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Kawoomba comments on Nash Equilibria and Schelling Points - Less Wrong
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Heh, if I can't convince you with "any possible math and logic", let me try with this great video (also that one) that shows the consequences of "reasoning via outrage".
Watched the first one. It was very different from the scenario we're discussing. No one's life was at stake. Also the shares were unequal from the start, so there was no fair scenario being denied, to get outraged about.
I'm not in favor of "reasoning via outrage" in general. I'm simply in favor of possessing a (known) inclination to turn down overly skewed deals (like humans generally have, usefully I might add); if I have it, and your life is at stake, you'd have to be suicidal to propose a 98 0 1 0 1 if I'm one of the people whose vote you need.
What makes it different from the video example is that, in the pirate example, if I turn down the deal the proponent loses far, far more than I do. Not just 98 coins to my 1, but their life, which should be many orders of magnitude more precious. So there's clearly room for a more fair deal. The woman in that case wasn't like my proposed E or C, she was like a significantly stupider version of A, wanting an unfairly good deal in a situation when there was no reason for her to believe her commitment could reliably prevail over the other players' ability to do the same.
A suggestion to randomize was made and denied. They fail at thinking. Especially Jo, who kept trying to convince herself and others that she didn't care about money. Sour grapes---really pathetic.
Whenever I come across highly counterintuitive claims along these lines, I code them up and see how they perform over many iterations.
This is a lot trickier to do in this case compared to, say, the Monty Hall problem, but if you restricted it just to cases in which Pirate A retained 98 of the coins, you could demonstrate whether the [98, 0, 1, 0, 1] distribution was stable or not.
Also, I'd suggest thinking about this in a slightly different way to the way you're thinking about it. The only pirate in the scenario who doesn't have to worry about dying is pirate E, who can make any demands he likes from pirate D. What distribution would he suggest?
Edit: Rereading the wording of the scenario, pirate E can't make any demands he likes from pirate D, and pirate D himself also doesn't need to worry about dying.
That shows one aspect of the consequences of reasoning via outrage. It doesn't indicate that the strategy itself is bad. In a similar way the consequences of randomizing and defending Podunk 1/11 times is that 1/11 times (against a good player) you will end up on youtube losing Metropolis.
Whoever came up with that game show is a genius.
"I will stand firm on A until A becomes worth less than C is now, then I will accept B or C. You get more by accepting B or C now than you get by trying to get more."
One rational course of action is to mutually commit to a random split, and follow through. What's the rational course of action to respond to someone who makes that threat and is believed to follow through on it? If it is known that the other two participants are rational, why isn't making a threat of that nature rational?