One of my employees posed this logic puzzle the other day.
Suppose some pirates have secured booty, and must now split the loot. Suppose also that they have a strong chain of command and that they’re democratic. The loot splitting procedure works like this:
The highest in command proposes the amount of loot to give to every other pirate.
They all vote.
If half or more of them vote yes, the loot is distributed. If less than half vote yes, the highest in command is killed, and they repeat step #1.
What is the optimal thing for the highest in command to do? (assuming perfectly rational pirates, of course!)
Solution spoiler alert!
The first thing to notice is that if there are 2 pirates, then the highest in command gets all of the loot. Thus, the last pirate in the chain of command has nothing to lose by accepting any other deal.
In a situation with 3 pirates, the highest in command must realize that the second in command has an incentive to kill the highest in command, because that will then allow him to collect all of the loot. Since the last pirate has nothing to lose, the optimal thing for the highest in command is to offer a tiny amount of loot to the last pirate, so that their votes together will prevent the death of the highest, and the succession of the second.
I’ll let you extrapolate this to a larger number of pirates.
But what if we allow a bit of human psychology in and say that the last pirate trusts the second pirate to fairly split the loot? The highest in command would be doomed.
I originally concluded that this was yet another example of how flawed the idea of rational actors in economic theory is, but now I’m not sure. I think the real flaw here is that understanding the myriad of different constraints on a real world problem simply makes applying rational actor theory intractable.