Hi, welcome back. In this lecture, I want to talk a little bit more about how using
models can help make you a more intelligent citizen of the world. And so,
we're gonna break this down into a bunch of set of sub-reasons about why models
make you better able to engage in all the things that are going on in this modern,
complex world in which we live. Okay, so. When we think about models, they're
simplifications. They're abstractions. So in a sense, there's a sense in which
they're wrong. There's a famous quote by George Box, where he says, "All models are
wrong." And that's true, right? They are. "But some are useful." And that's gonna be
a mantra that comes up throughout this course. These models are gonna be
abstractions, they're gonna be simplifications, but they're be useful to
us. They're gonna help us do things in better ways. 'K? So. In a, in a sense,
right? And this is a, a big thing in this course. Models are the new lingua franca.
They're the language of not only the academy, you know, which I talked about
some in the last lecture, but they're the language of business. They're the language
of politics. They're the language of the nonprofit world. Wherever you go, where
there's people are trying to do good, make money, cure disease, whatever it is that
they wanna do, right? You're gonna find that people are using models to enable
them to be better at what their purpose is. Okay? That's why they've really become
the new lingua franca. So, if you think back. Remember, I talked about this in the
first lecture. The whole idea of having a great books movement was that there was
these... set of ideas that any person should know. So within the hundred and so great
books, there were thousands of ideas. And one of our ad learners, Robert Hutchins
President of the University of Chicago. They had this thing that they wrote called the
Synopticon which was a list, right, as they put this together. This was kind of list of
sort of all the ideas that someone should know, that an intelligent person should
know. So what are those ideas? So one of those ideas was to tie yourself to the
mast. And this comes from the Odyssey, you know, this says the ship is going past the
sirens and he wants to hear the sirens beautiful love song. So what he does is he
has his crew tie him to the mast. He tie. Ties himself to the mast so he can listen
to them but pre-commit to not driving his boat over to hear the sirens, at the same
time he puts wax in the ears of his crew so they also won't be, you know,
encouraged to sort of drive the boat over there. Well this is an idea that recurs in
history when we think about. Cortez burning his ships, right, so his men won't
you know retreat, they'll continue to advance. So this idea to tie yourself to
math, is a real worthwhile thing. But here's the problem. One of, one of my
favorite websites is a website called Office of Proverbs. So on this websites,
it says things like he who hesitates is lost, a stitch in time saves nine, or
two heads are better than one, too many cooks spoil the broth. So you've got to
hear this really good advice, something that probably made it in the Synopticon,
but then you get something that says the exact opposite. Well, how do they
adjudicate between those two things? The way we adjudicate between those two things
is by constructing models because models give us the conditions under which he who
hesitates is lost, and then there's the conditions under which a stitch in time
saves nine. So when we talk about the wide diversity and prediction, we'll see why
it's the case that two heads is better than one, and we'll see why it's the case
that too many cooks spoil the broth. So, ironically, what models do is they tie us
to a mast, they tie us to a mast of logic and by tying us to a mast of logic, we
figure out which ways of thinking, which ideas in this Are useful to us.'K? So, if
you look at almost any discipline, whether its economics, and here what you see in
this diagram, is you see a description of sort of, this is a, a utility function for
an agent. And what that agent is doing trying to maximize their pay-off, right?
So, economists use models all the time. Biologists use models, as well. They,
they, you know, have, you know, models of the brain, where they have little axons
and dendrites going between the neurons. They have models of gene regulatory
networks. They have models species, right? Things like that. Sociology, we have
models, as well, right? So, there's models of, sort of. How your identity effects
your actions, and your behaviors and things like that. Okay, in political
science. We have models. Political science these days, this is a picture of a spatial
voting model. So they might say candidates are a little more conservative on certain
dimensions and voters are a little more conservative and you say that, well,
you're more likely to vote for a candidate who takes positions similar to yourself.
So my work at the University of Michigan we have something called the National
Election Studies that's run out of there where we sort of gather all this data
about where politicians are and where voters are, and that allows us to make
sense of who votes for whom and why. Okay? So models help us understand the decisions
people make. Linguistics, right? Here's another area, right? So you might think,
how can you use models in linguistics? Well, this little model here, you see
things where it says you see v's and n and p's in here, if you look closely. Well, v
stands for verb, n stands for noun, and well you gotta. And S stands for, you
know, subject, let's say, right? So you can do this: you can ask "What is the
structure of a language?" You can ask, formally and mathematically, what are the
structure of a language is, and whether some languages are more like other
languages or not, depending on how people, you know, set up their sentences. So in
German, where they may put all the adjectives. At the end of the sentence
that looks very different than let's say English. All right. Even the law. This is
a graph from one of my graduate students, former graduate student. Now, he's a law
professor, Dan Katz. Where he's got sort of a network model of which Supreme Court
justices, you know, who they appoint, so who, if someone appoints judges from some
other judge. By putting that data that's out there in this sort of model-based
form, we can begin to understand how conservative and how liberal certain
judges are. All right? So, there's lots of ways to use models, and there's even whole
disciplines now, that have evolved, that are based entirely on models. So, game
theory, which is what I was really trained in as a graduate student, is all about
strategic behavior. Behavior. It's the study of strategic interactions between,
you know, individuals, companies, nations. Right? And game theory can also be applied
to biology, right? So there's all sorts of stuff, right? When you go to, when you go
to, you know, college, you go to college, you'll find that there's game theory
models of just about anything. Right? So it's actually a field based entirely just
on models. Right? Why, right? [laugh] Why all these models, right? Why does
everything from linguistics, to economics to, you know, political science use
models? Well, cuz, they're better, right? They're just better than we are. So, let
me show you a graph, here. This is a graph from a book by Phil Tetlock. It's a
fabulous book. And in this graph, he, what he's showing is, he's showing the accuracy
of, some different, let me pull up a pin here. Different ways of predicting. So,
what you see on this axis, this calibration axis, right here. This is
asking, sort of how, showing you how accurate a model is. And this axis is
saying how discriminating is it, in terms of how particular, how fine of predictions
is it making. So, instead of saying is it hot or cold, it might be saying it's gonna
be 90 degrees, or 80 degrees, or 70 degrees. So this axis here, this up and
down axis, is discriminatoriness, discrimination, and this axis is how
accurate. So, what you see here, down here, are hedgehogs. So, these are people
who use a single model. Hedgehogs are not very good at predicting. Right? They're
terrible at predicting. Up here are people he calls foxes. Now, foxes are people who
use lots of models. They have sort of lots of loose models in their head. And, they
do much better at, you know, sort of at calibration, a little bit better at
discrimination, than individuals. But way up here, [laugh] better than anybody, are
formal models. Formal models just do better than either foxes or hedgehogs. Now
[inaudible] how much data is this? Tetlock actually had tens of thousands of
predictions. So, over a 20-year period, he gathered predictions by people. And
compared how those people did to models. And the answer is models do much, much
better. Okay. All right, so. What about people, then, who actually make
predictions for a living? So, this is a picture of Bruce Bueno de Mesquita, who
makes predictions about what's gonna happen in international relationships, and
he's very good at it. He's so good at it that they put his picture on the cover of
magazines, right? He's at, Stanford and NYU. Chair of the department at NYU. Used
to be, anyway. So, Bruce, uses models. He's got a very elaborate model that helps
him figure out, based on sort of bargaining position and interest, what
different countries are gonna do. But, just like George Box said at the
beginning, he doesn't base his decision entirely on that model. What the model
does is gives him guidance as to what he then thinks. So, it's a blending of what
the formal model tells him, and. Experience tells them so smart people who
use models but the models don't tell them what to do. Okay. Another reason models
have taken yeah they are better but they're also very fertile. So once you
learn a model. It's, you know, for one domain, you can apply to a whole bunch of
other domains, which is fascinating. So we're gonna learn something called
mark-off processes, which are models about dynamic processes. So they can be used to
model things like disease spread and stuff like that, right? We're gonna finally
learn though that you can also use them, this is sorta surprising, to figure out
who wrote a book. >> [laugh] And they say, how does that happen? Well that happens
because you can think of words, writing a sentence, as an anemic process. So
different authors, right, use different sequences of words. Different patterns. So
therefore we can use this mathematical model that wasn't developed in any way for
this purpose to figure out who wrote what book, okay? Totally cool. All right.
Another big reason. Models really make us humble. The reason they make us humble is
we just have to lay out sort of all the logic and then we realize holy cow, I had
no idea that this was going to happen, right. So often when we construct the
model, we're going to get very different predictions than what we thought before,
right. So if you look at things, here's a picture of a, the tulip graph, right, from
When there's a big, in the six-, seventeenth century, when there's a, you
know, this big spike in tulip prices. You can imagine that people thought that
prices were gonna continue to go up and up and up. Well, if you had a simple linear
model, you might have invested heavily in tulips, and lost a lot of money. So, one
reason that models make us humble is, never go back to the George Box code. All
models are wrong, right? So, a model is going to be wrong. But the models are
humbling to us, because they sort of make us see the full dimensionality of a
problem. So, once we try and write down a model of any sort of system, it's a very
humbling exercise, because we realize how much we've gotta leave out to try and
understand what's going on. All right. Here's another example, right? This is the
Case-Shiller Home Price Index, and what you see is, you see prices going up and up
an up, right? And then you see this, let me put a pin up here, precipitous crash
right here, right? A lot of people had models that just said, look, things are
gonna continue this way. There were a few people that had models that said things go
down. These people, the ones whose models went down, they made a lotta money. These
people thought it was gonna go up, didn't. So, we're always gonna see a lot of
diversity in models, and you're really not gonna know, often until after the fact,
which one is right. And so, one thing that's gonna be really important is to
have many models. So, let's go back to that fox-hedgehog graphite that we, I
showed you before. The, the foxes, the people with lots of models, did much
better than the hedgehogs, the people with no models. And former models did better
than. The foxes. Well, what would do better than formal models? Well, people
with lots of formal models. Right? So if we really want to make sense of the world
what we want to do is have lots of formal models in our disclosures. So what we're
going to do in this class is almost like, remember the old, like, sixteen, 32 box of
Crayolas? That's sort of what we're doing here. Right? We're just going to pick up a
whole bunch of models. And we're going to have them, right, they're fertile. We're
going to plot across a bunch of settings. So when we're confronted with something
what we can do is pull out our models. Ask which ones are appropriate, and in doing
so, right, be better at what we do. So the essence of Tetlocks's book, right? That's
where that graph came from with the foxes and hedgehogs is that, the only people who
are really even better than what he. He has a way of classifying what a random
choice would be. The only people who are better than random at predicting what's
gonna happen are people who use multiple models. And that's the kind of people that
we wanna be. Okay, so thats, sort of the big, intelligent citizen of the world
logic, right. There is, models, are incredibly fertile, they make us humble,
they help, you know really clarify the logic, and they're just better. Okay? So
if you wanna be out there, you know, helping to change the world in useful
ways, it's really, really helpful to have some understanding of models. Thank you
very much.