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"Fair" does not mean "increases entropy" in this context. We can split hairs about what exactly "fair" is supposed to be, it's probably central to this whole nebulous disagreement, but a lowest common denominator would be something like "has higher value than opportunity cost". This may even increase entropy in aggregate. A fair die does not make a fair game.

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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.

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