Hi. In this lecture and the next one, I'm gonna take on the question of why cultures differ, and why we see consistency within those cultures. And to understand why cultures differ, what we're gonna do is, we're gonna extend our pure coordination game. We're gonna extend it to multiple games. And the reason we're gonna do this is, we want to try and get some understanding of, why is it the case of that we see Protestant Europe up here, Africa down here, Latin America down here and so on? We want to try to understand, why do we see these differences across cultures? To do that, what we want to do is recognize that we played more than one coordination game. We played lots of coordination games. So here's some examples [laugh], this is gonna be fun. So, and let's just ask these questions. Do people wear shoes in your house? So when people come to your house, do they take off their shoes when they enter, or do they leave them on? Do you cross the street when the "don't walk" sign is flashing? So you're just in some city and you, you know, you're at the intersection there's a little "don't walk" sign. Do you wait or do you cross? Do you read the newspaper at the breakfast table? If your family's sitting around having breakfast, are you reading the newspaper or reading on your computer, or are you talking to people? Do you hug your friends when you see them? Whether you shake hands or bow. And do you interrupt someone who's talking? Each of these situations is a pure coordination game. If everybody else is wearing shoes in the house, you don't want to take your shoes off cause you're gonna get dirt all over your feet. If you're walking with friends, and they don't cross the street when the sign is flashing and you do, then they're standing on one side of the street and you're standing on the other. If you read the newspaper at the breakfast table and the other person's hoping to engage in conversation, well they're going to be staring at your newspaper. If you go to hug your friends and they go to bow or shake hands, that's going to be awkward, right? Important that you do the same thing. And finally, on interruption: if you're in a culture where people interrupt, then it's totally okay and there's, you sort of understand that in the context of the conversation. But if you're in a culture where people don't interrupt and somebody interrupts you, then you get completely caught off-guard and it disrupts the flow of the conversation, and people can get angry at one another. So it's important that we have that understanding of what the other people are doing, so that we can coordinate on these behaviors. So think about how you answered those questions, and I'll give you my answers to those questions. Do people wear shoes inside of my house? No. Do I cross the street when the don't walk sign is flashing? Unfortunately yes, cause that's what people in Ann Arbor do. Do I read the newspaper at the breakfast table? I'm embarrassed to say yes, I do. Do I hug my friends when I see them, yes. And do I interrupt people when they're talking? Again, yes, but that's again part of the culture of the academy. You know, when there's people are giving presentations, you raise your hand and you interrupt them or you say, wait a minute, I have a question, because it's all about having a productive dialogue. Now I don't always, in some situations I'll recognize that it's inappropriate for me to interrupt, but generally speaking these are my behaviors. Now if you answered no, yes, yes, yes, yes, then you're my people. You're a part of my culture. We're the same. We belong in the same place on Inglehart's map. Now if you didn't, you're from a different cultural group, at least on these five dimensions. So let's think about it for a second. Suppose we just had twenty coordination games. And we could think of 50 or 60 of them. One quiz I sometimes give my undergrads is to say, think of five coordination games that you have to play every day. And for the first twenty minutes, they'll be like, that's a really hard question. And then all of a sudden, they can think of ten or twenty. Because so much of what we do, it's important that we coordinate with the people around us. Even things like going to bed early or going to bed late. You have to coordinate what time you eat, what order you eat your salad and your meal in. All sorts of things are coordination games. So if we assume there's just twenty of these coordination games, and there's two answers to each one. Some of them have maybe five or six answers. Let's just suppose each one is just a yes or no thing. Then we get two raised to the twentieth power, which is bigger than a million. So there's a million different cultures you could get, just with these twenty coordination games. So, when I ask, why do cultures differ? We get this paradoxical result. They differ because everyone's trying to coordinate. [laugh] We're trying to coordinate within our culture, most likely, we're going to coordinate on stuff that's different than what another culture does and that means that the two cultures are going to differ. Let's push this a little bit further, and I'm gonna introduce something called Bob Axelrod's culture model. So, Bob's a colleague of mine from University of Michigan. He wrote this model of cultural emergence. And peop-, a lot of people use this. This is a widely cited paper to understand, sort of how cultures emerge, and why we see boundaries between cultures. So here's how Axelrod sets this up. He creates a set of features. Now, these features are like, they're coordination games. They're things on, like, you know, whether you read the newspaper at the table, where you store your ketchup, which side of the road you drive on, that sort of thing. Then there's traits. >> And the traits are what action you take on that feature. So, for example, if you think about how you greet people instead of just being shaking hands or bowing, it could be shake hands, bow, kiss on the cheek, hug, all sorts of things, waves. So, instead of there just being two options there could be a bunch of options. It could be seven options, ten options, twelve options. So, a person is just this vector of traits on features, just like we talked about: do you wear shoes in the house, do you store ketchup in the fridge, do you read the newspaper at the table, that sort of stuff. What Axelrod then does is, he puts people in social space. So each person, each one of these little dots, has a person in it. And the last assumption he makes, which is an interesting one, is that, after you assign these values, you pick a person. And then that person looks to their left or to their right, or north or south, in those four neighborhoods around them. And they say, "Do I want to interact with this person that I see?" So if you look back at this picture, this person looks up and they see this person sitting up here. So they look up here and look at that person and think, "Boy, do I want to interact with that person?" And what he assumes is you interact with a probability that's equal to the similarity between you. So basically, look across the traits and ask, "What's the probability we agree on a trait?" So if you don't agree at all, then you say, well, that person [inaudible] [laugh] on I'm not gonna interact with you. If you agree on everything you interact for sure, but then you don't have to change anything. If you agree 70, about 70 percent of the traits. Then what you do is you say, well, you know, we're pretty similar. And then what you do is you pick a feature. Randomly pick one of those feature[s], and then match the trait of that person. Now, it could be you already match that person on that trait, Which is fine. But if you don't then you'll switch and match. So, here in a nutshell is the idea. We're in this social space. If someone's somewhat like us, we interact with them. If we interact with them, we're playing a coordination game, and so we're gonna match in that game. Now if we interact on a game that we're already matching, great. And we also, again, the big assumption here is: If we need someone who is very different from us, we choose not to play with them and so therefore we don't change our behavior. The question is: what happens? Well, let's set up the following model, let's suppose that we've got five features and ten values, four neighbors and we let the similarity be just the percentage of traits that you agree with the other person. So we'll set up that model and see what happens. So before two people meet, we think of having a leader and a follower, and what's gonna happen is the leader may look like this, and the follower looks like this. Now the probability these two people are gonna meet is gonna be 40%. Why? Because they agree on this trait and they agree on this trait, so they agree on five traits. I'm sorry, two traits, two out of five. That's 40%. If they decide to meet, then what's gonna happen is, and they also then decide to look at this second game. Player two is gonna change their one follower. It's gonna change their one to a three to match the other person. So this is sort of how the model works, nothing very complicated. So we're gonna do this in NetLogo. And here I'll do it with five features, and I just have got twelve traits. This is the NetLogo model, and I've actually put a link to this on your website, because this is one that's not in the models library. So, on the syllabus, there's a link to this NetLogo model. So I'm gonna set this up. And the thing to notice here is that these checkerboards, each, in the center of each square is a person. And the boundaries around them, the thickness of the boundary, tells the likelihood, the probability that you match the person above you. So if that line is really dark, it means you don't match them at all, and if it's lighter, it means you match in high probability. So we'll let this go. It's ticking along and what you see is a graph here, is the number, the black line shows the number of different regions in the space, and the red line shows the size of the largest region. And the little dots on the graph are showing sort of the centroid, the center of mass of each of these regions. And as I let this go, you see that the number of regions are falling. The cultures are becoming similar. The largest region is also growing. But you still see that we're maintaining some cultural heterogeneity, right, there's some differences. And if I speed this up and let it run till it stops, what I get, which is sort of interesting, is I get separate cultures. So I get four different cultures here in a way. Five. I got this little one. So there's one little one here, and these other little cultures. And what you also see is, there's thick boundaries around them. That each one of their countries has thick boundaries to the cultures they are adjoint to. They have to have those thick boundaries. Because if they didn't have those thick boundaries, people would interact with their neighbors across those boundaries and then they'd become similar. So what Axelrod's model gives, which is really interesting, is it gives us that these similar regions emerge, but then you get multiple cultures, and the boundaries between those cultures are thick. And the reason they're thick is that if they weren't thick, people would interact across those cultural boundaries, and they'd become similar. So, what Axelrod's model gives us, which is really sort of fascinating, is, he makes this assumption that says: We've all got these traits. We look to our neighbors. If they're like us, we tend to interact with them. If they're not like us, we tend not to. And what he ends up getting is these distinct cultures with thick boundaries. And these thick boundaries means vast differences between the cultures. Now the thick boundaries emerge because of the fact that if there weren't a thick boundary, then what would happen is, I would interact with that person and would become more similar, and the boundary would disappear. So Axelrod's model shows how in a social space, we can get distinct cultures on multi dimensions, and those boundaries can be self-reinforcing. People don't interact across the boundaries, and the cultures remain disparate. So Axelrod's model is really powerful, it tells us how cultures can emerge and how distinct cultures can emerge with these thick boundaries and thick walls between them. What it leaves out though, and this is where we're going to go next, is any notion of consistency within a culture. Now that wasn't what he used the model to construct. It's not really so much a weakness of the model. It's not something he was focusing on. Where do we wanna go next is, we wanna ask: Can we construct the model that will give us that as well? So now we get this baseline model, the Axelrod model, and we wanna ask, can we go one level deeper and actually get consistency within the culture as well and within that model, can we say anything about whether it's gonna converge, and whether or not it explains other features of cultures that interest us. Okay. Thanks.
