We live in a complex world with diverse people, firms, and governments whose behaviors aggregate to produce novel, unexpected phenomena. We see political uprisings, market crashes, and a never ending array of social trends. How do we make sense of it? Models. Evidence shows that people who think with models consistently outperform those who don't. And, moreover people who think with lots of models outperform people who use only one. Why do models make us better thinkers? Models help us to better organize information - to make sense of that fire hose or hairball of data (choose your metaphor) available on the Internet. Models improve our abilities to make accurate forecasts. They help us make better decisions and adopt more effective strategies. They even can improve our ability to design institutions and procedures. In this class, I present a starter kit of models: I start with models of tipping points. I move on to cover models explain the wisdom of crowds, models that show why some countries are rich and some are poor, and models that help unpack the strategic decisions of firm and politicians. The models covered in this class provide a foundation for future social science classes, whether they be in economics, political science, business, or sociology. Mastering this material will give you a huge leg up in advanced courses. They also help you in life. Here's how the course will work. For each model, I present a short, easily digestible overview lecture. Then, I'll dig deeper. I'll go into the technical details of the model. Those technical lectures won't require calculus but be prepared for some algebra. For all the lectures, I'll offer some questions and we'll have quizzes and even a final exam. If you decide to do the deep dive, and take all the quizzes and the exam, you'll receive a Course Certificate. If you just decide to follow along for the introductory lectures to gain some exposure that's fine too. It's all free. And it's all here to help make you a better thinker!
The Standing Ovation Model
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From the course by University of Michigan
Model Thinking
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From the lesson
Why Model & Segregation/Peer Effects
In these lectures, I describe some of the reasons why a person would want to take a modeling course. These reasons fall into four broad categories: 1)To be an intelligent citizen of the world 2) To be a clearer thinker 3) To understand and use data 4) To better decide, strategize, and design. There are two readings for this section. These should be read either after the first video or at the completion of all of the videos.We now jump directly into some models. We contrast two types of models that explain a single phenomenon, namely that people tend to live and interact with people who look, think, and act like themselves. After an introductory lecture, we cover famous models by Schelling and Granovetter that cover these phenomena. We follows those with a fun model about standing ovations that I wrote with my friend John Miller.
Meet the Instructors
Scott E. PageProfessor of Complex Systems, Political Science, and Economics
Center for the Study of Complex Systems
Hi. In this lecture we're going to look at a model that's a favorite of mine, known
as the standing ovation model. Now this is a model that builds off the [inaudible]
model it's just really an extension. But it can allow us to sort of think about
threshold based models of participation and pure effects in a little more subtle
ways. Why standing ovations, those are kind of a funny thing to study. Well
here's why. Think about a standing ovation. When The performance ends, you
don't have a lot of time to decide whether you are going to stand up or not. You
gotta make sort of a fairly quick judgment. You're going to clap of course
but then you gotta decide do I stand or do I not stand. And then after the standing
ovation either starts or doesn't start you gotta make another decision, do I stand
up, do I follow these people, or do I you know stay sitting. So when you think about
human behavior there's going to be different models that we play with
throughout the course about how humans act. One model will be that people are
optimizing, that they make rational choices in all setting. When it comes
[inaudible] of a standing ovations that is probably a difficult thing to do because
it is all happening so fast. So instead, what people probably do is they follow
rules. So standing ovations are a nice place to sort of get people, it is a nice
domain to get people thinking about rule based behavior, about people following
simple rules and then ask me how the rules aggregate. So it is kind of the
[inaudible] model that way, right people follow rules in the aggregate and we are
going to see what is going to happen, only here right this is a model of ... I think
of it as like peer effect. Now, why, so we think of a standing ovation, one way to
think about it is as a peer effect. Right? Other people stand and then you stand.
What's nice about standing ovations, another thing that is nice about it, is
that it can also be information. So what I mean by that. So suppose you, you're
sitting in the theater and you notice that the woman sitting in front of you to the
left, you know is talking with her neighbor and she seems to know a lot about
the theater, about the performance you're going to see. And she seems like someone
who's a little more sophisticated than you are. So, play ends and you're kinda said
do I stand or not stand? And you see her just pop up. She pops up, she's applauding
like crazy. Well, you figure she's conveying some information that could be
useful to you about the quality of the show and so you decide to stand up. Right,
so it's not just that you're copying her for the sake of copying her, like in the
Granovetter model, like with the purple hats. Here you're copying her because you
think she's telling you something about how good the show is. Okay, so that's an
information effect. So what we want to do in a model that's going to capture these
sort of pure effects and information effects. So, just like in the Granovetter
model we're going to have a threshold, and there's going to be a threshold in which I
stand up but it is going to be somewhat different. So in the [inaudible] model,
the thresholds were the number of other people doing the action. Because spreading
the collective action, rioting, wearing the purple hat, was there are some other
number of other people I needed for me to do it. Here the threshold is going to be
related to the quality of the show. So you can think of it ... Let's suppose shows
have qualities between zero and one hundred And your threshold may be 70 or
60. Any show above 70 you stand, any show below 70 you don't stand. So if the
quality is above the threshold you stand. If the quality is below your threshold you
don't stand. But let's make this a little bit more sophisticated so let's suppose
instead of there just being you know you see the quality, let's suppose you get
something called a signal. Now the signal is going to be the quality plus some other
term. Some term E, which we can think of as an error, right? So you don't see the
true quality, you see the quality plus some noise. And now your decision to stand
doesn't depend on the quality of your threshold, it depends on your signal. And
the threshold. If your signal's above the threshold, you stand. If your signal's
below the threshold, you don't stand. Okay, so that's the model. Well, one more
thing, one more thing, because that was the initial decision to stand. Now you've
got decide, okay, after the sort of initial decision, do you stand once you
see other people standing. So we can assume is that you've got some sort of
threshold at Right, it says if ten percent of people are standing, I'll stand. Or
maybe if thirty percent of people are standing, I'll stand. Right? And that also
affects your behavior. So the rule really depends on just two things. One, this,
your individual, your initial threshold for quality. And then two, this second
threshold for how many other people have to be standing for you to continue to
stand. Okay? So that's the model. So now let's think through some of the results we
can get from this model. So the first claim is higher the quality of the show,
the more likely to be a standing ovation. Now why is that true? Well, think about
it. You stand if the quality plus the air, which is your signal, is above the
threshold. So if the quality is higher, your quality plus your air [inaudible] is
higher, you're more likely to be over the threshold, more likely to get a standing
ovation. Again, not surprising, one thing we want from models is we want them to
give us results that make sense, right, basic things that make sense. And then the
other stuff, right, maybe more surprising, but we want some stuff to really accord
with our logic right off the bat, okay? What's another result? Another result is
lower our threshold make our T level more likely to get a standing ovation. Why is
that true? Again, same logic, we need our signal only 40 plus appear to be bigger
than our threshold. So if my threshold falls from 70 to 50 to 30 to twenty, I'm
[inaudible] to stand up, right? Makes perfect sense, result three The lower X,
remember X was the percentage of people who have to stand for me to stand
subsequently, then there's going to be more ovations. Right, okay, that makes
sense as well, right. And the logic is you stand more than X percent stand, so if X
goes from, you know, 60%, if you need 60 percent of the people standing down to
ten%, you only need ten percent of the people standing, then you are much more
likely to get a standing ovation because if twelve percent of the people stand then
everybody stands up. Alright, now, what would cause X to be big? And what would
cause X to be small. So this is [inaudible] you should write down these
little variables in terms of stuff, and then you got to think, what does that mean
in the real world so what would it mean for X to be bigger, X to be smaller. That
is sort of how willing you are to stand based on other peoples standing. So big X
would mean... If you didn't stand initially you need to see a ton of people
standing before you stand. So this would represent people who are really secure in
who they are. A small act would be people who are really ready to jump on any
bandwagon, right? So five percent of people are standing and then they stand.
So this X tells us something about the people in the audience, right? Which is an
interesting thing to think about. Okay, let's go back to this signal. Remember I
said that you get this signal [inaudible] which is Q plus this term E what is E?
Well remember I said E is error, right, so I said that there is a quality of the show
that maybe like 55, and you don't see 55 maybe you see 58, 52. So it is variation
in what we perceive. Well another way to think of that variation but what we
perceive would be to think of it as diversity, right, if you and I care about
different things we have had different life experiences, we may interpret the
theatre, the performance differently then one another. And as a result what's a 50
to you may be a 60 to me, or what's a 70 to me maybe an 85 to you. So, because you
and I are different we are actually going to have different qualities. So this E
term Right, this Q plus C. We can think of this as either error or we can think of it
as diversity and so that, why does that matter? Well it matters because when you
think about interpreting the model, like what the model tells us in the one case it
will tell us well what happens if people have more noise in terms of how they
interpret this show oral kind of the way you can say, what does it mean if the
audience is more diverse? Right? Okay, so, well, what does it mean? Well, to do that
now we have to think a little bit, now we actually have to sort of do some math. So
lets do an example. Assume we have 1,000 people. The threshold for all these people
to make it simple is 60 and the [inaudible] is 50. So 50 is less than 60,
right? So that means people aren't going to stand for the most part. So there's no
error, no variation, nobody would stand up. Okay, so let's do a case first where
the error comes really small so its 50. Now the mean here is 50 Right, and the
error term is either between minus fifteen and plus fifteen. So someone who's got an
error of minus fifteen gives it a 35 and someone who's got an error of plus fifteen
gives it a 65. So it's right, 65 there. So all these people below 60, they're going
to sit. They're going to clap, they may clap nicely but they are going to sit
because it's below their threshold. So only this small set of people here stands
up so unless X is really small, what's going to happen here is few people stand
up, no standing ovation. But now let's increase the variation, let's suppose the
variation goes from minus 50 to 50. Well now the people give a score of minus 50,
they're going to give a score of zero. And the people who give a score of plus 50,
they're going to give it a score of one hundred. Now once again, the average score
is still 50, right, so that is less than 60, so the average person doesn't stand
up, but here all these people stand up. So they assume people are sort of uniformly
distributed between zero and a hundred, so they're equally distributed across there,
that means that forty percent of people will stand up. What that means is, unless
X is really small, as long as X is above you know, 40, below 40%, you're going to
get a standing ovation. And think about it, if you go to the theater and you see
30 percent of people stand up, you're likely to stand up. So we get here, where
we have this large diversity, or large air term, be more likely to get a standing
ovation. Okay, so that's claim four If Q is less than T, so if its a bad show, well
not if your a bad show, it's not a great show, you're more likely to get a standing
ovation if the variance in E is larger, right? And again that's because you stand
that Q plus E is bigger than the threshold if this has more, if there's more people
with big E's, you're going to have more people that stand, and that's more likely
to cascade into a full blown standing ovation. Okay, so let's think about what
would cause E to be big, well one thing would be... The audience, right? So if you
have an unsophisticated audience. You know maybe they don't get it. That means some
people will think it's great, some people think it's bad, you know, you're just
going to get more variation. Or, you could have a diverse audience, right? You could
have people from different backgrounds, you're going to get more variation. The
performance itself could matter. If it's really complex and hard to figure out,
that could cause variation. Or if it's multi-dimensional, if there's lots going
on, that could cause more variation. So, different attributes of the audience and
the performance could result in more variation in that E term, which could lead
to more standing ovations. So let's think about what we know. What did we learn?
Higher quality show, more likely to be a standing ovation. Not a surprise. Lower
threshold for standing, right? We are not going to do a standing ovation. Again, not
a huge surprise. So, are people are more willing to stand and jump on the
bandwagon, lower X? More likely to be a standing ovation or, you know, larger peer
effects when they call that. And the last thing is like more variation. When there's
more variation, more diversity, in that error term, then More likely to get
extinguished, and so here we've got these four sort of nice results that help us
sort of understand when we are going to get standing ovations and when we are not.
Now you could "say how much did the model help up?" Well my guess is that if you
just thought about standing ovations without constructing a model you might
figure out, yeah, better shows get standing ovations, you know, people more
willing to give standing ovations are giving standing ovations, and if people
are more susceptible to influence you are going to get standing ovations, but you
probably wouldn't have gotten this one. You probably wouldn't have gotten more
variation, now you might have if you learned the Granovetter model, right, but,
most likely you wouldn't have had it. Now, that's the simple standing ovation, let's,
let's ramp it up, let's have some fun, right? [inaudible] Let's do an advanced
standing ovation model, now I used to give the standing ovation model, as this
assignment for students and, they construct models a lot like the ones we
just did. Now what's funny is if you, if you don't give it to a student, if you
just ask somebody on the street to start describing a standing ovation or, just go
into the theater, they'll include two things that weren't in the model. Now
modeling requires leaving things out, but here are two things that almost everybody
leaves out of standing ovation mode. The first one is the theatre itself, right, I
mean your actually in a theatre, your not, in our model we just had these people who
sort of saw everybody, but that's not true. The other thing is this, most people
when they go to the theatre, they go with a date or a group. Sometimes you go alone,
right if I am traveling to New York or something without my family, I may go to
the theatre alone pick up one cheap ticket, but for the most part, when I am
sitting in the theatre, I know I said most people are there in groups, so now we can
ask Do these things matter? I mean these are features of the real world not in the
model. Do they matter? Well, let's see. Lets look at the auditorium first. Here
the auditorium After the standing ovation starts, mainly you have some site lines so
you get some sort of cone in which you can see who's standing and not standing.
Thinking about why that might matter, well Suppose, you know, I am sitting here I
have this cone. I am sitting here I get this cone. Here I have that cone. Here I
have that cone. So you see there are small cones and there's big cones. Let's think
about the difference between those two. So what's a small cone person? A small cone
person is somewhere in the front. They don't see anybody, right? But notice
almost everybody sees them. So, they influence everybody but they're not
influenced by hardly anybody. They're like celebrities. Right? They're celebrities
who like we all care what these celebrities do, but they don't care much
what we do. Right? Now, what about People in the back, because people in the back
they can see almost everybody, right? But, almost nobody can see them, right? Anybody
sitting in here, nobody can see these people, right? They can't look to the back
of their heads or turn around or something. Well, these are more like
academics, these are more like people like me, spend a lot of time studying how the
world works but not that many people pay attention to what we say. More people care
what Oprah or Ashton Kutcher say than what I say. So as a result, even though we have
a better sense of what's going on, right, nobody listens to us. Let's think about
the you know, ramifications of that. What that means is what we'd like is to get a
standing ovation if the performance was good, and we'd like to not get one if the
performance was bad. But what's happening is everybody is queuing off these
celebrities, who really don't know what other people think and nobody's paying
attention to the people in the back, who really do know what everyone thought. So
this means that maybe the system isn't going to aggregate as well as we'd like it
to. Right, so maybe we're not going to get the right answer as often as we would
expect to. Okay, what about dates? What about the fact that you know, hey look you
know, I got a date, going to the theater, how does that matter? Well think of this,
with respect to the X term, like before I said I'm going to stand, I'm going to look
around, I'm going to stand if, you know, X percent of people are standing up, but
once I've got a date, if she stands up then I'm probably going to stand up. So
what this means is, if you think about people in groups or in pairs, if one
person in that pair stands up, then everybody might be more likely to stand
up, which means that adding groups or adding dates or pairs means that you're
going to get more standing ovations because if one person could them both to
stand up that's going to increase the percentage of people standing up which
will in turn is going to create more of a standing ovation. Okay, so what do we got?
How do we increase the probability of standing ovation? Right? We had before we
had before. Higher quality show, right, lower threshold larger peer effect, those
are the obvious ones, right? More variation, the unobvious one. And now we
have two more. Use celebrities, put people in the front, right? Put people in the
front who are gonna stand up for sure. So pay somebody in the front to start an
ovation. And then big groups, create groups of people and then if one of those
people in the group stands up the whole group stands up, and that causes more
people to stand up. So now we've got six ways you can cause standing ovations and
I'm willing to guess that like these three might not be things you thought of, right.
The people in the front matter more and that you want to create groups. So the
model's actually helped us figure things out. Okay, so, wait, this point you can
say okay Scott, this is all fun and good, but this is standing ovation, not that
important. True, absolutely true, but again we are using this model, right, to
help us sort of make sense about rule based behavior in environments where there
are pure effects. One of the reasons we construct models is for fertility, so once
we construct a standing ovation model we can use it someplace else, but where else
can we use it? Well, we just studied, right, collective action problems or you
know, participation problems, in political uprisings, riots and things like that.
That looks a lot like the standing ovation model. And now you can think of who are
celebrities? Right? And who are ... What does it mean to have big groups in that
sort of context? Well, the celebrity is someone who has a lot of influence on
other people. So if you want to start a political uprising you need those sorts of
people. So this tells us something about that. It also works for things like
academic performance. Suppose you got a school that's under performing and you
want to sort of have people lift themselves up to work harder. How do you
do it? Well, you can think we need to sort of raise quality, lower, you know, sort of
lower these sort of thresholds of The barriers to be able to sort of engage in
this productive behavior. You can do things like use celebrities. Right? And
you can even create groups, okay, groups of students to work together to all do
well, right, and that may cause other people to do well. Urban renewal, right?
You can think of each one of these people instead of a, each one of these boxes,
instead of it being a person standing up you can think of it as someone fixing up
their house. Now what's interesting here is, let's go to that sort of variation
idea. Well you could think we want to improve some city, let's give everybody a
thousand dollars if they'll fix up their house. Well it could be that nobody does
it, because it doesn't push anybody above their threshold to fix up their house. But
the variation idea says if we give a handful of people a lot of money to fix up
their house, they may do it and then that could cascade. In fact a lot of people who
are studying urban renewal, push that sort of logic, that you should target
particular areas where people are likely to do it, get things started, and help the
process log rules. Alright, fitness and health, if you want to get a group of
people of society even to become more healthy, that's a lot like a standing
ovation. You need some people to do it and then you hope other people do it. Now that
could be pure effects, right I see other people being healthy, I want to just copy
them, or it could be information. I see them acting healthily, engaged in fitness
and then I think, you know what, they're doing better than I'm doing, so maybe, you
know, they seem happier and healthier, so I'll copy what they're doing. Even like,
right, this online course, if I don't... This online course is like a standing
ovation model. Each person deciding, do I stand up or not? Is the quality above my
threshold, right? So, if I want people to take the online course I can draw lessons
from the standing ovation model and think about how do I do it, you know, by using
celebrities. And that's sometimes what I did, right, is I tried to get a lot of my
friends who are celebrities from the academic world to say hey this is a cool
course. Alright, so, that's the standing ovation model. It's a pure effect model,
but it's also this sort of information model and it explains, again, why we see
groups of people all doing, you know, similar stuff. Right? Because we see other
people doing it, and then we copy them. And this tells us when we're likely to see
it and when we're not likely to see it. Okay, thank you. [sound]
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