Democracy on the high seas

Maritime photos!

Spent the weekend moving and I am still settling in, so today is just posing one of my favorite riddles.  About pirates.  Solution – and discussion of the solution – will be left until tomorrow(ish).

Imagine you are the captain of a pirate ship on the high seas, and you (and your crew) have just managed to loot/plunder 100 Pieces of Eight (“PoE” for those in the know).  Now is the fun part: dividing the booty.  Of course, being captain, you get to decide how many PoE you and the 9 other people on board get.  Also, this being a pirate ship, there is a strict hierarchy of crew members- as captain, you are the most important, then the first mate is second most important, and on down the line to the deck swabber.

Now to divide the booty, you (the captain) will suggest a division of the 100 PoE, and the crew will vote on the division (since you got to decide the division, you only get 1/2 vote… which also guarantees no “ties”).  If they vote for your division, it stands, if they vote against it, then they throw you overboard, and the first mate becomes captain, the third in command becomes first mate, and so on down the line (I guess the decks would no longer get swabbed).

Now the crew- being pirates and all- are completely logical, so each pirate votes according to the following (ordered) priorities:
1. They do not want to die
2. They want to maximize their own profit
3. They would like to kill as many other crew members as possible (again, these are pirates)

The question is: what division do you, as the captain, suggest?

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3 comments on “Democracy on the high seas

  1. […] Yesterday’s post had a riddle about 10 very logical pirates trying to fairly split up 100 Pieces of Eight (PoE).  Today we give the solution, which is a great example of backwards induction.  What we do is first imagine an easier situation, then solve for more complicated solutions using that.  Specifically, we’ll first assume we have 1 pirate, then 2, and so on, up to 10 (or however many we have on board!)  For ease of notation, we’ll name the lowest ranking pirate on the ship #1, the second lowest #2, and so on.  So if there are 8 pirates, #8 is the captain (and only gets 1/2 of a vote). […]

  2. […] gave an answer to the pirate riddle yesterday, but it was somewhat unsatisfying for a mathematician.  I mean, the pirates will run out […]

  3. […] quick addendum to my earlier posts on logical pirates.  I had searched for quite a while to find the .pdf I knew I had read about […]

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