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othercriteria comments on Nash Equilibria and Schelling Points - Less Wrong
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If C and E - and I'd say all 4 of them really, at least regarding a 98 0 1 0 1 solution - were inclined to be outraged as I suggest, and A knew this, they would walk away with more money. For me, that trumps any possible math and logic you could put forward.
And just in case A is stupid:
"But look, C and E, this is the optimal solution, if you don't listen to me you'll get less gold!"
"Nice try, smartass. Overboard you go."
B watched on, starting to sweat...
EDIT: Ooops, I notice that I missed the fact that B doesn't need to sweat since he just needs D. Still, my main point isn't about B, but A.
Also I wanna make it 100% clear: I don't claim that the proof is incorrect, given all the assumptions of the problem, including the ones about how the agents work. I'm just not impressed with the agents, with their ability to achieve their goals. Leave A unchanged and toss in 4 reasonably bright real humans as B C D E, at least some of them will leave with more money.
...because it's very hot in Pirate Island's shark-infested Pirate Bay, not out of any fear or distress at an outcome that put her in a better position than she had occupied before.
Whereas A had to build an outright majority to get his plan approved, B just had to convince one other pirate. D was the natural choice, both from a strict logico-mathematical view, and because D had just watched C and E team up to throw their former captain overboard. It wasn't that they were against betraying their superiors for a slice of the treasure, it was that the slice wasn't big enough! D wasn't very bright--B knew from sharing a schooner with him these last few months--but team CE had been so obliging as to slice a big branch off D's decision tree. What was left was a stump. D could take her offer of 1 coin, or be left to the mercy of the outrageously blood-thirsty team CE.
C and E watched on, dreaming of all the wonderful things they could do with their 0 coins.
[I think the "rationality = winning" story holds here (in the case where A's proposal passes, not in this weird counterfactual cul-de-sac) but in a more subtle way. The 98 0 1 0 1 solution basically gives a value of the ranks, i.e., how much a pirate should be willing to pay to get into that rank at the time treasure will be divided. From this perspective, being A is highly valuable, and A should have been willing to pay, say, 43 coins for his ship, 2 coins for powder, 7 coins for wages to B, C, D, E, etc., to make it into that position. C, on the other hand, might turn down a promotion to second-in-command over B, unless it's paired with a wage hike of one 1 coin; B would be surprisingly happy to be given such a demotion, if her pay remained unchanged. All the pirates can win even in a 98 0 1 0 1 solution, if they knew such a treasure would be found and planned accordingly.]