Cooperation, Defection, Civilization

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        

Society is a prison. No, not (necessarily[1]) in the sense that we are here as punishment; yes, in the sense that we are here not by our own will and we are, more or less, trapped here along with everyone else. This should actually inform our approach to a number of things, including how we organize society.

Before we return to the issue of society, we must first examine two thought experiments: The Prisoner’s Dilemma and Newcomb’s paradox. Taken together, these two games[2] will provide us what we will need for the core purpose of this article: Examining society, how it functions, and how we should behave and structure society to achieve optimal outcomes.

The Prisoner’s Dilemma is one of the simplest games in game theory and is often used as part of an introductory class, often to explain core concepts. We do not need to fully understand the game for this article, but we do need to understand a handful of core concepts. First, the game:

Two men (1 and 2) are arrested for committing some crime. They are being interrogated. They can cooperate (C, c) or defect (D, d)[3], which is to say that they can remain silent (i.e., each not incriminate or testify against the other) or agree to testify. If both men cooperate, they will each receive one year in prison; if both men defect, they will each receive three years in prison; if one man cooperates and one man defects, then the cooperator will receive five years in prison and the defector zero. As this is a simultaneous (not a sequential) game, we will start with the table/normal form (not the tree/extensive form):

  1. Although also not necessarily not (at least partially) in the sense that we are here as punishment. ↩︎

  2. Yes, I am aware that Newcomb’s paradox does not meet the ‘classical’ definition of a game (in game theory); no, I do not care. ↩︎

  3. n.b., both ‘cooperate’ and ‘defect’ are from the perspective of the criminals collectively — the perspective of law enforcement is irrelevant in this. ↩︎

Player 2
c d
Player 1 C (-1, -1) (-5, 0)
D (0, -5) (-3, -3)

Second, outcomes: As there are no truly ‘good’ outcomes for the two men, all payoff values are negative or zero. If you find it easier, you could also assign positive values instead.

The absolute values are not the point (here), so focus, instead, on the relationships (e.g., full cooperation pays better than full defection). In game theoretic terms, there is a dominant strategy in this game: defection. Let us examine this from the perspective of player 2 (the players are identical in this particular game):

Prisoner's Dilemma - Extensive Form Game Tree Sequential game tree: Player 1 chooses first (C or D); Player 2 observes and responds (c or d). Payoffs: (Player 1, Player 2). Player 1 C D Player 2 (observes C) Player 2 (observes D) c d c d (-1, -1) (-5, 0) (0, -5) (-3, -3)

As can clearly be seen, it is more ‘rational’ for 2 to defect regardless of what 1 chooses to do. Both players can always expect a higher payoff from defecting. This presents some obvious challenges for anyone who would prefer to cooperate, or, perhaps, who would prefer to increase cooperation generally in society.

Newcomb’s paradox is not classically or technically a game in the game theoretic sense, but we will be treating it as one. First, the game:

You are presented with a table on which there are two boxes. One is open and one is closed. The open box contains a sum of money ($1000); the closed box contains either nothing ($0) or a significant sum of money ($1,000,000). You may take either both boxes or just the closed box, but there is a catch: The contents of the closed box were determined by a very accurate Predictor (P) before you entered the room; if P believed/decided/calculated that you would take both boxes, then there is nothing in the second box.

The answer is immediately obvious to most men, but the issue is that there is a split in which answer most men deem ‘obvious’ — some say you must obviously take only the second box and some say you must obviously take both. There are (mathematical) rationalizations for both. In game form:

Newcomb's Paradox – Extensive Form Game Tree Predictor P moves first and chooses whether to predict one-box or two-box. Player N then chooses One-box or Two-box without observing P's prediction (information set shown). Payoffs are the monetary amounts received by N. P Predictor Predicts One-box Predicts Two-box N Player N Player One-box Two-box One-box Two-box $1,000,000 $1,001,000 $0 $1000

Remember: At step two (where you, the player [N] act), you do not actually know if you are in potential universe 1 or potential universe 2. Those who try to defend ‘two boxing’ will look at these outcomes and claim that there is only one rational move: defect (i.e., two box), as it always has a higher payoff. I view this as mistaken, but men generally will not or cannot change their intuition on this. I would actually contend the form of the game is closer to this:

Newcomb's Paradox – Extensive Form Game Tree (99.99% Predictor Accuracy) Predictor P moves first. Player N chooses without observing P's prediction (information set shown). Predictor accuracy = 99.99%. Individual predicted (expected) payoffs shown under each terminal box. P Predictor Predicts One-box Predicts Two-box N Player N Player One-box Two-box One-box Two-box Predict One-box $1,000,000 Predict One-box $1,001,000 Predict Two-box $0 Predict Two-box $1000 $999,900 $100.10 $0 $999.90 Predictor accuracy = 99.99% (p = 0.9999) Expected payoff (One-box strategy) = $999,900 Expected payoff (Two-box strategy) = $1,100

Under this understanding of the game, the expected payoff of one boxing is $999,900 and the expected payoff of two boxing is $1100. Of course, the two boxer will still feel that two boxing is the correct choice. Anyway, analyzing the paradox is not the core purpose of this article.

Third, the analysis of the nexus. We are currently living in a society comprised of cooperators and defectors; this imposes a cognitive burden — almost exclusively on cooperators. In fact, things are much worse, because the presence of so many defectors means not only that (would-be) cooperators must be constantly vigilant for defectors, but also that the cooperators themselves are constantly being pulled downward into the morass that is the level of the defectors. Civilization (at least a cultured one worthy of being called such) requires cooperation; defectors are, at best, anchors slowing progress, and they are more often landmines. The detection and removal of defectors is vital to society.

So what does Newcomb’s paradox have to do with the Prisoner’s Dilemma? Well, they are the same problem: The one boxer is the cooperator and the two boxer is the defector.[1] This is, perhaps, not such good news if you are inclined to two box.

These are not matters about which society can be indifferent. In a very real sense, civilization itself is a very complex and extended cooperation game. In order to maintain a society or a civilization, millions of men must cooperate across thousands of years. This is no small task. One of the most important tasks of a ruler is to ensure the continuity of the civilization over which he rules; one way to do this is to maximize cooperation. Think of the payoff matrix from the Prisoner’s Dilemma: defecting is rational. How can the ruler change the likelihood of cooperation? There are two possibilities.

First, the ruler can punish defection or reward cooperation. This is obviously more complex in cases (like our game) where crime is involved, but the general principle holds. Punishing defection and rewarding cooperation both change the logic of the game by changing the payoffs. Ignoring the crime aspect (for the sake of the hypothetical), punishing ’snitching’ with five years in prison would significantly change the calculus of the players.

Second, the ruler can remove (would-be) defectors from society. This could be done a number of ways, but such concrete means are not the point of this article. By removing defectors, the ruler would decrease the cognitive burden on cooperators and generally raise the level of cooperation in his society. Over a course of generations, defectors could theoretically be virtually eliminated.

Now, subjecting all members of society to some orchestrated prisoner’s dilemma and then sterilizing (or simply executing) all defectors is probably a bit too extreme for most men (and would likely also not yield optimal results). This sort of change, this sort of guiding or shepherding of the population takes time — a lot of time. But there are very effective means for nudging things in the right direction. First, serious crimes must be severely punished — no ‘rehabilitation’ for murderers or rapists. The death penalty is the ultimate curb of the defector; it ensures that he will never defect again. And yet we should not wait for the criminal (defector) to commit some heinous act if we can curb his wickedness before it rises to that level. Second, anti-social or anti-society trespasses (even if typically considered ‘minor’ crimes) must be punished severely. The litterer, the tagger (yes, graffiti is a crime), and all manner of other vandals of today are the robber, rapist, and murderer of tomorrow. All crime is defection and all defectors share a psychology, a disposition, and an intuition. Sufficiently punishing these defections will have a longitudinal eugenic effect. Removing fingers from vandals today decreases the murder rate centuries in the future. It is, in fact, the duty of the ruler to enact these policies; to fail to punish the defector is to become a defector oneself, for, ultimately, all defection is dereliction of duty.

And, so, to answer the (admittedly somewhat sensationalist) title of this article: Should we execute the litterer? Perhaps not, but repeated or egregious offenses should surely be met with punishments that will discourage rational men, and the irrational criminal can hardly be deterred from his appointment with Master Hans. We owe this to those who will come after us and the very existence of civilization rests on our willingness to do our duty — i.e., not to defect. The murderer ends the life of one man, but the litterer, the nuisance, the vandal murders society itself and with it countless lives. The anti-social crime is never minor, and we must never view it as such. Defection, like the defector, only ever grows worse when left unpunished.

  1. This is, perhaps, of some value if you plan to commit crimes and then be caught with at least one accomplice or co-conspirator. ↩︎