Half the problem is that, in practice, 'fair' often ends up defined as "in favor of my and my in-group's interests" by choosing a principle that coincides with

Half the problem is that, in practice, 'fair' often ends up defined as "in favor of my and my in-group's interests" by choosing a principle that coincides with those interests to maximize. It matters whose costs we're measuring here and it matters how we measure that. See what responses you get when, e.g., you change the problem to be deciding who gets the liver among two twins who are identical except that one is, say, a Republican and the other a Democrat, or some other situation where the only difference in utility is which of two opposed groups would be aided by their survival. Then compare the responses you get to how much that person approves or disapproves of the respective beliefs.