[Puzzler] Pirate Booty

[Mike]

[Eliahad]

I saw the explanation for this one elsewhere, so I'm going to bow out.

[Mike]

I love this one. I'd never seen it before today. I was very proud of myself for getting the right answer.

[Eliahad]

I was being faaaar too altruistic when I was trying this puzzle. I just couldn't understand people being that dickish. I would not make a good pirate.

[Zen]

The version of the answer I found had 10 Pirates and 10 pieces of gold, so I couldn't tell if my solution was right. I think I was too generous, but on the right track. (Could you put a link to the solution if there is one with the same formulation as yours?)

[Phoebe]

Do they anticipate what will happen in all possible future decision rounds as part of their rational decision-making procedure in the first round?

[Eliahad]

Yes.

[Eliahad]

It's a Ted-Ed video.

[Mike]

When I first sat down to this, I started from the point of view of the Captain and imagined what happens if I give everyone an even split. But then it occurred to me that the other four pirates could vote to murder me, and then they could split it four ways and each have more... and then three ways, and then two. So I thought maybe I have to offer all of them larger shares to keep them from killing me. I quickly realized I need to start from the other end.

INVISIBLE SOLUTION:

[poorpete]

Going to check the solution after, but posting my guess first, which I assume is wrong:


Update: So close... but so wrong...

[Zen]

Mike: you assume correctly about the 10 pirate scenario. It is easier with a smaller amount of booty that isn't so divisible. When it is 500, you think about the fact that there's so much of it and people should be greedier.

[Phoebe]

I really don't get it, unless they have to follow the same decision procedure every time without fail and cannot make/break deals and promises with one another along the way.

[Mike]

[poorpete]

I feel bad for C + E. is happy.

[Zen]

[DMDarcs]

Pareto efficiency to the extreme!

[Phoebe]

Ok, if it's a decision procedure, then it sets up a situation where But I feel the others would make deals to avoid this, to meet the condition of supposed perfect rationality that was also set up in the problem. It's a Game Theory type paradox - rationality actually demands cooperation.

[Mike]

When you run into two guards in the woods, one of whom always lies and one of whom always tell the truth, you're not facing any semblance of reality. When the jailer brings you a handful of pills that may or may not be poisoned, why would they give you the balance scale? And then, having given you the scale, why let you use it only twice?

It's an exercise in logic.

[Stan]

[Mike]

Stan WINS!