unreasonable result. Intuitively, one is not inclined to acquiesce to the mugger's demands - or even pay all that much attention one way or another - but what kind of prior does this imply?...