Morality and Cooperation for Geeks

A society is not viable without cooperation among its members.  We have seen that such cooperation requires adherence to social norms, including those the immediate purpose of which might not be obvious. Let’s make this point more forcefully by considering a formal model of human interaction that abstracts away everything but the barebones issues.

Imagine two spies, Gadi and Palti, working in tandem, who are captured and put in separate interrogation cells. They are each offered the same deal: if you rat out your buddy and he remains silent, you go free and he’ll go to jail for life and never be seen again (and bear in mind that your friend got the same offer). If you both rat, you both get long (but not life) prison sentences; if you both remain silent, you both get short prison sentences.

At first blush, that last part suggests to each of them that nobly remaining silent is the way to go: if they’re both silent, the outcome is better for both of them than if they both rat. But, thinking it through more carefully, Gadi realizes that, while he doesn’t know if Palti will rat or be silent, he – Gadi – is better off ratting either way: if Palti rats, Gadi better rat too or he’ll never be seen again; if Palti is silent, Gadi need only rat to be free as a bird. This reasoning is absolutely compelling; in fact, it’s so compelling that Palti comes to the same conclusion and the two of them have many years in a cell together to discuss whether ratting was the right choice.

We don’t need to be prisoners to face the Prisoners’ Dilemma, as it’s commonly called. The essential elements of the story are that two parties can either cooperate with each other (remaining silent in the case of the Prisoners’ Dilemma) or defect, that the parties must make their choices independently and simultaneously, and that the ordering of preferences for each party is:

<I defect, you cooperate>    is better than

<both cooperate>                  is better than

<both defect>                         is better than

<I cooperate, you defect>.

This comes up in many real-world situations. Buyer and Seller can benefit from a transaction, but each can profit more by cheating at the other’s expense. Two world powers can benefit from an agreement to avoid an arms race, but each can profit more by cheating. In all these cases, a rational player would cheat.

One can extend this reasoning to situations with more than two players. For example, if we all do light fishing in the communal lake, we all have lunch and a lake full of fish; if we all do heavy fishing in the lake, the fish will be depleted faster than they can reproduce and we all have lunch and supper but a dead lake. So, I figure to myself, either enough others will fish heavily to deplete the lake anyway, so I might as well live it up, or enough others will behave, so I can afford to live it up. The chances that my few extra flounders will tip the scales are negligible. Everybody else thinks the same thing and so much for the lake.

How do we get out of this dilemma? It’s apparent that we can because, for example, merchants do make deals all the time without cheating each other.

One possibility is that we are simply altruistic. We each have, as I have been arguing all along, an instinctive moral sense. So, I might not rat out my comrade simply because his well-being and freedom are important to me. This is quite true but, alas, we also have other instincts, and a careful analysis of human behavior suggests that, while altruism is common, it is far from an adequate explanation of observed human cooperation.

A more plausible explanation can easily be intuited by contemplating our friends, Buyer and Seller. It is true that Buyer can make extra profit by taking delivery and then not paying and Seller can make extra profit by shipping counterfeit merchandise. But how many times can they get away with this before nobody will do business with them? Buyers and sellers, who want to stay in business for the long term, care about their reputations; in fact, online market places make this explicit by enabling participants in a transaction to rate the other side. The Prisoners’ Dilemma is a one-shot event and hence not a fair representation of typical human interactions, which are ongoing.

To try to capture human interactions with a slightly more realistic model, let’s consider the case of repeated Prisoners’ Dilemmas: we play one round, the players’ choices are revealed and payouts are made, then we play the next round and the next and so on. Each player wants to maximize his payoff over time. What can we say about the behaviors of rational players in this scenario? Are they doomed to cheat as in the one-shot version? Note that, whereas in the one-shot version a player need to choose between two options (cooperate or defect), in the repeated version a player needs to choose from among many possible strategies: always cooperate, always defect, alternate between defecting and cooperating, defect if the other player defected in the previous round and otherwise cooperate, defect only if the other player defected in the previous two rounds, defect six times if the other player defected in the previous round, toss a coin, toss a biased coin, toss a coin if the other player defected in the previous round but otherwise cooperate… You get the idea.

Unlike the one-shot Prisoners’ Dilemma, there is no single strategy that offers a maximal payoff regardless of the other player’s behavior. If the players are limited to strategies that are blind to the other player’s past actions, then always defecting is indeed the optimal strategy. But a player can do better by being responsive to the other player’s past actions. Consider for example a strategy, called tit-for-tat, in which a player defects only if the other player defected in the previous round; in other words, he cooperates in the first round and mimics the other player forever after. If Gadi thinks that Palti is using this strategy, then under most circumstances, Gadi will maximize his own payoff by playing the same strategy (and the same is true from Palti’s perspective). Since tit-for-tat has this property, we say that it is an equilibrium strategy. The nice thing about this strategy is that if both players stick to it, they will cooperate forever.

Note that tit-for-tat is not the only equilibrium strategy. Always defecting is also an equilibrium strategy. So is cooperating until the other player defects and then defecting forever (“grim trigger”). There are many others. But at least cooperation is possible.

Did you notice that little “under most circumstances” I slipped in just before? Let’s get back to that. Assuming my opponent believes I’m playing tit-for-tat, under what circumstances will it actually be optimal for him to cooperate with me as long as I cooperate with him?

The answer is that it depends on how much he values future returns. Suppose Buyer and Seller make a transaction exactly once a day. Assuming no one cheats, each gets one unit of joy from the deal. If they keep this up for, say, a year they’ll each make 365 units of joy. But how much is that unit of joy that Seller is expecting to get a year from now worth to him today? Presumably less than one full unit: if Seller is a live-for-today kind of guy, it’s worth a lot less; if he’s a save-for-tomorrow kind of guy a little less. In the first case, we say that Seller has a high discount rate; in the second case, we say he has a low discount rate.

Here’s the punchline: if and only if Seller has a high discount rate, it might be worth it for him to cheat. It’s easy to see why: he’d rather make a quick buck at my expense today than to make more than that in the future, since he heavily discounts the future. A guy with a high discount rate is a guy you don’t want to do business with.

So, for long-term cooperation we need players with low discount rates who choose a tit-for-tat strategy. But, as legal scholar Eric Posner notes, there’s one more requirement. Let’s call people with discount rates low enough that it pays for them to cooperate the good types; the guys with the high discount rates are the bad types. It’s not enough for Seller to be a good type; he also needs to convince Buyer that he’s a good type so that Buyer will want to do business with him.

In the formal model, as Posner explains, there’s actually a way for Seller to persuade Buyer that he’s a good type and will deliver the goods. Let’s think about those 365 units of joy Buyer and Seller might each get if they do business together. If Seller is a bad type those 364 future units of joy are worth, say, 50 units of joy today; if he’s a good type, they might be worth 250 units of joy today. So, if and only if Seller is a good type, he can afford to give Buyer a gift worth 100 units today in anticipation of getting it back through future business. The gift signals to Buyer that Seller is a good type.

That’s the formal model. In real life, there are numerous ways that people signal that they’re good types. They dress and groom themselves in ways that suggest that they can afford to pay a price in money, time and effort to profit from long-term cooperation. They are polite, as formal as necessary, careful about table manners and generally make a display of their ability to control impulses. Of course, they do this not only in interactions with specific business associates but in interaction with their whole society. Different communities develop different sets of behaviors for this purpose. Members of a community need to demonstrate loyalty to the social norms that have evolved in this way in their community in order to convince others that they are good types who can be depended on to cooperate for the long-term.

In short, the requirements for cooperation in a community are tied to the three moral foundations we considered in previous posts: a preference for fairness (tit-for-tat), the ability to defer pleasure (low discount rates), and loyalty to the community’s traditions (signaling low discount rates).

Okay, this was a tough one. In the next few posts, I hope to repay your patience with some Heidi-baiting.

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