All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
Elegantly Greedy Pirates (Posted on 2013-04-20) Difficulty: 3 of 5
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.

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 3.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts re: Power of the supermajority (spoiler) | Comment 4 of 5 |
(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
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (9)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information