You have 1000 pirates, who are all extremely greedy, heartless, and perfectly rational. They're also aware that all the other pirates share these characteristics. They're all ranked by the order in which they joined the group, from pirate one down to a thousand.
They've stumbled across a huge horde of treasure, and they have to decide how to split it up. Every day they will vote to either kill the lowest ranking pirate, or split the treasure up among the surviving pirates. If 50% or more of them vote to split it, the treasure gets split. Otherwise, they kill the lowest ranking pirate and repeat the process until half or more of the pirates decide to split the treasure.
The question, of course, is at what point will the treasure be split, and what will the precise vote be?
After that, consider solving the problem when a two-thirds or three-fourths majority is required. Try to generalize the result.
(In reply to Power of the supermajority (spoiler)
by Steve Herman)
If a mutiny will occur iff there is no majority of pirates voting
for the split, it can be said a mutiny will occur for a required vote of (n-1)/n for 1000 pirates where n is 4 - 7, 11 - 22, 32 - 500, or any n > 1000.
As to practicality, it would seem a mutiny should occur for any n where a pirate would be killed. Even if the odds are 1:999, it would make sense that the 1 would fight for his survival. (Of course, being outnumbered and considering his chances, he might accept death over a real threat of torture...still that begs the question of greediness, heartlessness and perfect rationality).
Posted by Dej Mar
on 2013-04-21 00:32:42