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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.