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.