The Prisoner’s Dilemma

It’s a classic thought experiment, mathematical problem and a cause of much philosophical debate. Over the years it has found its way into every sphere of existence from serious lecturing to game shows to, on numerous occasions, real life. It has been argued as being the basis for all religion, and its place in our society. And to think that it, in its purest form, is nothing more than a story about two men in a jail- the prisoner’s dilemma.

The classic example of the dilemma goes roughly as follows; two convicts suspected of a crime are kept in single custody, separated from one another and unable to converse. Both are in fact guilty of the crime, but the police only have evidence to convict them for a small charge, worth a few months in jail if neither of them confess (the ‘cooperation’ option). However, if they ‘rat out’ on their partner, they should be able to get themselves charged with only a minor offence for complicity, worth a small fine, whilst their partner will get a couple of years behind bars. But, if both tell on one another, revealing their partnership in the crime, both can expect a sentence of around a year.

The puzzle comes under the title (in mathematics) of game theory, and was first formally quantified in the 1950s, although the vague principle was understood for years before that. The real interest of the puzzle comes in the strange self-conflicting logic of the situation; in all cases, the prisoner gets a reduced punishment if they rat out on their partner (a fine versus a prison sentence if their partner doesn’t tell on them, and one year rather than two if they do), but the consequence for both following the ‘logical’ path is a worse punishment if neither of them did. Basically, if one of them is a dick then they win, but if both of them are dicks then they both lose.

The basic principle of this can be applied to hundreds of situations; the current debate concerning climate change is one example. Climate change is a Bad Thing that looks set to cause untold trillions of dollars in damage over the coming years, and nobody actively wants to screw over the environment; however, solving the problem now is very expensive for any country, and everyone wants it to be somebody else’s problem. Therefore, the ‘cooperate’ situation is for everyone to introduce expensive measures to combat climate change, but the ‘being a dick’ situation is to let everyone else do that whilst you don’t bother and reap the benefits of both the mostly being fixed environment, and the relative economic boom you are experiencing whilst all the business rushes to invest in a country with less taxes being demanded. However, what we are stuck with now is the ‘everyone being a dick’ scenario where nobody wants to make a massive investment in sustainable energy and such for fear of nobody else doing it, and look what it’s doing to the planet.

But I digress; the point is that it is the logical ‘best’ thing to take the ‘cooperate’ option, but that it seems to make logical sense not to do so, and 90% of the moral and religious arguments made over the past couple of millennia can be reduced down to trying to make people pick the ‘cooperate’ option in all situations. That they don’t can be clearly evidenced by the fact that we still need armies for defensive purposes (it would be cheaper for us not to, but we can’t risk the consequences of someone raising an army to royally screw everyone over) and the ‘mutually assured destruction’ situation that developed between the American and Soviet nuclear arsenals during the Cold War.

Part of the problem with the prisoner’s dilemma situation concerns what is also called the ‘iterative prisoner’s dilemma’- aka, when the situation gets repeated over and over again. The reason this becomes a problem is because people can quickly learn what kind of behaviour you are likely to adopt, meaning that if you constantly take the ‘nice’ option people will learn that you can be easily be beaten by repeatedly taking the ‘arsehole’ option, meaning that the ‘cooperate’ option becomes the less attractive, logical one (even if it is the nice option). All this changes, however, if you then find yourself able to retaliate, making the whole business turn back into the giant pissing contest of ‘dick on the other guy’ we were trying to avoid. A huge amount of research and experimentation has been done into the ‘best’ strategy for an iterative prisoner’s dilemma, and they have found that a broadly ‘nice’, non-envious strategy, able to retaliate against an aggressive opponent but quick to forgive, is most usually the best; but since, in the real world, each successive policy change takes a large amount of resources, this is frequently difficult to implement. It is also a lot harder to model ‘successful’ strategies in continuous, rather than discrete, iterative prisoner’s dilemmas (is it dilemmas, or dilemmae?), such as feature most regularly in the real world.

To many, the prisoner’s dilemma is a somewhat depressing prospect. Present in almost all walks of life, there are countless examples of people picking the options that seem logical but work out negatively in the long run, simply because they haven’t realised the game theory of the situation. It is a puzzle that appears to show the logical benefit of selfishness, whilst simultaneously demonstrating its destructiveness and thus human nature’s natural predisposition to pursuing the ‘destructive’ option. But to me, it’s quite a comforting idea; not only does it show that ‘logic’ is not always as straightforward as it seems, justifying the fact that one viewpoint that seems blatantly, logically obvious to one person may not be the definitive correct one, but it also reveals to us the mathematics of kindness, and that the best way to play a game is the nice way.

Oh, and for a possibly unique, eminently successful and undoubtedly hilarious solution to the prisoner’s dilemma, I refer you here. It’s not a general solution, but it’s still a pretty cool one 🙂

Goodwill to all men

NOTE: This post was meant to go up on Christmas Eve, but WordPress clearly broke on me so apparently you get it now instead- sorry. Ah well, might as well put it up anyway…

 

Ah, Christmas; such an interesting time of year. The season of plenty, the season of spending too much, the season of eating too much, the season of decisions we later regret and those moments we always remember. The season where some families will go without food to keep the magic alive for their children, the season where some new feuds are born but old ones are set aside, and the season where goodwill to all men (and women) becomes a key focus of our attention.

When I was young, I always had a problem with this. I had similar issues with Mother’s Day, and Father’s Day even more so (I don’t know how I came to know that it was an entirely commercial invention, but there you go), and whilst Christmas was awesome enough that I wasn’t going to ruin it by seasonal complaints, one thing always bugged me about ‘the season of goodwill’. Namely, why can’t we just be nice to each other all the time, rather than just for a few weeks of the year?

A cynic might say we get all the goodwill out of our systems over Christmas in preparation for being miserable bastards for the rest of the year, but cynicism is unhealthy and in any case, I try to keep it out of my bloggy adventures. Plus, we are capable of doing nice stuff for the rest of the year, even if we don’t do so much as some might think we should, and humans never cease to be awesome beings when they put their mind to it. No, it’s not that we give up being nice for the rest of the year, but more that we are quite clearly eminently able of being more nice but not, seemingly, all the time.

Goodwill to our fellow man is not the only seasonal occurrence that seems more prevalent over the festive period for no obvious reason; many of our Christmas traditions, both old and modern, follow a similar thread. Turkey, for instance; whilst it’s never been Christmas fare in my household for various reasons, I know enough people for whom a turkey dinner plus trimmings is the festive standard to know that these same people never have the bird at any other time of the year (I know you Americans have it on Thanksgiving, but I don’t know enough about how all that works to comment). I saw a comment online a couple of weeks ago about eggnog (another seemingly American-specific thing), and mentioning how this apparently awesome stuff (never tried it myself, so again can’t comment) is never available at any other time of the year. A response soon followed courtesy of a shop worker, who said there’s always a supply of it tucked away somewhere throughout the year in the shop where he worked, but that nobody ever bought it outside of December.

We should remember that there is something of a fine line to tread when we discuss these ideas; there are a lot of things that only occur at Christmas time (the giving of gifts, decorations, the tree and so on) that don’t need any such explanation because they are solely associated with the season. If one were to put tinsel up in June, then you might be thought a bit odd for your apparent celebration of Christmas in midsummer; tinsel is not associated with anything other than festive celebration, so in any other context it’s just weird.  This is particularly true given that tinsel and other such decorations are just that; decorations, with no purpose outside of festive celebration. Similarly, whilst gift-giving is appreciated throughout the rest of year (although it’s best to do so in moderation), going to all the trouble of thinking, deliberating, wrapping secretively and making a big fanfare over it is only associated with special occasions (Christmases or birthdays). Stuff like turkey and eggnog can probably be classified as somewhere in the middle; very much associated with the Christmas period, but still separate from it and capable for being consumed at other times of the year.

The concept of goodwill and being nice to people is a little different; not just something that is possible throughout the rest of the year, but something actively encouraged as being a commendable trait, so the excuse of ‘it’s just a feature of the season’ doesn’t really cut it in this context. Some might say that quite a lot of the happiness exuded at Christmastime is somewhat forced, or at the very least tiring, as anyone who’s looked at the gaunt face between the smiling facade of a Christmas day Mum can tell. Therefore, it could be argued that Christmas good cheer is simply too much work to keep up for the rest of the year, and that if we were forced to keep our smiley faces on we would either snap or collapse in exhaustion before long. Others might say that keeping good cheer confined to one portion of the year makes it that much more fun and special when it comes round each year, but to me the reason is slightly more… mathematical.

Human beings are competitive, ambitious creatures, perpetually seeking to succeed and triumph over the odds. Invariably, this frequently means triumphing over other people too, and this is not a situation that lends itself to being dedicated to being nice to one another; competition and the strive to succeed may be key features behind human and personal success, but they do not lend themselves to being nice to one another. Not infrequently, such competition requires us to deliberately take the not-nice option, as dicking on our competition often provides the best way to compete with them; or at the very least, we sometimes need to be harsh bastards to make sure stuff gets done at all. This concept is known in philosophy as the prisoner’s dilemma, which I should get round to doing a post on one of these days.

However at Christmas time achievement becomes of secondary importance to enjoyment; to spending time with friends and family, and to just enjoying the company of your nearest and dearest. Therefore, comparatively little actually gets done over the Christmas period (at least from an economist’s point of view), and so the advantage presented by mild dickishness to some others for the rest of the year disappears. Everything in life becomes reduced down to a state where being nice to everyone around us best serves our purpose of making our environment a fun, comfortable place to be. At Christmas time, we have no reason to be nasty, and every reason to be nice; and for that reason alone, Christmas is a wonderful thing. Merry Christmas, everybody.