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Hi. In this final lecture for this course I just wanna go back and think about some
of the reasons we initially gave for why you might wanna learn models. And I'm
gonna talk about sorta how the models we've learned has helped us accomplish
those goals. So you remember the first reason we had was just to make us an
intelligent citizen of the world. And let?s think about some of the models we
covered in this class that help us become more intelligent. So we learned the growth
models. And those growth models showed us that countries can accumulate fairly rapid
growth rates just by investing in capital but at some point. When they get to the
frontiers of what was known, they need innovation. To create growth, But then we
also saw that innovation has this sort of doubling effect. That you get the direct
effect from innovation and then you also get the effect it also make sense to
invest in more capital. So there are a couple different things just about
economic growth rates. The Kernel-Blango game also made us, a more intelligent
citizen of the world. Made us understand that, how in some sorts of strategic
competition it makes sense to add new dimensions. Explained, helped us
understand some of the tactics people used in war, helped us explain some of the
tactics terrorist groups may use, as well. So that model was also useful. We had
Markov Models. Markov Models helped us understand that maybe we shouldn't
necessarily think about trans continuing in a linear way that they may fall off.
They helped us also to understand situations in which history doesn't
matter. So there could be some situations where a new intervention if it just
changes the state doesn't really do any good and the intervention that changes the
probabilities makes us all better off. And that Markov largely is an example that's
becoming clear better thinkers. Other examples of that are, are discussions of
tipping points. Remember when we talked about tipping points we had this idea
that. You know if you see a kink in a graph like here you could say oh my gosh
this is a tip. Then we said no that may not be the case. That could just be a
growth model. So remember we had that very simple growth model. That exponential
growth model, had sort of a, an increase A place [inaudible]. Looks like it's really
changing its slope here, Because that wasn't a tip. You know what a tip was. Is
a tip was a situation where, the likelihood of different outcomes was
drastically changing [inaudible] to a point in time. And now we know the
difference between tipping points and path dependence. Now, path dependence means
there's sort of gradual changes in what's gonna happen as events unfold. So tips are
somehow different than path dependence, which in turn were different from Chaos.
So may having growth models, ticking point models, path dependent models, Markov
models, percolation models, which gave us those tipping points, SIR models, those
disease models, we have all sorts of new intuitions to make [inaudible] understand
why does something?s you know perhaps look linear, why do some things look S shaped.
Like diffusion things and why do some things just take off like our growth
model. So we have some understanding of the shape of things that we're likely to
see, and what causes things to have particular shapes. So that was really,
really useful. We also learned how to use and understand data. Remember there are
tons of data out there. We did some very simple things, like category models and
then we did some more scientific things like, linear models. And we even did
things like, prediction models at the end were we should how we can combine all
kinds of predictions to get the wisdom of crowds. So what we saw is that, we can use
these models to make sense of all the data we see out there in the real world. You
can even go there with Markov models, remember we sort of, linked our Markov
models to data. So, a lot of our models were abstract. Think of some of the models
like the game of life, right, which made us [inaudible] that didn't relate to data,
but many of the thinks we d id like the growth models, the linear models. Do
relate, in real ways, to data that's out there, and can help you make sense of that
fire hose of information that's pouring out at you every day. Or, if you prefer,
the hairball of information, And finally, we constructed some models that helped us
make better decisions. [inaudible] simple decision theory models. We talked about
some very simple game theory models, like the prisoner's dilemma. Some collective
action problems, And then we talked about mechanism design. [inaudible], okay, how
do we construct a model of a particular situation to help us design institutions,
design [inaudible], you know, write contracts, design policies, so that we get
the outcomes that we want. And we only did that in a very simple way. But we still
got some really deep insights, This notion of incentive compatibility. How do we
create incentives so that people tell the truth? They reveal their hidden
information. Or they take an action that we want, even though that action's gonna
be hidden. And, we also saw something?s we want to do may not be possible. So, the
model tells us what we can do and what we can't do or the model may tell us, like in
the case of auctions that it really doesn't matter how we do it depending on
how people behave. And, on that last point; depending on how people behave.
That may be the most important thing the about model thinking. How do people
behave? We talked about three different models. We talked about people being
rational. We talked about people following rules. And, we talked about people having
psychological biases possibly. And we sum some cases like the game that we had to
race to the bottom. Remember we had to be two-thirds of everyone else gas. We saw
some cases have the assumptions you made on the behavior had huge effects on the
outcomes. And we saw other cases like a markets, exchange markets were didn't
matter at all. That you pretty much gonna get the same outcome regardless of how
people behave as long as there's reasonably coherence in the actions they
take. And finally, you know, we saw by thinking models that things always don't
often aggregate the way we expect, right? So now, when we add up a bunch of stuff,
more is different, as Phillip Anderson said, right? That when we add up things
and we aggregate, we can get all sorts of interesting things In particular, we can
get systems that go to equilibria. We can get systems that produce patterns. We can
get systems that are almost random, and we can get systems that are complex. And by
constructing these models, we've learned, why do different systems Produce different
kinds of outcomes. How do we possibly intervene these systems? What actions are
people likely to take in these systems? How events are likely to unfold? How do we
collectively understand what's gonna happen in these different parts of the
world? Now this course was just an introduction, and it's really sort of baby
steps, and it's meant to entice you to look deeper, to take more modeling
classes. And to recognize that, even though most of us take mathematics, we
take calculus, and we're doing things like the double integral of arc-secant of XY or
some [inaudible] complicated thing. But we can also use mathematics to try and help
us make sense of the world. And we can use computation to do the same thing as well.
And so what's nice is, by constructing these models they're this crutch for us,
they help us clarify our thinking, we're better thinkers, we use data better, we
can design and strategize better and we're just more intelligent citizens. I hope
you've enjoyed taking this class. I've certainly had a lot of fun putting it
together and I've learned a lot in the process and I apologize for any confusion
and technological glitches and delays and things like that, but we've done the best
we can do. I particularly want to thank Tom and Leia, two undergraduate. >>
[inaudible] machine who have helped me throughout this whole process, They've
just been absolutely fabulous, they've given me incredible support and they've
helped a lot in all sorts of ways you can never imagine. And to all of you out there
taking this course again, thanks a lot for everything you've done, I appreciate all
the you know, friendly and helpful comments you've given along the way, and
if you'd like to stay here in Ann Arbor. Go blue.