Parable of the Dammed
Once upon a time, two families fought a bloody feud over the border of their properties. After many years of escalation, neither family could afford to continue the fight. They both wanted to negotiate a truce, but the original issue still had to be settled: where was the border of their lands to be drawn? They needed a Schelling point, so they settled on a river which ran roughly through the middle of their territories.
For a short time, there was peace.
Soon, though, a clever couple from one of the families hatched an idea. Each morning, they walked down to the river and dropped a few large stones into it. Before long, half a dam had built up on their side of the river. The water was driven toward the opposite bank, which was steadily washed away. Over time, as the river ate away the opposite bank, the couple extended their dam further, and so the river’s course was gradually pushed sideways. The couple’s family gained territory, while the opposed family lost it.
At this point, the story diverges, and many versions of the tail are told.
In one version, the couple push too fast. Soon the river has moved deep into the territory of the other family, and the family responds by attempting to break the dam. Violence escalates, and the feud breaks out anew—but peace is even harder to come by, now, since the river has been permanently destroyed as a Schelling point.
In another version, the push is slow. The couple bequeaths the task of dam-building to their children, and to their childrens’ children, and the river shifts slowly over the course of generations. With each generation, the resources of the couple’s descendants grow, and their family grows with it—while the resources of the opposed family slowly dwindle. Nobody ever takes much note of the river’s slow drift, until eventually the opposed family dies out altogether.
In most versions of the tale, the river’s movement is quickly noticed, but a return to violence is deemed unacceptable. Instead, the opposed family begins dropping rocks of their own. Soon both families are dumping rocks on their respective sides of the river, building up dams, aiming to drive the water against the opposite bank. This bloodless but expensive feud escalates. Along some sections of the river, each side expands until the two dams clash in the middle, blocking the flow of the whole river, and water backs up and bursts the banks. That doesn’t stop the dam-building—rather, each side builds tall walls alongside their dams, in hopes of flooding the other family’s land while preserving their own. The two families quickly bankrupt themselves in an arms race to build the tallest walls along their respective riverbanks.
Word goes out of the strange practices, the two families pouring all their resources into a competition of great dams and flood-walls. Travellers passing through town stare in bemusement, and wonder what strange force would lead the families to waste so much resources on a minor stream through the woods.
Moral(s) of the Story
I see two main takeaways to this parable. First, Schelling points can be moved by changing the underlying territory. The river’s course can be physically moved. This generally costs some real resources (e.g. building the dams); modifying the world is rarely free.
Second, when players compete to move a Schelling point, they often end up in an all-pay auction: all players spend the resources required to move the river, but only the player with the “highest bid” (i.e. tallest dam) gains anything from the competition. In general, all-pay auctions often lead to all players spending more than the value of winning: at any point, either family can gain by building their dam just a bit taller, even long after their dam-building expenditures far exceed the value of the land.
This applies to most of the “strategic negotiation”-style situations where Schelling points play a prominent role, and in particular I see the parable of the dammed as a prototypical model of politics. Politics is an all-pay auction, in which “bidders” (i.e. anyone spending time/resources on political influence) compete to move Schelling points. The Schelling points which people compete to move include obvious things like laws, but also more subtle Schelling points like social norms.
Both families are conquered by an outside force. Stripped of their land in all but name, the natives continue to build dams and flood-walls to attract tourists, but their hearts are no longer in it.
The squabbles of Genoa and Venice were indeed quashed by Napoleon.
Related: if you spend most all of your time feeling miserable for complicated reasons consider that you’ve had a campaign of memetic maneuver warfare successfully staged against you. Run an audit of who is living rent free inside your head. The following sentence stem can be illustrative: The bad thing that would happen if I stopped believing [X] is...
This won’t catch everything as more complicated beliefs have a net of justifications. But it will catch low hanging fruit.
I know this is two years later, but I just wanted to say thank you for this comment. It is clear, correct, and well-written, and if I had seen this comment when it was written, it could have saved me a lot of problems at the time.
I’ve now resolved this issue to my satisfaction, but once bitten twice shy, so I’ll try to remember this if it happens again!
glad it was helpful! I like Core Transformation for deeper dives looking for side effects.
So for some realism which the original story didn’t call for —it’s a “parable trying to make a point”, not a “detailed historical account of territorial feuds in 15th century Albania”—, we can look at how this works out in practice. To do this, we look to The Kanun of Lekë Dukagjini, which describes the sort of laws used to deal with this kind of thing in 15th century Albania. My details might be iffy here, but I did read the book and remember some parts.
In practice, there are several points of intervention, if I’m remembering correctly:
After the first murder, the extended family of the murdered goes after the murderer, to the extent that he can’t safely go out of his home. If he is killed, the feud ends on the part of the murdered’s family.
At any point, one of the families can ask a more powerful figure to mediate; in some regions this can be a cleric. The resolution might involve substantial amounts of money to be paid, which, crucially, is set beforehand by law, in excruciating detail depending on the conditions.
The lands wouldn’t in fact be the most valuable resource here; it would be the working power of adult men, who can’t get out because they would be killed in revenge. This cripples both families economically, so they do have an incentive to cooperate.
So, in practice
I get the impression that this ends with the clever couple getting killed in the middle of the night by one of the more violent and impulsive cousins of the second family, and maybe the second family paying some reparations if they’re caught. Probably less than, you know, if they’d killed a normal couple. That, or the dam gets destroyed. Or actually, the husband from the clever couple would have to ask the Patriarch of the family for permission, who would veto the idea because he wants to make the truce work, and is hesitant to lose more of his sons to a new feud. Also, with or without the discount factor rural people in Albania have, doing this kind of thing wouldn’t be worth it. Or actually, the clever couple learnt in childhood that this kind of thing wasn’t worth it, and got some lashes in the process.
The Schelling point wasn’t the river, the Schelling point was someone more powerful than you telling you not to start trouble. This is harder to game. Also, you don’t have “the government”, you have “the more powerful village cacique,” or the priest, which works because you don’t want to hell when you die.
You do see a thing in rural Spain with territory boundaries being marked by stones, and those stones being moved, which kind of works if one side doesn’t spend time in the land.
I’m here for the parables and the pun titles. Thanks for providing me a little of Scott Alexander during the SSC drought.
Seems very consistent with views of rent-seeking as a negative-sum game.
Seems inconsistent with the Coase Theorem, and perhaps why, at least moderately impartial, third parties are better suited to mediating disputes than those directly involved. But when talking about politics and government where to find such an impartial 3rd party?
This is a great comment. It made me realize that Coase can be applied to a dollar auction, which is really neat.
Let’s unpack that.
In the dam story, a Coase theorem solution would mean that each family pays the other to not build dams (since building a dam imposes an externality on the other family). In principle, this could work out to net-zero cash changing hands, since each family pays the other. It would just fix the incentives. So yeah, that does sound like a pretty good and feasible solution in the two-player case.
The usual failure mode of the Coase theorem is that it requires too much coordination when in many-player scenarios, so what would that look like? One generalization is to apply Coase directly to the prototypical all-pay auction: the dollar auction, an all-pay auction in which one dollar is auctioned off. Bidding in the dollar auction imposes an externality on the other bidders—they effectively lose their bid amount. Coase says that bidders can solve this by paying other players to not bid. In a many-player scenario, it won’t make sense for any one player to pay the others enough to stop bidding (e.g. with 100 bidders in an all-pay auction, I’ll want to pay the other bidders at most ~1 cent). If many players each offer to pay all the other players to stop bidding, then it can work, but that also creates a potential free-rider problem and coordination will be hard with so many people.
What rent?
The rent-seeking is all the efforts to build the dams that exceed the benefits of getting the additional territory. Using rent-seeking in a very broad sense a al political economy/public choice literature. Clearly there is some type of benefit each side gets from increasing their territories—that would be the rent they expect to collect by having ownership of the additional territory.
Each side if paying more to move the property line (reassign the property right to come area) than they are getting from actually owning the land. This occurs after they have already agreed on an allocation of property rights. Per Coase, all the remaining adjustments would then be payments by one side to the other for access/use or ownership. But why would they respect the allocation of rights by Coase more than the allocation they agreed among themselves?
Coase either needs Leviathan or a well shared and respected view of property rights. This last point seems a bit similar to a critique I heard James Buchannan made of David Friedman’s Machinery of Freedom thesis. That is, the theory fails if all protection agencies do not hold the same fundamental understanding of property rights. Perhaps that same problem plagues Coase in this type of setting. In other words, Coase requires a shared property rights regime that is generally accepted, as is the external enforcement of those rights by outside parties. I had never real considered that type of constraint on Coase before.
Do you have some pointers to the many-player problem you mention—hopefully not too mathy or with a good verbal summary of the argument. Or is what I’ve just “discovered” the general thrust of that problem?
I picked up my understanding of Coase from Law’s Order.
This seems wrong. Even in the example at hand (i.e. the dams), there’s no Leviathan or respected property rights, just a negotiated border, yet we can still apply the Coase method: families pay each other to respect the border. This does require some method of credible precommitment (though iteration can largely substitute for that), and an ability to not “pay” if one family outright invades, but it doesn’t seem to require any property rights other than the ability to hide one’s own money.
In a 2 player dollar auction, I can offer you 50c not to bid, and then bid 50c myself. If you outbid me with 51c, then you only gain 49c.
For this to work, we need trust that I will pay you iff you don’t bid. Either I pay you early, and then trust you not to bid, or you don’t bid, and trust me to pay later, or we both trust an escrow.
Coase theorem doesn’t hold if either family would take the money, and then try to move the river anyway.
The parable shows a few things that IMO are more important than the things you mention:
Disputes are not necessarily resolved when the first agreement is reached. If the border was important enough to fight over, it should be important enough to fight again when one side tries to move it (or when it passes some threshold. This is a problem in the real world, too—https://en.wikipedia.org/wiki/Border_irregularities_of_the_United_States has a number of examples of rivers that move, and the borders sometimes move and sometimes don’t, but either choice requires discussion and agreement.
Schelling points/lines are useful for identifying candidates for agreement, but they’re not enforcement mechanisms. There must be some underlying reality that the agreement is about.
While I intuitively agree with the first takeaway (that moving Schelling points is usually expensive), I think that politics do not have to be a zero sum game. Look at EU or at coalitions creating governments within one country (you US citizens do not have that, I realize). Anyhow, I think that logical resolution would be to punish the cheating family with war as in reiterated prisoners dilemma.
Technical nitpick: the game is nonzero-sum, since net value can be destroyed (i.e. by building big useless dams). This is very different from zero-sum, since there are mutual relative gains to be had by agreeing to not destroy value.
Problem is, in the real world, there aren’t always clear up-front standards for what constitutes “cheating”. Also war is really really expensive, and we don’t always have the foresight to publicly precommit.
In a fourth eventuality the opposed family notices the couple’s flagrant breach of the peace agreement and induces a third party to intervene and render their opinion on whether hostile dam-building is a violation of property dispute norms. The third party arbitrator sees an opportunity to grow fat from the conflict and continually requests ever larger bribes from both sides before eventually drawing an arbitrary line in the ground and calling it a border. Of course the border isn’t amenable to either family, but they are powerless to challenge the will of the arbitrator because that would post facto make their bribes a waste and not improve their situation one bit. The arbitrator realizes there is a lot of free slack to be gobbled up in these property disputes and starts up his own racket.
Moral: don’t trust anybody to be fair to anybody but themselves.
This was a great comment right up until the moral. This is economics, mate! People “being fair” is irrelevant, we’re just talking incentives and negotiation and the rules of the game.
You’ve restated the moral in euphemistic terms. Some people do have the idea that they can trust others to give them a fair shake. That’s wrong. You’re right that the couple is behaving unfairly because of their own self-interest and the fact that they can get away with it, but regardless their actions are still unfair.
There’s a big difference between “we can’t trust people to be fair” and “fairness is irrelevant”. Irrelevance means that the rules remain the same even if people do try to be fair. In the arbitrator example, it may be that the arbitrator is trying to be fair but neither family wants a fair outcome, or it may be that the arbitrator has different ideas about what’s “fair”, or the arbitrator may be a whole company/government/institution in which each individual is trying to behave fairly but there’s selection pressure for those who pull in more resources. The picture ends up similar in all cases: the arbitrator has the power to impose their own preferred solution, ignoring the will of the families, so long as they don’t push too far and break the Schelling point (i.e. so long as they don’t demand so much so fast that the families mutually agree to find a new arbitrator).
I am not saying that the couple is behaving unfairly because of their own self-interest. I am saying that whether-or-not the couple is behaving unfairly is irrelevant; the rules of the game remain the same either way, and behavior can come from selection just as easily as intent.
Have you read Ursula K. LeGuin’s book “Changing Planes” by any chance? If I recall correctly, there’s a chapter where the viewpoint character is visiting a library, and reads a legend about two rival cities with a river border, and the outcome is rather similar.
I like this story, and I think you could do a second version in which you just tell the story, without any analysis incorporated. I think that some people who might be confused or turned off by the analysis because they’re unfamiliar with the jargon might learn more from just reading the story itself.
It actually sat in my drafts pile for several months in exactly that form. I figured people wouldn’t get the (intended) point without explanation, but also adding the explanation felt kind of awkward.
It’s good either way :) I just think it’s poetic, and might “work its way in” in the way that good stories do on its own if readers give it time.
Pull the rope sideways—not the river ;)
Great post!
I like the story as illustrating inefficient fighting over resources and entitlements. However, I am not sure your interpretation of moving focal (or Schelling) points works?
In general, a focal point is needed when you have to choose something without being able to explicitly coordinate on it (and when there are multiple equilibria). Here the families do coordinate—they negotiate. As a fairness norm, I’d guess that choosing the middle of the river works because the river “ran roughly through the middle of their territories”. When one conflict party afterwards manipulates the river, the river becomes useless as a border, and trust is destroyed (ending 1), or one conflict party just does not notice what happened and seemingly has limited attention or limited information (ending 2), or the destruction of trust again leads to wasteful fighting (ending 3). Endings 1 and 3 can be interpreted as the “bad” Nash equilibrium of a repeated game. Standard game theory does not offer convincing solutions for why one of the possible equilibria (cooperate or don’t) is chosen, so focal points may be part of the answer, but then the river is not the focal point; rather, “cooperation” is the focal point.
Since the parties agreed to use the middle of the river as the border and then one of the parties had the idea to manipulate it, the story may illustrate a problem of incomplete contracts.
Negotiation was actually one of the central topics in Schelling’s original book on the topic. The problem is that, in a negotiation, there’s an effect similar to not-being-able-to-coordinate. There are multiple Nash equilibria, but players prefer different equilibria. Each player will say whatever seems most likely to make their preferred equilibrium happen, but other players know they will say those things, so the “communication” actually has zero information content (at least with respect to which-equilibrium-to-choose). This means players must coordinate on an equilibrium, despite generally discounting everything the other players say about which equilibrium to choose. Thus, the Schelling point becomes relevant—e.g. borders are drawn along rivers, even without any “sense of fairness”.
That is very interesting. I have not read Schelling’s book, and having worked a lot with and/or read things applying Nash’s bargaining solution as an axiomatic version of bargaining and Rubinstein-like alternating-offers games over the years, it seemed to me that agreeing on sharing rules should be considered distinct from uncoordinated behavior. In this sense, I do buy the point that a river can be an “agreement focal point”, but only if it is roughly in the middle. It seems to me that the fairness focal point would be a 50:50 split, and using a river instead is a pragmatic deviation from that, because of the fact that the river is a barrier and any crossing and violation of the agreement can be observed easily. I doubt that you could “shift the focal point” by damming because that constitutes such a violation, and then the focal point becomes non-cooperation. (Concerning the incomplete contracts I mentioned: In practice not even that will work, because when the other side sues you, a judge would probably rule against you but that may depend on the legal system.)
Remember, “fairness” itself is not always a focal point, and even if it is a focal point there can still be plenty of others. Nash bargaining & co involve a symmetry assumption, independence of irrelevant alternatives (or some substitute for it), etc. These are elegant mathematical assumptions, and they are sometimes intuitive focal points in real negotiations, but not always. Symmetry, in particular, is very often not a realistic condition in bargaining (and not just because players have different BATNAs, which Nash already accounts for). Also, in practice utility functions are not observable, and the “no substantive communication” issue means that I can’t trust what the other player claims about their utility/BATNA (though of course mechanism design can counterbalance this problem sometimes).
I agree in general, though afaik there is just no really rigid theory for what constitutes a focal point—it can be anything that is salient. If you let people play in a lab and give them game matrices with multiple equilibria with identical payoffs, then coloring one equilibrium can make it focal point; but in reality many things can seem salient. Maybe it’s somehow built into our genetic and cultural code what we coordinate on—e.g. what’s best for “all” or what’s best for “our group” etc. (IIRC, Ken Binmore suggests something along the lines of “Evolution makes us find Nash bargaining solutions fair” in the book Natural Justice, but I don’t remember what his evidence is to support that.)
Concerning symmetry and Nash: you can model the Nash bargaining solution asymmetrically, but of course it’s unclear whether that helps. Models like Rubinstein’s are elegant but not really realistic in their assumptions and neither in their implications.