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Hi, welcome back. Okay, so, last lecture, we talked about

Â how using models can make us more intelligent citizens of the world.

Â How we could just sort of understand how the world works a lot better.

Â How was sort of the new lingo [unknown]. Alright, in this lecture, we're going to

Â talk about how models make us clear thinkers, and this is one of the big

Â reasons why people use models, because they could help us think more logically

Â about how the world works. Okay, so this is sort of a multi-step

Â process. So, let's, let's see exactly how it place

Â out. So, the first thing you do when you write

Â down a model is you name the parts. So, let me take a simple examples.

Â Suppose I just want to write a model of where people go for lunch.

Â And suppose it's a small town, and there's really just sort of, you know, four

Â restaurants. So, there's restaurant 1, restaurant 2,

Â restaurant 3, restaurant 4. So, those are parts, right?

Â But what else is parts? Another part is people, right?

Â So, these individuals, and they've got to decide where to go, right?

Â Which restaurant do I go to? Well, now, we have to ask, what are the

Â relevant parts of the people? Well, you know, this guy is wearing shoes,

Â but the thing is his shoes probably aren't a relevant part.

Â So, we name the parts really, but what really matters, and the shoes probably

Â don't matter. And what does it matter if he's wearing

Â mittens or, and if we put a hat on him. His hat isn't going to have much of an

Â effect on which restaurant he goes to, okay?

Â So, what does matter? Well, one thing that matter is how much

Â money he's got, right, and how expensive these restaurants are.

Â So, this restaurant may be cheap and this restaurant may be expensive.

Â But this may be someone that's got a lot of money.

Â So, how much money you have is going to be one determinant with of which restaurant

Â you choose. Another thing that's going to matter is

Â how much time he has. Does he have only 15 minutes, right?

Â Or does he have a whole half hour to go have lunch, and different restaurants make

Â it in different amounts of time. A third thing, maybe and I'll write this

Â fancy little signal here for preferences. This is how economists and social

Â scientists write preferences down, these are just, you know, what he likes.

Â Maybe one of these is a Mexican restaurant, maybe one of these is an

Â Italian restaurant. So, he's got different preferences over

Â the different restaurants. So, these are all things, these are all

Â sort of relevant parts that go into the model, alright?

Â Once we've laid down the parts, then we've got to think about the relationships

Â between those parts. So, models help us sort of identify the

Â specific relationship. What you see on the left is a simple game

Â theory model. This is called a extensive form game where

Â one player, here's player 1, takes, makes some sort of decision, and then another

Â player, player 2 takes some sort of decision, and then the players get

Â payoffs. So, once you sort of name the parts, then

Â the next thing you're going to model is identify the relationships between those

Â parts and how things play out. So now, you got the parts, you got the

Â relationships. What you can do is you can think through

Â the logic. So, let me show you how complicated this

Â is and how models are so useful. Let's do sort of a, a simple thing that I

Â sometimes play with my undergraduates. Suppose I want to build a rim for the

Â earth to be shot through, build a big basketball.

Â I'm going to shoot the earth through the rim, but I want to give a little bit of

Â space so you can make it. So, I'm going to put one meter, sort of

Â all the way around, right? So, there's a little bit of a gap of one

Â meter, and then the earth can go through just that little bit of spacing, one meter

Â all the way around. Well, now, I'm going to ask the question,

Â what should the circumference of that rim be?

Â How big around does that rim have to be, assuming that the earth is, let's just

Â simplify it and say, it's 25,000 miles around the equator of the earth.

Â How big around does that rim have to be if I want 1 meter of clearance all the way

Â around? Think about it.

Â Okay, now let's do a little math. So, we know the formula for circumference

Â of a circle, right? Circumference is equal to pi times D,

Â right? Now, what I want is I want to find the

Â circumference of that rim and that's going to be pi but my diameter is going to be

Â the diameter of the earth. And if I think about it, remember I've got

Â this rim here, and I want the earth to go through, but I want 1 meter on this side,

Â and I want one meter on that side, so it's going to be, the diameter of the earth

Â plus 2 meters. So the circumference of my rim is going to

Â be just pi times the diameter of the Earth plus 2 meters.

Â Well, that's pretty easy to, to solve, right?

Â Because that's just going to be pi times the diameter of the earth plus pi times 2

Â meters. Well, pi times the diameter of the earth,

Â you already said, was 25,000, and pi times 2 meters is just going to be 6.28 meters.

Â So, the circumference is going to be 25,000 and 6.28 meters.

Â So, that's probably not what most of you guessed, right?

Â So, by writing down a very simple model, just a, you know, model for the

Â circumference of a circle, we're able to figure out exactly how big that room has

Â to be, and it's often very different, right, from what our intuition would have

Â suggested. Okay.

Â So, working through the logic is a big reason why models make us clear thinkers.

Â Now, the next thing models do is they allow us to inductively explore.

Â So, let me give a, sort of a fun example of this.

Â Suppose you have a room, right, and we've got this room here.

Â And there's a door, there's one little door right here that people can come out

Â of and the problem is jammed in the door, right, so that, you know, as people try to

Â exit this room, somebody gets jammed in the door.

Â So, the question is like, how do you figure out a better way to prevent people

Â from getting jammed? But one thing you might do is you might

Â put a post right here. And this post might prevent people from

Â you know, bumping into each other as they come out because they come here and they

Â sort of bump into the post and they have to go around and that prevents things

Â from, from sort of getting bunched up near the door.

Â So, the interesting here is once you construct a model of the room, when you

Â put a bunch of people in the room, right, so heres people and then you have them run

Â out, you can ask, whats the effect going to be of putting the post and can

Â conductively explore better ways to sort of position things in the room to prevent

Â people from getting piled up, okay? Now, once we've sort of went through the

Â logic and explored things, we can ask what, what exactly happens in our model.

Â Now remember, when we talked about types of outcomes earlier on.

Â I said, theres only four things that can happen in a model.

Â One is It can go to some sort of nice equilibrium, like the planets, you know, I

Â mean, like, I'm sorry, like, if I drop my pen, it rests on the floor in equilibrium.

Â It can be some kind of cycle, right, like the planets orbiting the sun.

Â It can be completely random, right, it can be just, you know, totally unpredictable

Â and random, or it can be complex. And so, one thing that models like, let us

Â do is figure out which of those things is going to happen.

Â So, let me throw something out there. Suppose we're looking at oil, which is a

Â commodity and we want to ask what about the price of oil?

Â What about the demand for oil? What can we say about those things.

Â Well, let's think about it. The demand for oil is, you know, probably,

Â you can depend on the size of the economy. And so therefore, you'd expect since the

Â economy tends to grow at a fairly constant rate, you'd expect, you know, the demand

Â for the total supply of oil to probably slope up, right?

Â What about the price of oil? Well, the price of oil depends on a whole

Â bunch people who are sort of have some, you know, they might have some in reserve,

Â and they're bargaining and they're buying and selling, and all sorts of crazy stuff

Â can go on. So, if I were going to make a guess, I

Â would say, you know, that the supply of oil is some sort of nice pattern, right?

Â The total world demand and supply of oil is probably a nice pattern, but if I look

Â at the price of oil, it's probably crazy, okay?

Â And so, in fact, if you look at it, that's exactly what we see.

Â So, here's oil production right here, and that satisfy sort of this nice upward

Â slope. But if you look at the price of oils, the

Â price of oil which is down here, that's just crazy.

Â It's completely unpredictable. It's what we call complex.

Â It's not random, right, but it's complex. So, the model, sort of if we construct

Â models of these two things, we can see why, you know, total production of oil

Â goes up and why the price of oil is so hard to understand, okay?

Â Next, identify logical boundaries. This is one of my favorites.

Â So, there's a website called opposite proverbs.

Â And on this website, you see these statements like these two.

Â Two heads are better than one, and that's certainly true.

Â Often, it's the case that two heads are better than one.

Â And too many cooks spoil the broth and that's often true as well, right?

Â It is true that too many cooks do spoil the broth.

Â Well, here's the problem. There's, are the opposite, right?

Â The same is with a stitch in time saves nine, and he who hesitates is lost.

Â So, if you just have these sort of proverbs or mantras that you sort of

Â follow, they're not going to do any good because there's always going to be an

Â opposite proverb that you know, says, do the op, do the opposite thing.

Â So, which one do you follow? What models enable us to do is find the

Â conditions under which one thing holds and one thing doesn't.

Â So later in this course, we're going to see, when is it exactly the case that two

Â heads are better than one, and when is it exactly the case that too many cooks spoil

Â the broth? So, even though these proverbs are

Â opposite, there are conditions under which each one holds, alright?

Â Okay. Last thing.

Â Communicate. One of the real beauties of models is they

Â allow us to communicate our ideas and what we know really simply.

Â So, let's take politics, for instance. And suppose you want to ask me, Scott, how

Â do you, how do people vote exactly? Now, I can say you know, petty [unknown] I

Â think that people, you know, they like candidates, they don't like candidates.

Â And then there's issues, there's these things called issues.

Â And it, there's a question like, you know, is the candidate, did they take positions

Â on issues that you like, or they don't take positions on issues you like and

Â they, they balance these things and they watch debates.

Â And it can go on and on and on and you might really have no idea, when I'm done,

Â how I think people vote. Well, let's place some standards with our

Â simple model and I said, okay, so, here's how it works.

Â There's going to be a voter and there's going to be two candidates, so here's my

Â voter and here's candidate 1 and here's candidate 2.

Â Now, what the voter does for each of these candidates is, they've got some sort of

Â likability. So, they can say, so there's likability of

Â candidate 1 and there's likability of candidate 2.

Â And this is just sort of like, you know, how friendly do they seem, do they seem

Â trustworthy, do they seem honest, that sort of stuff.

Â So, this is, you know, we'll put Likability here.

Â Now, the second thing that I'm going to say is that people care about policy.

Â Now, for policy, what they care about is sort of this set of issues.

Â So you can think of policies, what I'm going to say is the voter, I'm going to

Â put a little left right continuum, to say the voter over here is going to be a

Â little bit conservative, right? And then, for these candidates, I'm going

Â to say, well, candidate 1 is over here. He's kind of liberal.

Â And candidate 2 is really conservative, right, over here.

Â So, this is what candidate 2 is. So now, here's my model of how people

Â vote. What they do is they sort of, say, okay,

Â well, how likable is each candidate, right, so look at the likability of

Â candidate 1 and the likability of candidate 2.

Â And then, they ask, how far apart is, here's my sort of policy, you know, I may

Â be a little bit to the right. How close are these candidates to me?

Â Well, candidate 1 is, is pretty far away. Candidate 2 is a little bit closer.

Â So then, how people vote depends on the combination of these two things,

Â likability, and how close somebody is on policy space.

Â Notice how that's a much clearer way of explaining exactly how I think and enables

Â me to communicate much more clearly to other people how is it that I vote, okay?

Â Alright. So, that's how models make us clearer

Â thinkers. Now, what we're going to do next, once we

Â sort of, you know, got this understanding of models helping us think logically, is

Â we could take those logical models and bring them to data.

Â Thank you.

Â