Cooperation Working At Scale?

Why cooperation sometimes works well at scale, even globally - and some multilevel game theory and higher dimensional issues which are addressed.

Cooperation isn’t a scarce resource.  As Malcolm Ocean joked, “Why can't we all just get along? It's not because there isn't enough ‘along’ to go around. There's plenty and we can make more.” And I talked about stag hunts and difficulty scaling cooperation in a previous post, before we get further into why it fails at scale, it’s important to understand why it mostly works, why there is a natural tendency to cooperate. After that, I will go back to explaining why scale presents new challenges, especially in the realm of geopolitics, and then try to explain why that difficulty explains a large part of why cooperation so often works at other scales.

Humanity has a long history of making this work

Given all of the warnings in previous posts about how hard cooperation is, it’s easy to forget that humans are great at it, and generally expect that it will work. Continuing the trend of introducing a new game theory concept each post, the “irrational” behavior in the ultimatum game helps explain what is happening.

In the ultimatum game, one person is offered a dollar, and told to split it with another person. They can keep as much of it as they want, as long as the second person agrees - but if the second person says no, neither person gets anything, and the game ends. That is, they present an ultimatum; accept some percentage of the money, or we both get nothing. If you think about this narrowly, person two is better off saying yes to any amount, since they get something, and if they say no, they get nothing. So the (shortsightedly) rational decision for each is for the first player to offer 1 cent, and the second player to say yes. And really, it costs nothing for the second player to say yes, so he could just say yes even if offered nothing.

But, as most people are thinking, the other player won’t be OK with that - it’s unfair! And people who are shown this game, in general, agree with - and when experiments were actually run, in 1982, that’s what Güth, Schmittberger, and Schwarze found. In the initial pilot, they ran the game 9 times, and in 6 of the 9 trials, offers were above 40 cents, and the most common offer was an even split, 50 cents.

To explain why the people making the offers so often picked an even split, we can think about what these people were thinking about. And mostly, the answer is fairness, and cooperation. People see an even split as the most fair option, and the recipient of the offer will cooperate if it’s fair, or at least close. And if the person making an offer is greedy and shortsighted they can make a minimal offer. But if they are smarter, even a greedy player will think the other person will punish them - and they are correct. In the above 9 cases, all 6 offers above 40 cents were accepted, and the three remaining offers, two for nothing, one for 10 cents, were rejected. Fairness pays off.

But why? Later experiments explored what people do in response to ultimatums at different levels, and these confirm that people being offered free money will refuse if it’s seen as too unfair, if the person making the offer is going to get much more. But why would someone say no to free money, just because someone else was getting more? The answer, again, is fairness.

And researchers have found that people evolved to cooperate, and to play fair. So even if it’s not optimal in a given case, it shouldn’t surprise anyone that people try to be fair, and to cooperate, since we’re evolutionarily programmed for it.

But the common refrain we teach our children is that the world isn’t fair - and if everyone evolved to cooperate, and it has so many benefits, it makes sense to ask why things aren’t more fair. What is it that makes cooperation not be more universal?

Cooperation doesn’t scale well, redux.

In one-on-one ultimatum games, when there is another individual, people will hesitate to make an unfair offer because there’s a person that will respond. When the ultimatum is with a group, they feel much less pressure to cooperate. In a previous post I explained the multi-person prisoner’s dilemma that Douglas Hofstader ran, in which only 6 of the 14 participants cooperated, but following that, he ran a larger ultimatum-game like contest in which he asked the general public to play. The rules were fairly simple - up to one million dollars would be given away to a lucky winner, depending on how many entries were received. The prize was one million dollars, divided by the total number of entries received. That means the prize wasn’t split between entries, it was instead being reduced for every person who entered.

If everyone somehow cooperated, despite the difficulty of coordinating such an outcome, and only a single entry was received, that person would be given the full prize - but few people would expect that to happen. Instead, we expect selfish individuals to prioritize winning a smaller amount over the cooperative gain to whoever wins. But Hofstandter’s game was trying to prove a point, so to make it easier not to cooperate, people were allowed to submit an entry consisting of a number, denoting the number of entries they wished to submit. 

In fact, Hofstadter was right in expecting that when the game was public, and it was easy to defect, he didn’t need to worry about distributing the money. In addition to over a thousand perhaps semi-cooperative single entries, which themselves brought the prize down to under $1,000, there were 33 people who asked for a million tickets - any one of whom already guaranteed the prize was a measly dollar. 

But worse, he said, “dozens and dozens of readers strained their hardest to come up with inconceivably large numbers,” such that the prize was guaranteed to be zero. 11 people asked for 1 billion tickets, making the prize a tenth of a penny, i.e. nothing, while another 9 asked for a googol tickets, and an additional 14 asked for a googolplex, while still others attempted complex mathematical constructions to create far larger numbers. Hofstatder ended his column by reporting “that to evaluate which one was the largest, became a very serious problem, and in fact it is not even clear that I, or for that matter anyone else, would be able to determine which is the largest integer submitted. I was strongly reminded of the lunacy and pointlessness of the current arms race, in which two sides vie against each other to produce arsenals so huge that not even teams of experts can meaningfully say which one is larger—and meanwhile, all this monumental effort is to the detriment of everyone.”

We can see this as an indication and explanation of failure; a minority of participants poisoned the game. If they had been altruistic, hoping to maximize total benefit, Hofstadter noted that each of 10,000 potential participants should roll “a 6,667-sided die,” and only send in an entry if they rolled, say, a 1. And while I doubt many did so, it’s possible that some fraction of readers did that, and cooperated by sending in nothing at all. Alternatively, if the approximately 2,000 entries each submitted a single entry, one would have emerged with around $500 - a bit more than the $440 spent by entrants in total on postage. But at scale, at least with this setup, simple cooperation fails.

And yet, it works.

Despite the failures above, cooperation works well - which makes sense on one level, since humans evolved to cooperate in small groups. But per our central thesis, as the groups get larger, this instinct gives way to ingroup preferences, rivalry, or other issues. We have discussed why it fails in different ways in previous posts, but we also need to ask a different question - why does it work so well? That is, how and why do humans manage to cooperate at great scales? Companies are able to coordinate groups of thousands, and in some cases, millions of workers. Countries manage the far greater feat of coordinating millions, and in some cases, well over a billion people. And despite the threats and risks, humanity as a whole seems to have managed quite an impressive degree of cooperation. So, what’s going on? Is cooperation easy or hard? And is it common, or rare?

Depending on who you ask, you’ll get different answers, though I think they are largely complementary.

One approach is to deny that larger scale cooperation is, in fact, cooperative. In this view, companies work by coercing workers into being exploited for their labor, allowing those at the top and their cronies to hijack the fruits of the workers labor. Similarly, countries are run by a more-or-less explicit coalition of those who want things to stay stable. As we’ll see, this is certainly the case in some non-democratic societies - but those who more fully embrace this view would say that any pretense to democracy is a sop to deceive the public. They don’t think there is any cooperation, and the entire mechanism merely exists to allow political players and perhaps those who control them secretly, or less so, to ensure they can remain in control, and impose their will on others.

Of course, as much as this sounds like cynicism and conspiracy thinking, it’s not entirely false. Yes, there are groups and individuals who benefit from their positions and the structures that allow them to control others. But even if we accept this fully, it seems that it fails to fully explain the degree of cooperation that exists.

For a more compelling (or at least less cynical) explanation, we’ll go back to our game theorists. If you remember, there was a brief discussion in the previous post about group cooperation and punishment. There, the situation was that people could decide to spend their “tokens” to either cooperate, gaining money for everyone, defect, gaining somewhat more money for only themselves, or enforce, punishing those who defected by removing their gains. And this explains, to some extent, how larger scale cooperation works. We have enforcers in society, where we pay police and courts to make cooperation the best move. This explanation seems straightforward, and reasonable enough, but it fails at a large enough level.

Countries Cooperating, or Not

Without going back to Aristotle’s definitions, I’ll start the history with Jean Bodin. In his 1576 treatise, “The Six Books of the Republic,” he starts by talking about the idea of a state and the notion of sovereignty, where a ruler has the “power to set and to break the law" without consent. In a future post I’ll talk about enforcement, trust, and coercion, but for now we’ll take these as a given - something gives national governments a “monopoly on violence,” that is, and exclusive ability to enforce laws, if necessary, with guns. And this is reserved for the sovereign.

This notion of sovereignty relies on having a ruler set above the citizens, as opposed to the modern concept of rulers subject to laws - but it established the idea that a state was in charge. But in charge of what, exactly? Boudin’s list includes declaring war, making peace, appointing and dismissing officials and judges, reviewing or changing their decisions, including pardons, allocating or seizing land or other property, and establishing currency. All of these are, ultimately, enforced by the threat of violence. And all of these are the same as what modern states do - with the slight provision that instead of a single ruler, there is usually a defined power structure that is empowered to do these things.

Countries cooperating, then, might seem to follow the logic that applies to individuals. If they can agree on the rules, they can appoint enforcers, and instead of trying to play some version of the 8 billion person ultimatum game where everyone on earth can defect, they can play the types of game described in the last post for group cooperation and punishment, and they’ll only need to get around 190 countries to cooperate - a much more tractable problem.

This gives us a multi-level cooperative structure. Individuals have local communities and local governments that impose rules and aggregate their preferences. In a democracy, the local governments or elected representatives then make cooperative agreements to build generally positive policies at the national level. And the national governments then play geopolitics, with varying levels of cooperation. This ranges from negotiating and signing treaties to advance joint goals, to arguing with each other about international law and how treaties should work, to failing to cooperate at all by declaring and fighting wars.

Unfortunately, we evidently lose something at the top level - namely, the monopoly on violence. At each lower level, there was an overarching structure or enforcement regime that can be used to provide enforcement. Individuals can appeal to communities or local law enforcement to enforce norms or explicit rules. Local groups and sub-national organizations can similarly appeal to the national government or the judiciary. And all of this relies on having functional states with a monopoly on violence, and the resulting ability to enforce decisions.

When nations disagree, they go to international organizations like the UN. And you probably don’t need to be convinced that the UN’s power to enforce anything is sharply limited. At that level, countries with power can enforce or ignore rules as they wish. Russia and Israel (especially when backed by the US) can ignore the rules that other countries want enforced about how wars are fought and restrictions on occupying land that isn’t yours under international law. The US and China can each impose tariffs against international trade laws. Even “binding agreements” like the Nuclear Non-Proliferation Treaty are ignored by some signatories; Israel didn’t sign, but India, Pakistan, and North Korea all did, and are flagrantly violating their treaty obligations. But they have nuclear weapons, so no-one is going to force the issue.

In the end, sovereignty fundamentally relies on the ability to maintain a monopoly on violence, and that is critical to enabling cooperation - but states are unwilling to yield that right to international organizations.

Eppùr si muòve

But again, despite the explanations for why all of this isn’t going to work, as Galileo apocryphally responded, it moves. That is, despite all of this tidy explanation of why geopolitics cannot work, and that governments couldn’t possibly create cooperative agreements, geopolitics nowadays mostly works just fine. This may be shocking when we see the apparent widespread violation of various norms, until we remember that for every country ignoring international law in some given area, dozens are not. News reports, for non-cooperative reasons, focus on the exceptions - because things mostly working well isn’t a good headline.

There are at least three distinct explanations for Humanity’s success. The first one I’ll discuss is that politics is personal, the second is that norms are powerful, and the last is that there are punishments and incentives which don’t rely on violence, and which stabilize the international system.

Politics, even at the international level, is in part a personal matter. Heads of state interact with each other relatively frequently, and have friendships and interpersonal enmities just like any social group. Former Heads of State stay in touch, and while the left may grind its teeth and Trump’s abrasive personality, he has a lot of ability to get things done. In a very different way, Bill Clinton was interpersonally also magical in his ability to convince people; Republicans evidently had agreements not to meet with him one-on-one, because they repeatedly saw how he managed to be almost supernaturally convincing - and the same was true on a geopolitical level, where he was incredibly successful at pushing the US agenda forward.

But international politics is only in part personal. Another aspect is the pressure of norms. I’ll need to discuss the relationship between norms and cooperation more fully in other posts, but people don’t actually consider every possible action when making decisions. And this matters on both a personal and on a geopolitical level.

I’m eating dinner with my family, and I could eat with my fork and knife, or with my fingers. To the extent that my children see only the former, and have it drilled into them, (very imperfectly, given my personal failings,) they will be less likely to even consider the “rude” actions of grabbing a piece of cake with their hands in the future. But it never even occurs to them to do things like getting scissors to cut things instead of using their knife, or using the butter as lip balm - not because these wouldn’t work, but because they are not in the realm of what they’ve been exposed to, and they are aware of basic norms about eating.

Similarly, diplomats and government officials are generally inculcated with norms about how international relations is conducted. Fighting a war of conquest is norm-violating, but the norm against doing so is at best weak. (At the same time, it’s no longer the obvious thing to do, as it once was.) Kidnapping foreign diplomats, on the other hand, is so far outside the realm of acceptable that it doesn’t even occur to people.

But aside from interpersonal relationships and norms, there are national interests. And those interests extend far beyond joint avoiding war. The McDonalds Theory of international politics was the claim by Thomas Friedman, true for decades, that no two countries with a McDonalds even fought a war. That wasn’t a fluke or silly joke, it was noticing that countries with western-style free economies, not-coincidentally those countries in which McDonalds was willing to open branches, had too much to lose to be willing to fight wars with each other.

While the McDonalds theory eventually failed, the underlying logic still matters. A story by Thomas Friedman about an incident where India and Pakistan were engaging in some saber-rattling explains this clearly. At the time, the risk of war between these two nuclear powers suddenly seemed real - not to politicians, but to companies and the markets. At that point, Western companies which offshored jobs to Indian subsidiaries and companies with extensive outsourcing started talking about shutting things down and moving to other countries. When the political leadership in India started getting calls from some of the largest companies in the country, those companies were all very clear; if you don’t back down, our companies will be ruined, and your economy will collapse.

Clearly, there are players whose vested interest in the international system who can provide incentives of an entirely different type than external enforcement. Economic interdependence turned the large-scale prisoners dilemmas for countries deciding whether to invest in militaries and to invade each other into stag-hunts, where as long as others were following the rules, the costs of defecting from international norms was high, and the benefits for cooperating were large. As long as everyone knows the rules, this can be very stable - and it was, for decades.

Coalitions and Multi-Level Games

The new model of enforcing cooperation, however, creates a new challenge when industries or other groups want different things.

I won’t try to define multi-level games here, but I will give an example. Before 1913, when the Seventeenth amendment was enacted, Article I, Section 3 of the Constitution dictated that senators were elected by state legislatures. Instead of voting for a Senator, voters would vote for their local state legislator, and those legislators would then vote for Senators. Among other things, this was a check on federal power, since state legislators would (presumably) not choose to elect people who wanted more centralized national power at the cost of state-level powers and rights. Not coincidentally, the US government became far more centralized since then.

There were problems with the indirect election of Senators, primarily corruption, and deadlocks. Corruption was the simple fact that state legislators would sometimes sell their votes to candidates. Deadlocks, though, were a different issue - sometimes, state electors could not agree on who to send to Congress. And this illustrates a separate problem, which we’ll talk about soon, which is the fact that multidimensionality can make consensus impossible. However, the essential nature of elections was that coalitions needed to be formed at both a state level, to choose a senator, and then at a national level, to pass laws.

The same dynamics play out internationally; countries form coalitions internally, and then those coalitions send someone to the UN. And for those who think that this is a problem with democracy, see Acemoglu’s Coalition Formation in Non-Democracies - regardless of how we run these systems, we have these dynamics.

What makes this problematic is that multi-level games are different than traditional games in a specific technical way. In traditional games, there is guaranteed to be some stable strategy, or probabilistic combination of strategies, that works best in the sense that no player can do better by changing strategy. The above linked paper by Hausken and Cressman shows this isn’t true for multi-level games. And this means that even when people’s preferences do not change over time, and even when we don’t have problems with Arrow’s theorem and inconsistent group-level preferences, we can end up in situations where no stable policy decisions can be reached.

I haven’t seen a clear example of this, so I’ll try to come up with one. Imagine, for example, a three-country world with democratic binding international laws. Extremistan has are two stable coalitions in a parliamentary government, pro-business, and pro-environment. Whichever side is in power gets to negotiate with foreign governments. A binding climate deal would strengthen the left, and gain supporters, making it viable. In the opposite direction, deals for oil and gas investments would be economically beneficial, generate jobs, and strengthen the right, making this approach viable as well. What is definitely not viable is a compromise deal which strongly benefits neither side. Moderatia, on the other hand, has a strong centrist ruling coalition. They could agree to a compromise, but will be politically vulnerable if there is an extreme deal in either direction. And finally, Wishwashia has very fickle voters, and the leaders will vote for any deal over nothing - but the electorate their spends too much time watching political pundits, so they change their mind to match whoever seems to have the most political momentum globally.

Now, one side is in control of Extremistan, and an extreme deal is reached. At this point Moderatia’s ruling coalition will collapse, and a new coalition will be elected to offer something to Wishwashia to change the deal to a moderate one. This leads to the ruling party in Extremistan falling, and the other party gaining power with promises to induce Wishwashia to change to an extremist deal in the other direction.

But this isn’t the only reason that we might find an inability to reach a stable consensus.

Multidimensional Bargaining and Logrolling

Back in the world of single-level games, where people (or groups) can directly negotiate what they want, there’s a fairly simple and impressively predictive class of model, agent-based rational actor models. For example, a dissertation from someone I know applied this type of model, which impressively predicted a decade of Iranian decisions based on the internal dynamics of different power actors in the country. How does it work?

It starts by making some huge simplifying assumptions; all the actors are rational, have linear preferences, and only care about a single issue at a time. This might seem to go too far, but it accurately describes the internal decision making even inside of a regime that has some extremist and irrational groups. To get an answer, it generalizes something like the median voter theorem, where a coalition ends up deciding on a preference- and influence-weighted median. That is, the decision will be whatever puts equal numbers of power on each side of the compromise.

But an interesting fact about the idea of a median is that it only exists in a single dimension. If you remember high school statistics, you can find the median just by picking pairs of the most extreme values and throwing them away until you get to the middle. But in more than one dimension, this stops working, because there isn’t a unique ordering of most extreme positions.

To see this, in the above graph, we can try a few different ways of picking the median. If we try to eliminate the items with the largest and smallest absolute values, we are left with the two red points and the approximate median noted by the empty circle on the leftmost figure below, while if we order by y-value we get the figure in the middle, and if we order by x-value we get the figure on the right.

If policy debates were always dominated by a single dimension, the conclusion will be something akin to a median, but that’s when logrolling, which I’ve written about in the past rears its ugly head. The essential issue is that different groups can trade what they care about in one dimension for a concession in another dimension. This is often viewed negatively - the dirty parts of political negotiation that involve compromising with the enemy. However, as you might suspect given that the 2016 Ribbonfarm post I just linked to was titled The Future of Compromise, I’m not against compromise. And as I pointed out there, I see lots of ways for logrolling to grease the wheels of democratic compromise. But it does make things less stable, and less predictable.

Predictability Matters

People can usually trust others to pursue their own interest. As we said in previous posts, that’s the basis of capitalism, and as noted above, it’s also the basis for much of the stability in geopolitics in the latter part of the last century. As we mentioned last time, as long as I know that others will abide by their bargains, I can cooperate, which is why enforcement is critical. But the stability here is critical, and it relies on predictability - in the case of geopolitics, usually the predictable self-interest of the different countries. As we said above, the predictable self interest, alongside the interconnected economy and the wastefulness of conflict, provides a key incentive to cooperate.

As I’ve said many times in the past, the hard part of decision making under uncertainty is the uncertainty. That’s not to say that unpredictability is always bad - there are many scenarios where the optimal strategy is probabilistic. Variety is the spice of life, but unpredictability is salt - a little bit in the right places is great, but too much will ruin things. And it seems clear that through most of human history, life was oversalted.

The best strategy for Rock, Paper, Scissors is a simple example where using each a third of the time, picked randomly, is the optimal strategy for all players. But despite being random, this isn’t unpredictable or uncertain - it’s predictable randomness. Uncertainty, where we don’t know the rules of the game, or don’t understand the strategies available to others or their goals, is almost always unpleasant in large quantities.

Individuals hate uncertainty about their lives, since it usually causes stress and unhappiness. Businesses hate uncertainty, because it’s far more expensive to need to plan under uncertainty about decisions than to just maximize profits in straightforward cases. And domestic governments hate uncertainty, because it makes planning harder. I won’t go into high-modernism here, but one rationale for centralization and central planning is that it makes things predictable. This is certainly a problem when the planning fails to capture real variability, or creates fragility due to standardization, as James Scott explains in Seeing Like a State. On the other hand, having a predictable system allows for far better coordination - and that’s true an many levels.

Governments are put in place in part to allow this - they reduce risks to people and businesses, and help coordinate for better outcomes. The first part is directly about reducing uncertainty, and the second part benefits from reduced uncertainty as well. And on an international level, it’s easier to negotiate when your partners are predictable as well. Unfortunately, as we’ve discussed, there are some fundamental issues with stable and coherent preferences in global geopolitics. Thankfully, self-interest is a powerful motivator, and as I mentioned at the beginning of the post, reasons that global geopolitics is tricky - the instability and incoherence of individual actors, groups, and countries - are a barrier to self-interested cooperation.

Conclusions

We saw that cooperation at the largest scale poses new and additional challenges, due to the lack of enforceability, the instability of multi-level games, and the unpredictability of outcomes in these largest-scale interactions. But there are incentives to solve these problems, and the world mostly muddles through with cooperation, due to some combination of the interpersonal cooperation among leaders, the norms that have been build, and the self-interest. And the last of these doesn’t just create incentive to negotiate and abide by international deals - it creates incentives to reduce unpredictability at smaller scales, including enforced rules.

But as I’m hoping to talk about next time, there are some critical problems with this sort of top-down approach, and the recent discussion between Elle Griffin, starting here, and Peter Clayborne, author of Anarchy Unfolds, gives me the perfect hook for discussing why anarchy, understood in charitable terms, is at the same time good and bad, easy and impossible, promising and tragic.