Continuing from yesterday…

### 8. Centrality

The concept of subordination primarily applies to teams which have some inner organizational structure, such that members of the team have strong expectations about what other members will do — whether because a teammate has encouraged these expectations (as leaders expect their followers to continue to follow them) or because the nature of the teamwork depends on it (as a unit in a battle-line excepts the units on its right flank and its left flank to continue fighting courageously).

In more informal types of cooperation, where a group of agents have common goals but no specific means of coordinating each others’ behavior, neither condition applies. Such agents need not have any special expectations about what their allies are going to do; nor is it likely that their choices are imperiled by their dependence on precise predictions about their allies’ choices. On the contrary! Most frequently these loose teams face the problem that all of the allies have the (perfectly accurate) expectation that they will fail to cooperate effectively, so they will not achieve their goal, so there is no sense in making an effort to achieve it.

I’m going to give an example of a (non-competitive) game to illustrate this point. (Skip ahead a few paragraphs if you understand coordination games inside and out.) Adam, Bob, Carl, and Daniel would like to eat dinner; they prefer not to eat alone, and would be happiest if all four of them could eat together. But could they possibly arrange to all be at the same restaurant at the same time? What kind of witchcraft could bring about such a miracle?

Let’s take pity on these poor kids and simplify the problem: we’ll say there is only *one restaurant* in their town, so all they need to do is be there at the same time on the same evening. So each picks a time that seems likely, goes to the restaurant, waits ten minutes to see if his friends show up, and goes home if they don’t. If they were randomly picking times between 6pm and 9pm, there is a roughly 0.3% chance that any two of the friends will run into each other at the restaurant (simplifying a bit to assume they pick one of the eighteen 10-minute slots starting at 6:00). The chance at least two of them will show up to the same slot is substantially higher (30%, if I did the math right), but the chance that *all four* of them will arrive at the same* *time is infinitesimally small. — And this is assuming they all check the restaurant every night! If they also need to pick the day of the week they think is likeliest, the odds plunge further.

Moving back a step, we can also say that the chances of success are low enough that *they may stop trying*, especially if the walk to the restaurant is long or if their top preference is an ABCD dinner and they have mixed feelings about the other permutations. For example, if Adam thinks Bob and Carl are both a little bit awkward and so a dinner alone with just one of them would be painful, he’ll set a low value on his 16% chance of having dinner with one other person (AB, AC, or AD). If they all know the odds are low enough that some of the other guys will stop trying, that decreases their odds of finding a friend waiting at the restaurant further: and iterate.

This illustrates the overarching difference between the coordination problems *organizations* (and armies) face and those that less structured alliances deal with. In this example, there is no cunning enemy to defeat; selfishness plays no role, no one has any way to take advantage of his teammates; the structure of the problem is very simple; success not require balletic levels of synchronized, skillful coordination. And yet they can all predict *exactly* what their “teammates” are most likely to do (stay at home)! This is exactly the reverse of the problem of insubordination: ABCD are entirely predictable and yet they all lose.

I did, of course, assume that they choose *randomly*. The late Thomas Schelling observed that groups do not, as a rule, choose randomly in these situations. If a group faces a set of options which all lead to equally good outcome, subject only to the constraint that a good outcome requires the entire group to choose the same outcome without communicating, they will look at superficial features of the options (which do not affect the outcome at all) and try to find an option whose superficially salient features make it unique.

Given a map with many hills and one bridge, people spontaneously understand to meet on the bridge. Given a map with many bridges and one hill, they meet on the bridge. Meeting in a town, they’ll wait in front of the town’s tallest building. Given a list of letters with no salient features whatsoever, they will turn to the formal properties of the list and coordinate on the *first* item listed. (Equilibria which form not because of a choice’s effect on the outcome of the interaction but because their salience facilitates this kind of spontaneous coordination are called *Schelling points*.)

So we might imagine ABCD all fixate on 6:00, the earliest possible time when they could all have dinner, as naturally salient. Or they may know that 7:30 is a “normal” dinner time, so they all think it is the most likely time to find other people there. Or perhaps Bob and Carl happen, by sheer luck, to arrive at the restaurant at 8:10 one night, and ever after that becomes the time when they expect to find each other at the restaurant.

Salience can have the same effect on *limited* use of coordination. Let’s say ABCD can communicate to fix a meeting-time, but with strict limits: Adam can send a time to Bob, while simultaneously Bob sends a time to Carl, Carl to Daniel, and Daniel to Adam. If each of them good-naturedly tries to follow the suggestion he was given they are no more likely to meet than they were with no communication. (If the four randomly-chosen times don’t coincide, it doesn’t matter whether each man goes to the time he chose or a time one of the others chose.) If one of them is willing to settle for a dinner for two, he can flip a coin to decide whether to go to the time he chose or the time he was given; if all of them did this, then for example Adam would have a 25% chance of having dinner with Dan and a 25% chance of having dinner with Bob. That’s the best they can do (and that, only assuming all of them are interested in dinner for two!)

Compare this first scenario to limited communication this rule: Adam can send a time to Bob, and Adam can also send a time to Carl, and a time to Daniel as well. Now none of the four have *any direct evidence* of Bob’s, Carl’s, or Daniel’s intentions. Three of them only know a place Adam has suggested, and Adam has received no suggestions from anyone. *Nonetheless*, if Adam sends the same time to all of them, and each assumes he has sent the same time to all of them, Adam’s suggestion is now uniquely salient (it has become the Schelling point); they will all arrive at that time because it is unique, and expect everyone else to arrive at that time for the same reason. So naturally, the four friends finally get their dinner.

Note that Adam has no power to reward or punish the other three. The second communication rule gave Adam a central position in the messaging network, and this centrality gave his messages a unique salience. Adam did not have to threaten, cajole, or order. In fact, it wasn’t even *necessary* that he *suggest* the time with the intention of coordinating dinner. (If Adam had recently told the other three that an immensely fat man has reservations to eat at the restaurant every night at 7:50, *this piece of information itself* could be enough to make 7:50 the most salient meeting-time.) The important thing about the second coordination rule is that no one else is allowed to suggest other times after Adam has announced one.

In fact, even this condition is too strict. It would be fine if, for example, the communication rule was A>BCD, B>A, C>A, D>A. Adam sends everyone a time, everyone sends Adam a time; Adam ignores everyone else’s suggestions (he knows at most one friend could meet him there, and they know…), everyone follows Adam’s. Adam’s centrality has been preserved.

Note that if each of the four men were allowed to simultaneously send suggestions to the other three, the group would know *more* about one another’s intentions, but would be *less* likely to successfully arrive at the restaurant at the same time. Centrality has been destroyed, no message is more salient than any of the others, and so coordination is impossible. Once again ABCD have no better option than to fall back on a guessing game. More communication, less information: a paradox that is unlikely to surprise a neoreactionary.

Within an institution, each member must be able to predict the reactions of the others to his attempts to coordinate and direct them, so institutions must be constructed to establish expectations that the institution can force its members to meet, and vice-versa. Conversely, informal cooperation outside of an institution does *not* require subordination, and a rigorous examination of the underlying differences shows that managing the expectations of loose alliances poses the opposite problem. Nonetheless, it leads to a parallel guideline: for a loose alliance to converge on a common course of action (when choosing from multiple equivalent options) each ally must be able to predict how the others will react to communication within the alliance about which course to converge on, so an alliance’s system of communication must be constructed to give one suggestion special salience. There are multiple ways to accomplish this (drawing lots, for example), but giving one ally a central position in the communication system is the most versatile and durable choice.

Centrality is an important strategic concept for institutions as well as for alliances. Institutions have more internal structure and more power over subordinates, so convergence is easier. When superior can make a decision and tells his subordinates what to do, it doesn’t matter how much they have discussed the other options. Thus some institutions have more leeway to reap the benefits of free discussion, and to gather all of the relevant information subordinates want to provide.

Centrality *can* be a powerful means of promoting subordination. (There are a number of insubordination-dynamics which are riskiest for the subordinate when tried alone, but safe and/or rewarding when multiple subordinates are able to communicate freely.) But centrality is most important for nonhierarchical relationships within an institution. A group of men who carry out the instructions of their superior as a team (or even several groups, given the same instructions and working together) are in roughly the same position relative to each other and independent members of a loose alliance. Even if the men are (reasonably) obedient and subordinate, *if their orders require them to cooperate, the effects of their actions hinge on the choices of their comrades, and their expectations about their comrades’ choices will shape their own.* In other words, you can order a team of men to row a boat, but you can’t actually make them *row* unless they can figure out appropriate expectations about how the other oarsmen will be rowing the boat.

*(Tomorrow: Drilling)*

*Part of a series on **Strategic Concepts**:*

- Basic Strategic Concepts
- Machiavellian Strategic Concepts I: Subordination
**Machiavellian Strategic Concepts II: Centrality**<*You are here*- Machiavellian Strategic Concepts III: Drilling & Disengagement
- Machiavellian Strategic Concepts IV: Hierarchy

[…] T. Latham: (4 part series) Machiavellian Strategic Concepts Part I: Subordination, Part II: Centrality, Part III: Drilling & Disengagement, and Part IV: Hierarchy. Latham dons the hat of a modern […]

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