Now we come to the final topic from my notes on political analysis—at least from the first half of the class. I’ll probably do another series of posts at the end of this semester, but for now, this is the final word on power.

“How many divisions does the Pope have?”

Thus spake Joseph Stalin in response to Churchill’s concerns about the Vatican’s views.

So far in this discussion of power, we’ve focused on hard power—threats, bargains, consequences—the kind of stuff that Stalin could respect. But what about the Pope? Does he not have power just because his only divisions are brightly dressed swiss pikemen?

It turns out (sorry Stalin) that there is such a thing as soft power, and to talk about soft power we have to talk about expectations, and to talk about expectations, we’re going to talk about John Maynard Keynes and beauty contests.

Newspapers used to have these beauty contests, where they’d have six pictures of women, and people would choose the most beautiful woman. If you chose the candidate with the most votes from other people, you got a prize. So, in choosing a woman, there’s a first order question (or so posits John Maynard Keynes):

Who do I think is beautiful?

Then there’s a second order question:

Who do other people think is beautiful?

Then there’s a third order question:

Who do other people think other people think is beautiful?

And this, Keynes theorized, is the same thing that happened with the stock market when it crashed.

The beauty contest is what’s known as a coordination game, where either both players win or both players lose (as opposed to a zero sum game like rock paper scissors.) Another example of a coordination is walking down a sidewalk. If both people walk on the same side, they both lose and bump into each other. If they walk on different sides, they both win. Here’s that scenario modeled as a normal form game.

Let’s assume that the Rs and Ls refer to a universal left and right rather than the left and right from each of their perspective. If it helps you can think of it as actually east and west, or as totally abstract concepts.

So in extensive form games, expectations are easy to pin down, because all the pay-offs are known. But it’s more complicated in normal form games, as we saw with the dominant pig scenario from last post. So how do we figure out how players will act?

One way to predict the outcome of a game is with Nash Equilibriums. You can determine the Nash Equilibrium of a game by creating a strategy profile—a list of strategy choices for each player. An outcome is a Nash Equilibrium if no player can strictly gain by unilaterally deviating—that is, they can’t gain by doing something different while the other player keeps doing the same thing.

In the above game, the four strategy profiles would be (R,R), (R,L), (L,R) and (L,L). (R,L) is consistent with itself because if Joe thinks Jay will play L, Joe will play R—and, if Jay thinks Joe will play R, Jay will play L. So that outcome, and (L,R), are Nash Equilibriums. You can see that neither play would strictly gain from deviating. Let’s say Joe is walking on the L side and Jay was walking on the R side, and Jay is texting and not looking up at all. So Joe knows that Jay is not going to change his strategy. Joe would gain nothing by deviating from his path—by lurching over to Jay’s side and running into him. So, they have found themselves in a Nash Equilibrium.

John Nash proved that every finite game has a Nash Equilibrium. So anything can be modeled and have a prediction. There’s only one complication with random play, so you might not be able to predict which Nash Equilibrium will be the resolution—but you can still make a prediction.

So how do we explain non-coordination when it happens? When you do an awkward dance with someone, not sure which side to walk around them? And how do we make sure everyone is making the same prediction? Really, in the Joe and Jay game, there’s a third Nash Equilibrium. If you think each strategy has equal probability, you may as well play randomly. If you do that, you’ve got a ½ chance at coordinating and getting a good outcome.

But people don’t play randomly. These games don’t exist inside a vacuum. If you ask a group of people to write down the name of a flower, and to attempt to write down the same flower as the majority, the vast majority will—independently—name rose (really, we did this in class.) So to explain coordination, we have to look at psychology, and social sciences. This guy Thomas Schelling found that people coordinated around “focal points,” which had special properties that other strategies did not.

One property was prominence—a choice with a special meaning specific to the group playing the game. So if you asked a group of Floridians, all of whom knew that everyone in the game was from Florida, to name a state, they’d say Florida, because it’s a prominent state to that group.

Another property is uniqueness. If you give people a set of options, and ask them to coordinate around one, they’ll coordinate around the one that stands out. This is true even for this game:

Although (C,C) is not the best outcome, it is unique, and this is the strategy profile that the players would coordinate around.

Then there’s simplicity—which is why people agree to meet up at round number times like 1:00 or 12:30, even though those numbers are arbitrary.

Finally, there’s precedence. This is good because it solves the problem for a long time. It’s bad because it solves the problem for a long time. A few examples of this are the base ten system, the Gregorian Calendar, the dimensions of printer paper, and language itself.

So, back to soft power and expectations. The Pope isn’t powerful because he has a lot of divisions, he’s powerful because he can coordinate expectations. By utilizing the broad reach of his position he can direct a large group to coordinate around a specific goal—he can make a strategy prominent.

So, that’s all I have on power and political analysis. I hope it’s been an informative and interesting series, and I hope to continue it at the second half of class, in which we’re learning about aggregation, the prisoner’s dilemma, and why war?