a pirate puzzle

Ahoy, me hearties! Lisette sent me a great, grand logic puzzle today. I was able to approximate the solution rather quickly (I do remember some game theory), but fully describing its elegant and paradoxical outcome took a little longer.

There are 100 pirates on a pirate ship. There is much celebration and debauchery as they have just stolen a 1000 gold pieces. The next morning, they decide it is time to divide up the treasure among the crew.

These pirates are perfectly rational and democratic. The system for division works as follows:

The fiercest pirate (pirate 100) proposes a way to split the gold. For example: 13 to myself, 7 to pirate99 (the next fiercest pirate), 22 to pirate98… The pirates then vote on this proposal. If 50% or more vote yes, they divide up the gold. If less than 50% vote yes, the proposing pirate is tossed overboard and the next fiercest pirate makes a proposal. This continues until a proposal is excepted by 50% or more.

Being fierce, all the pirates enjoy tossing others overboard but, being greedy, they prefer gold to entertainment. Being rational, they are interested in self-preservation, and they dislike being tossed overboard themselves. Each pirate knows the proposing order and, despite bad hangovers, each always votes in his best interest.

If you are the fiercest pirate, what proposal would you make? What is the maximum amount of gold pieces you can get without being thrown overboard?

The pirate puzzle appears to have been first published in Scientific American in 1999 along with an even more interesting variant. When you have developed the solution to the above question, consider the answer if the pirates were less successful plunderers and there were 100 pirates with only 20 pieces of gold.

The text of the original article along with the solution to both variants can be reviewed here, but don’t visit until you are confident you have the answer. If you need a hint, view Tristan’s comment here by highlighting the white space.

Bonus link: practice your pirate-speak