All right, in the previous lecture we talked about multi-criterion decision making, right? We had lots of different dimensions and you weighted alternatives according to those dimensions. In this lecture we're going to move in a slightly different direction. We're still going to consider multi-criteria, what we want to do, is we want to have a spatial model. So the difference here is that instead of just wanting sort of more square footage or a larger lot, you're going to have an ideal point. So there's going to be sort of perfect amount that lies between too much and too little. So these are known as sort of spatial choice models. Now spatial choice models originally started by thinking about geographic choice. There's a guy named Harold Hoteling who's an economist who thought about, imagine you're on a beach and there's an ice cream vendor, you know, 50 feet to your left and there's another ice cream vendor 40 feet to your right. You made decide well, you know, since the one to my right is closer what I'll do is I'll go and, you know, buy my ice cream from the one that's closer and I don't have to walk as far. Well you can take that idea and you can apply it to attributes of a good. So for example, I love Indian food. Right? And I like my Indian food to be reasonably hot. We can imagine one of the dimensions, then, in Indian food, is whether it's, you know, cold, right? In terms of, you know, cold in terms of how spicy it is. Or you can imagine [inaudible] means it's really, really hot. So I could all the Indian restaurants. I could put, you know, one Indian restaurant here, Indian restaurant one. Indian restaurant two. Ending in restaurant three and this is how hot their food is. And so, there's me as a consumer and I'm trying to decide. Okay. Where do I go buy. Do I go buy from Indian restaurant one, Indian restaurant two, Indian restaurant three. What could be that if since I like my food really hot. This is my ideal point right here. I'm go to Indian restaurant one because it's closest. So, this is the idea that there's, what each person has is sort of a preference, an ideal point and then buy right the thing, they purchase a firm right, that offers the product that is closest to their ideal point. So this is hi, Hoteling's idea. It was Anthony Downs, who was also an economist that, so, sort of moved into political science. And what Anthony Downs did, he said, now we can apply this to how people vote what we can do, we can put politicians, right, somewhere between left and right. So, maybe, you know, this might be the Democratic candidate for president, let's say, and this might be the Republican, so, both are, you know, Democratic sorted to the left, Republican sorted to the right, but their not really completely extreme. And then you've got a voter who perhaps sits right here and the voter's got to decide okay to I vote for the democrat or vote for the republican. And what they do is they look at this distance. How far am I from the democrat? This would be distance one. And how far am I from the republican. This is distance two. Remember I talked about this sort of in an earlier lecture about why we construct models and using this model the voter can say well you know what since I'm closer to the democrat, I'm gonna vote for the democrat. So this is a, a fairly simple spatial model. You know what we want to do is we want to ramp this up a little bit, so. Let me ramp this up just in two ways. One is you can take this model to data, so this is work by Andrew Gellman, Columbia University. Anyway what Andrew does is he looks at Supreme Court Justices and so here's a whole list of Supreme Court Justices, I realize this is a little blurry but here's people like Justice Blackman, right? And here's Judge Scalia and here's Judge Ginsberg, Justice Ginsberg. And what you can do is you can chart. Ideologically, where they are in t-, over time. Where this, here, is to the left, and this here is to the right. So you notice that Scalia's up here on the right, and Blackman's down here to the left. So what you can do is you can sort of use this model to keep track of where the different Supreme Court Justices are. What's interesting about this, is, then when you think about, where does a president, who does the president appoint? Well, the president may also have some ideal points. If they're a liberal president, their ideal point may be down here. If you have a conservative president, their ideal point may be up here. And they're gonna want to appoint a judge that has the same sort of ideologies that they have. So, it's really nice, very simple model. But you can take it to data, and then you can use that data to understand how people, how presidents appoint judges. And also, how the [inaudible], how the ideology of the court has changed over time. Okay, we want to do this, we want to sort of take this model and show how we can expand it to more dimensions. So before, that was just one dimension, hot, cold, left, right but we can do the same thing in more dimensions. So let's go back, right, to the car example, remember? I'm just trying to decide between the Ford and the Chevy and I said there might be two things. There might be sort of the speed of the car, right, and there might be comfort. Right, once again [inaudible] and what I do is I decide which of these two cars is closer? Okay, so lets do this in a, a sort of a fun example, in terms of getting a burger. So, you know I like burgers, a lot of people like burgers and we can think of what's my ideal burger? Well, my ideal burger might have two pieces of cheese and it might have two patties. And two tomatoes. And also some ketchup, let's say, four tablespoons of ketchup, four tablespoons of mayo. And I'm a pickle guy, four pickles. So, this is my ideal burger, right? And so we can write that down. And so, more carefully, [inaudible] is a better font. [inaudible], this is my ideal point. And this would be, if I do this out, it's not in two dimensional space, like it's in multidimensional space. I can't draw it, because this is six dimensions. Right? But this is where computers are nice because I can code this into a computer and it's just a vector of length six. We're not gonna decide, where do I go for lunch? Should I go to McDonald's and get a big Mac, or go to Burger King and get a Whopper? What we can do is we could say, okay, let's look at my ideal point, which is right here, and let's look at the Big Mac. The Big Mac has two pieces of cheese, which is great, two patties, which is great. No tomatoes, not so good. Not enough ketchup, not enough mayo for me. And a few too many pickles. You know, like, pickles seems to have, you know, a few too many pickles. So I could ask, how much do I like that Big Mac? What we can do is we can take my ideal point and the Big Mac and take the difference. So here the difference is zero. Here the difference is zero. Here the difference is two. Here the difference is one. Here the difference is zero and here the difference is two. Now notice I've got these little lines on the, on the, on this side of difference. That means I'm taking the absolute value of the difference. Otherwise, because there's, you know, it's got two to few tomatoes. If you put a minus two here and a plus two here the two few tomatoes and the to many peoples would cancel out, right? So what I can do is I can add all these things up and say my total distance from the Big Mac is five. Let's suppose I walk across the street and now I decide, let's see how the, the whopper stacks up. Well, the whopper has. Two pieces of cheese, that's great. It's got one patty, so it's off by one. Two tomatoes, that's great. Little long, not quite enough ketchup but perfect amount of mayo, perfect amount of pickles. So it's only off by two. So my distance from the. Big Mac, right? That, if we go back, was five. And my distance from the Whopper was only two. So, we could, you know, represent that by, here's the Whopper and here's the Big Mac. This is only a distance of two for me, and the Big Mac is a distance of five for me. So what I could do is, I could, if they're writing down my ideal burger, I can look at the Big Mac, look at the Whopper, and say, you know what? I'd rather buy the Whopper, because it's closer to me, it's closer to my ideal point. Now this is really good, 'cause this is a way, this is a thing I can use to figure out, you know, what should I choose? What burger should I buy? And also, I can use this to figure out, who should I vote for? Because instead of thinking of these as Big Macs and Whoppers, I could think of their, maybe there's two dimensions to policy, right? So one dimension could be some sort of social policy between liberal. And conservative and there could be some sort of fiscal policy, right, between liberal and conservative. So this would say I'm sort of socially liberal but on fiscal dimensions I sort of lie in-between liberal and conservative. And so this would be my ideal point, not in sort of big mac whopper space, but in political space. And then what I could do is I could vote for the party or the candidate that is close to me. Another thing we can do with this model, and this is sort of cool, is, remember we talked about how we can use this positively. So suppose I watch one of my friends, right, what do I mean by positively, right is to figure out explain why we see what we see. So suppose I watch one of my friends and I, and I go in and I see that my friend doesn't go to Burger King. My friend goes to McDonalds and gets the big mac, but I don't know anything about my friend's ideal points, but I do know about the big mac and the whopper. Well notice the big mac and the whopper are the same on this dimension, this dimension, this dimension. Same amount of cheese, same amount of ketchup, same amount of mayo. So what I could do is I could just wipe out those categories, right because they're the same, and then it comes down to number of patties, tomatoes, and pickles. So now if I see my friend buying the big mac. What can I infer? I can infer either that they like, sort of, two patties, or that they don't like tomatoes. Or that they really like pickles, or some combination of those things. And so what I can do, by looking at choices, I can understand what someone's ideal point is. And again, once we've got this idea in our head, we can go to data, and we can figure stuff out. So for example, let's look at political parties. So what you can do, and this is a map by Michael [inaudible], using some data from Poole and Rosenthal, to nominate scores. And what this does is it takes every single member of congress, and it looks at all their different votes. Now, based on their votes, you can figure out, how conservative are they and how liberal are they? Now, nominate breaks thing down into two dimensions. You think of this being one dimension and another dimension. So, just for our purposes, let's suppose this is a social dimension. Right. And this is a fiscal dimension, right. So this is money up and down here, right, and this is more policies on this dimension. So what you see is you see, look, all the Republicans lie to the right on the social dimension and the Democrats all lie to the left. And if you look, this is a particular map looking at the Tea Party which is a movement within the Republican Party, and if you look at the Tea Party, people are pretty well evenly mixed. So, what you can do is by taking this modeled data, what you can figure out by looking at the choices people made, this is sometimes called revealed preference, you look at the choices people make, in this case, you know, politicians voting and you can map out where they are ideologically. And see you notice the Democrats are all to the left of Republicans on social issues, but on the fiscal dimension, it's a little bit more complicated, right? Okay, so, that spatial model is really cool. We can use spatial models to figure out sort of, what we should, where we should. Buy Indian food. Who we should vote for. Which car to buy. Whether to go to Burger King or McDonalds, right, by looking at these dimensions and seeing how close something is to ideal point. Now we can also take these models to data and do more serious things. We can figure out you know, where Supreme Court justices are and where members of Congress are ideologically, and whether it's on one dimension or two dimensions. We can do the same thing for products, right so we could do that same sort of matching, and look at different products, in space, whether it types, whether it's types of coffee, right, whether it types of automobiles, and we could look at people's. Decisions on which to buy and we could figure out sort of are people, where people's preferences really lie based on the cars they buy or based on the coffee they buy. So spatial model is really powerful, helps explain what people do and helps us make better choices ourselves. Thank you.