After a long season of plunder, a pirate team of five Prudent Pirates has amassed a booty of 500 golden coins. Before they part their ways, the five decide to divide the treasure.

They that they will each propose a division strategy in order of their seniority: first the oldest pirate will propose the strategy for the division of coins. All five will then vote on it, and if at least half vote "Yes", the strategy will be used to divide the coins. If the majority rejects the plan however, the oldest pirate will be killed, and the whole process will be repeated with the remaining pirates, with the second oldest proposing his strategy.

Since all the pirates are very prudent, each one will want to claim as many coins for himself without getting killed. Given this, how many coins will each of the pirates (5 - 1, with 5 being the oldest) get, and why? What strategy will the oldest pirate propose?

So, A proposes a 498 - 0 - 1 - 0 - 1 split, expecting to get support from C and E. A figures E will support him, because E gets nothing otherwise.

However, if E is really smart, he rejects the split. A gets killed, and it's now B's turn. B is suddenly very nervous, because the line of analysis isn't holding up. He knows that E appears to be acting irrationally. D also sees what E has done, and starts getting ideas, too.

Suppose D offers a 499 - 0 - 1 - 0 split as the canonical analysis implies. Now look at what happens if D votes it down: B gets killed and the choice passes to C. At this point, C knows that he can't offer a 499 - 0 - 1 split, because he knows that E appears to be irrational. He also knows he can't offer a 498 - 2 - 0 split because D appears to be irrational. His only hope is to offer something more equitable.

Based on this analysis, D probably offers something more equitable.

The bottom line is that by appearing to be irrational, E improves his lot considerably. As Shakespeare said, "there's method in his madness."

Posted by Jim Lyon on 2002-08-19 10:06:13