Omega kidnapps you and an alien from FarFarAway Prime, and gives you the choice: either the alien dies and you go home with your memory wiped, or you lose an arm, and you both go home with your memories wiped. Nobody gets to remember this. Oh and Omega flipped a coin to see who got to choose. What is your choice?
As usual, Omega is perfectly reliable, isn't hiding anything, and goes away afterwards. You also have no idea what the alien's values are, where it lives, what it would choose, nor what is the purpose of that organ that pulsates green light.
(This is my (incorrect) interpretation of counterfactual mugging, which we were discussing on the #lesswrong channel; Boxo pointed out that it's Prisonner's Dilemma where a random player is forced to cooperate, and isn't that similar to counterfactual mugging.)