The pirate game is one of the most well-known mathematical puzzles. In the game, five entirely rational pirates, A, B, C, D, and E, find a treasure of 100 coins. The hierarchy of the pirates is determined by their names in alphabetical order, so A is the most senior pirate while E is at the bottom of the chain. Given that their newfound loot needs to be spread, the pirates devise a mechanism to allocate the coins.
First, the most senior pirate will propose an allocation plan of the 100 coins to all the pirates. Then, the pirates will vote on the plan(a tied vote count being successful), with the most senior pirate being thrown overboard if the plan fails and the entire process restarting with the new most senior pirate. Each pirate will vote and propose plans in such a way to maximize the amount of loot they receive while prioritizing their survival. Furthermore, pirates are bloodthirsty, so if they would stand to get the same number of coins regardless of whether a plan succeeds, they will choose to vote against it and overthrow the most senior pirate.
To find out what happens with five pirates, we need to start small and first look at one pirate. If E was the only pirate on board, he would simply allocate all the coins for himself and vote in favor of the plan. Similarly, if only D and E were on board, D would also give himself all the treasure and the plan would pass successfully in a 1-1 vote between D and E. However, if we add C to the equation, the same plan does not work, as both D and E would vote against C. To remedy this, C instead takes 99 coins and gives 1 coin to E. This is enough for pirate E, knowing that voting out C will lead to D taking the entire bounty, to vote in favor of the plan. By the same logic on pirate D, the distribution between B-C-D-E would be 99-0-1-0. Finally, pirate A only needs to woo C and E with a single coin as pirate B’s proposal would leave them with nothing, and thus the final allocation plan is 98-0-1-0-1.
Interestingly, we can draw parallels between this simple puzzle and the issues that are found in a modern democracy. In the pirate game, only one pirate actually ends up with a favorable result and almost all of the loot, while the others get a tiny percent of the pie. This stems from the fact that just like the current American electoral system, voters only have 2 options; to overthrow or not. The pirate in power, pirate A, has no incentive to make the proposed plan fair and equal, only to make it better than overthrowing him. Pirates C and E are forced to choose the lesser of two evils, while B and D are neglected because their votes are not necessary. Democracy might mean equal votes, but it clearly does not mean equal power.