Do social preferences break "I split you chose"?

Hypothesis: Social preferences undermine the fairness, efficiency, and stability of “I cut, you choose” rules.
A lot of people chafe at the assumptions behind game theory and standard economic theory, and I don’t blame them. If those theories were right, there are a lot of things in our daily lives that wouldn’t work as well as they obviously do. But I came up with an example of the opposite: an everyday institution that would work a lot better if we weren’t so generous and egalitarian — if we didn’t have “social preferences.” Maybe; this is just a hypothesis, one that I may never get around to testing, but here it is.
“I cut, you choose” is a pretty common method for splitting things. Academically, it is appealing because it is easy to describe mathematically. It is a clean real world version of a classic Nash bargaining problem. There is a finite resource and two agents must agree about how to split it. The first person divides it into two parts and the second is free to pick the biggest. It is common in domains where the resource is hard to split evenly. The splitter knows that the picker will choose the larger part, and that he or she can do no better than getting 50%. This incentivizes the splitter to try for a completely fair distribution. Binmore has a theory that cultural evolution will select for social situations that are stable, efficient, and fair, and “I split, you choose” has those qualities, in theory.
It sounds fine, and I’ve seen it work great, but I’ve also seen it go wrong, particularly among the guilty and shy. In the splitter role they get anxious and in the receiver role they tend to pick the smaller share. It might sound heartless for someone to exploit that, but my wonderful boss did: He was splitting a candy bar with an anxious friend and proposed “I split, you chose.” He volunteered also to be the splitter, and proceeded to divide the bar blatantly 70/30. What did the victim do? He knew he was being manipulated, he watched the split with horror, but, however wounded, mysteriously picked the smaller share. Social preferences, in that case make “I split, you choose” into an institution that is neither stable nor fair and, if it’s efficient, it’s only because every possible outcome is equally efficient.
That’s interesting because we normally think of game theory as this sterile thing that implies a selfish existence whose only redeeming value is that it’s contradicted by our social preferences, which make everything better. But, if I’m right, this is a clean example of the opposite. Game theory would be offering a very nice clean institution, and social preferences break it.

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