Prisoner’s Dilemma

Despite our best efforts, it seems math is always there to thwart our brilliant ideas. Whether it be believing in lucky dice rolls or getting on a streak in blackjack, math is there to remind us, it’s all probability. A poor man once said… ” Always bet it all when you are on a winning streak”.

Despite math and logic, we are always looking for the psychological edge and interrogation is a prime example. Consider a scenario where there are two suspects who are believed to have worked together to commit a crime. A clever cop thinks, I know I’ll reward them for telling the truth. The cop individually goes to each suspect with the following…

If one confesses and the other doesn’t, the one who confesses gets off for free, while the other does 10 years. if both confess you each get 6 years, but if neither confess they each get only a year of jail. What would you do?

Believe it or not, you should confess every time. This is because no matter what the other person does, confessing lowers your jail time, and same with the other suspect. This means they will both get 6 years in jail if both individuals act rationally, and self-interested. Whereas cooperation would get them only 1 year!Image result for prisoner's dilemma

This is the so-called prisoner’s dilemma and despite the example being quite specific, it actually comes up quite a bit. It occurs whenever two parties acting bad, is better than a party acting good, while the other is bad. (think politics). This is an important concept which I try to consider whenever proposing an system for people to use, you need to make sure there is an incentive for cooperation rather than taking advantage of others.

This is the sort of thinking you need to have whenever you are in charge of competition, and recognizing little kinks in your proposal which allow for such stalemates can often make a seemingly good plan fail miserably, all because neither group wants to help the other. In many ways this is similar to the government shutdown, in that both groups don’t want to concede, and thus they both end up hurting each other rather than allowing productivity to happen. This is why I love math, because it shows up when you want it to and can often make things more robust, but at the cost of clarity and understanding unfortunately. That needs to change.

One Comment

  1. Austin, I watch many crime and police shows, from NCIS to The Andy Griffith Show. In the modern criminal shows, they use the tactic of “I already got a confession from your buddy in the next room over. (even if they didn’t) Why don’t you confess too and I’ll see if I can talk to the judge.” Cops are always trying to put humans behind bars for as long as possible.
    The prisoner’s dilemma makes sense if you first hear it, but when you dive deeper into math and logic like you did, you can see that it makes less sense the more you look at it. Two criminal buddies always go into the interview room with the idea of not ratting the other out, giving quadrant four of the chart in your post. If both confess to doing the crime, then they get equal time in jail together. But when you compare both admitting to one confessing and one not, something to me just doesn’t add up. The one that doesn’t personally confess (but the buddy admits putting the first one at the scene of the crime, probably with other evidence too), is sentenced to jail for longer than if they both confess. The one who did confess gets cut a deal.
    But if you think about it, your options are one year, six years or ten years. One year makes the most sense, so wouldn’t stubbornness on the criminal’s part pay off? It doesn’t look like it. You could go in thinking you will only get one year, but then your buddy rats you out, and you end up with a decade behind bars.
    I agree that this puzzle doesn’t make much sense and that reforms are necessary.
    Do race and gender play a role in these sentences? Like if a white guy and black guy both commit a crime together and both confess, will both get the same sentence? To me, it’s always interesting to see what the connections are between TV and real life.

Leave a Reply

Your email address will not be published. Required fields are marked *