Trump and Pirates

Here is a famous math problem I never before wrote about:

Puzzle. Five pirates discovered a treasure of 100 gold coins. They decide to split the coins using the following scheme. The most senior pirate proposes how to share the coins, and all the pirates vote for or against it. If 50% or more of the pirates vote for it, then the coins will be shared that way. Otherwise, the pirate proposing the scheme will be thrown overboard, and the process is repeated with the next most senior pirate making a proposal.

As pirates tend to be a bloodthirsty bunch, if a pirate would get the same number of coins whether he votes for or against a proposal, he will vote against so that the pirate who proposed the plan will be thrown overboard. Assuming that all five pirates are intelligent, rational, greedy, and do not wish to die, how will the coins be distributed?

You can find the solution in many places including Wikipedia’s Pirate game. The answer is surprising: the most senior pirate gets 98 coins, and the third and the fifth pirates by seniority get one coin each. I always hated this puzzle, but never bothered to think through and figure out why. Now I know.

This puzzle emphasizes the flaws of majority voting. The procedure is purely democratic, but it results in extreme inequality.

That means a democracy needs to have a mechanism to prohibit the president from blatantly benefiting himself. With our current president these mechanisms stopped working. Given that Trump does everything to enrich himself, the pirates puzzle tells us what to expect in the near future.

We, Americans, will lose everything: money, clean air and water, national parks, future climate, health, social security, and so on, while Trump will make money.



  1. Konstantin Knop: pp. 9-15

  2. T Banerjee:

    Equating Democracy with Majority Rule is always a contentious issue. But thanks for the puzzle.
    Two variations for time pass:
    1) What happens if the proposer is not allowed to vote?
    2) What happens when the proposer can also vote and a pirate votes for a proposal if by doing so s/he has nothing to lose?

  3. Jonathan Kariv:

    Isn’t this kinda a function of having way more coins than pirates though? If you have 199 pirates or more you get no one having more than 1 coin, which is more or less as equitable a distribution as possible. Of course you do get some people dying for enough pirates so…

  4. Jack:

    Trump’s net worth has dropped quite a bit since he because president.


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