This is Why We Can't Have Nice Things

Imagine for a moment a group of English shepherds. Each has his own flock, lives in his own home, and in general looks after his own affairs. However, all the shepherds graze their flocks on the same piece of land, the Commons. In this way, they are are all members of the same community.

Suppose the Commons can comfortably support about 5,000 sheep, and any more will result in a gradual degradation of the pasture's productivity. Even if this limit is already reached (say, by 100 shepherds with 50 sheep each), it is still in the individual shepherds' best interest to purchase more sheep. This is because the cost (in penalty to pasture fertility) will be divided evenly among the five shepherds, while the profit (increased wool production) belongs entirely to the shepherd.

This is true for each of the shepherds, and thus, the best strategy for them is to acquire more sheep. Because this strategy should continue to be used regardless of the other participants' strategy (since it always results in greater profit than loss), it effectively constitutes a Nash Equilibrium.

Thus, despite their actions turning the Commons into a barren wasteland, the shepherd virtually have to, just to avoid someone else doing the same thing first. This individually rational decision results in the group as a whole suffering.

Another example is the classic 'splitting the check' problem. Suppose you go out to dinner, and rather than paying separately, your group of five friends agrees to just divide the bill by the number of people and have each pay that much (another formulation, the 'business card method', involves drawing a business card from a hat and having that one person pay the entire bill, but it is mathematically the same as splitting the check). How much should you spend on your meal?

As much as possible, of course (or at least, up until the point where $1 more of cost is at least $0.20 of value). Whoever has the most expensive meal is getting a bargain, while anyone with a lower-than-average cost is getting shafted. Now the question: Why aren't these two problems the same?

The answer (besides the obvious ones about this not involving sheep nor being a thinly-guised plea for greater ecological regulation) is that in the 'splitting the check' problem, the people you're dining with are your friends. At some level, you don't want to screw them over.

So why can't the shepherds be friends, too? Well, there's nothing inherently jerkish about herding sheep, but the truth is that they can't all be friends for psychological reasons.

According to observations by Robin Dunbar on the size of primate societal groupings compared to primate brain size, humans (supposing we follow the same trends as other primates) should have an optimal group size of around 150. This is known as Dunbar's Number. Simply put, you can only really think of about 150 other individuals as actual people, while the rest are simply part of the background of everyday life. A far more detailed and humorous explanation appears in this article: What is the Monkeysphere?

A possible way around this limitation is through the use of organizations. Namely, I suspect one may have a specific organization (Christianity, Communism, NAMBLA...) as part of their 'monkeysphere', separate from any members to whom that person feels close. Thus, instead of considering another person's well-being to be of value, you may consider the advancement of the organization's goals to be of value.

This ability to concieve of abstract ideals may well be what permits humans to form larger, organized societies, while less conceptual creatures are limited to only other creatures. Though the evidence supporting Dunbar's Number is essentially anecdotal, the theory goes a long way towards explaining many sociological issues.

Next Time: The World Ends With You (fingers crossed)