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The Bedrock of Fairness

Early in the story, Z is hungry, and X and Y are not. Z says that he thinks that because he is hungry, 'fair' is defined with him getting more pie, while X and Y disagree. This seems like a slightly strange story to me, but here's a much stranger one:

Z is hungry, and X and Y are not. X thinks that it would be fair to give Z 1/2 the pie, but Z and Y both think it would be fair to split the pie 1/3;1/3;1/3. In other words, the person who is arguing the fairness of the unequal distribution is not the person who would benefit from it. This feels much less likely to me than the above story. In fact, it informs the following, which I submit: when people have a disagreement about what is fair, each person's opinion usually favors a positive outcome for himself.

If I accept this intuition as true, I can see to reasons why it might be true: One, that in cases where each person thinks fairness means being more generous to another party, they can easily find a compromise, because people are always willing to accept gifts. Two, that 'fair' is really just another word for 'compromise,' in which competing entities agree to a division of a resource simply in order to resolve conflict without violence. The latter seems more likely to me, at least as an explanation for the origin of the idea of fairness in our minds and our vocabularies.

An objective definition of 'fair' seems like it would have to be identical to 'moral'; what is the 'moral' distribution of the pie?