>> Amy Draves: Thanks so much for coming. I am happy to welcome Damon Centola who is
speaking about his Theory and Experiments on the Spontaneous Evolution of Culture. He is an
associate professor at the Annenberg School for Communication and the School of Engineering
at the University of Pennsylvania, where he is also Director of the Network Dynamics Group.
His work addresses who behavior is spread through social networks using computational models
and online experiments to study innovation diffusion, social epidemiology and cultural
evolution. His research has appeared in journals such as science and the American Journal of
Sociology. Damon, thank you.
>> Damon Centola: Thank you. Hey everybody. This is a normal turnout. I had a joke
prepared. I am going to give you my joke anyway even though it’s a small audience.
>>: [inaudible].
>> Damon Centola: Is this being recorded? Who knows? I gave a talk a year ago at Apple. Do
you guys know that apple doesn’t really have a really have a research division? It’s like
basically you are talking to VP’s, but I went in there with like this massive Lenovo PC and
plugged it in and everyone was like, “Do you have a MAC? Do you own a MAC?” They kept
giving me this thing and I was like, “Yeah, I own a MAC, but this is my research machine.” And
I plugged it in and then in front of all the VP’s it crashed and then the Windows symbol came up
in the reboot. That’s a great way to start my relationship with Apple.
So I’m going to talk today really about how collective behaviors emerge and part of the
discussion is going to be about how social networks affect this. So the literature and discussion
on this historically have focused on this kind of idea. You basically have a population of people
connected in some kind of complex topology and then you have a single individual who is sort of
seated, think of this as like an epidemiology model and that person basically spreads the
contagion, whatever it is, to their neighbors network, and they spread it to their neighbors, and
their neighbors, and so on and so forth. Then ultimately it spreads throughout the population.
So this is my work for the last 7 or 8 years, working on these kinds of models and then the book I
am working on now works on this kind of thing as well. What I am going to talk about today is a
significant departure of this way of thinking. So I am not going to talk about diffusion as a
process of spreading from person to person of a single kind of contagion. What I am going to
talk about is the way that norms evolve. And norms, unlike these kinds of contagions, aren’t
binary things. You don’t just adopt or not adopt.
A norm is something that evolves as people interact with one another. They form a kind of
reciprocal relationship where I adopt a behavior, and you see my behaviors, and you respond in
kindness to try to coordinate and I see your responses and I respond in kindness and so on and so
forth. This sort of interactive dynamic January 18, 2016evolutionary force that allows over a
population entire sort of spontaneous changes in the sort of normative behaviors that people are
engaged in. And this changes both in our beliefs and our emotions, but also in sort of ways in
which we form expectations for one another’s behaviors. One of the things about this kind of
process is once it takes hold it can form over an entire population, a kind of stable, normative
equilibrium.
Once this happens there is kind of a thing that happens in our minds where we tend to justify the
equilibrium that happens to exist. We say, “Well this is better than other possible equilibrium.
There is some reason why the world looks like this. There is some reason why we engage in
these behaviors.” We tend to think it’s either justified on some sort of moral grounds or that it’s
functional in some way, but there’s a lot of work, in fact my own work on this thing called The
Emperor's Dilemma, that shows that there are a lot of really disadvantageous norms, un-desirable
norms, that form and can evolve, and can spread through populations. And even become self
enforcing where people are sort of punishing each other for deviating from things that no one
wants.
So the fact that these things can emerge and sort of become stable, even though they are not
functional at all raises the question of, “How is this possible that norms form over a society when
the content of the norm itself doesn’t justify this process?” There are 3 big answers and these
answers date back to Hobbes, and Hume, and Rousseau. These are the answers we have been
sort of given over the last 200 or 300 years. The first one is that there is some kind of centralized
authority governing this process. There is a government or a firm that has an agenda and
encourages people, through incentives, for cooperation or disincentives for deviants, to
coordinate with a certain behavior people see each others coordination and that creates lock end.
It’s a perfectly valid solution for this problem, but in many cases there are no institutions. There
is no top down authority governing lots of the social norms that we see in society. Too many
lings like linguistic norms, patterns of bargaining an agreement, patterns of politeness and
agreement of gender connections. There is no centralized authority dictating this stuff explicitly.
So it raises the question, “Well how do these sorts of norms get off the ground? How do we
form large scale conventions when there is no centralized authority?” One of the most famous
answers to this is Harsanyi and Sellten’s work on equilibrium selection and they won the Nobel
Prize for this. They essentially said, “Well look, when people are choosing between two options
one option is typically slightly better. I mean better in the sense that it has a higher payoff or it
can be better in the sense that it is slightly less risky.” So individually we all gravitate to that
option, then we see each other gravitating and we all collectively coordinate on that particular
option and that forms an equilibrium over the population. Again, it’s a perfectly valid solution
and it applies to some cases, but there are pretty thick institutional assumptions here as well. It
means that basically the set of options in the world are finite, we all know what those options are
and we all know ahead of time what the payoffs for those options are.
So it means that there is basically universal knowledge and universal common knowledge and
again that’s rarely the case, particularly in markets where lots of new things are emerging, where
new options can come up. So the final kind of solution is there is some kind of informational
feedback. So I think here of like a best seller list or a polling system where it kind of samples the
population. It says, “What are people doing,” and then reports that back, we see this list and we
say, “Oh most people are doing this.” So we all, because of the popularity, perceive an
informational signal. We all start doing that thing and then of course that becomes reinforcing.
More people see it; more people do it, so on and so forth. Again, this is something that happens
a lot. We see this with media, books and music.
But often these kinds of behaviors that we are interested in can’t be explained by this kind of
phenomenon, because once again this requires a fairly thick institutional assumption. It requires
that there is some mechanism that’s actually polling the population and then some centralized
system that reports it back that sort of states where the best seller list is and then everyone is
paying attention to that best seller list, which means everyone knows it exists and that it’s
relevant. Again, that’s a really heavy institutional assumption. So my question is: Without any
of these institutions existing how do we get institutions, large scale conventions, off the ground
in the first place, the sort of state of nature questions? And the answer people have come up
with, Granovetter, Young, Ellison and other’s is that there is a social evolutionary process, just
by virtue of people interacting with other people in social networks and locally coordinating,
basically in pairs. As pairs interact with pairs, interact with pairs and so forth there can be kind
of a collective evolutionary process that forms a global coordinated norm even though no one
individually is trying to form or even aware of the fact that there is kind of a global process
going on.
So we have models of this, but when we think of studying this empirically it is extremely
difficult to get a grip on and the reason for this is in the kind of sequence of history once a norm
kind of takes hold it becomes codified and institutionalized. So when we look back and we say,
“Why does that norm exist?” We can always look back and find an institution that makes that
norm seem more solid than it historically was. So an example is that at some point they expand.
If I say, “Why do we use the term spam to refer to junk e-mail?” It’s a weird thing to do, sort of
idiosyncratic. People will point to a Monte Python skit, spam, spam, spam, spam and other
people will say, “Well programs used to eat spam; I don’t think that’s true.” Other people will
say, “Well it’s a weird thing, a canned meat product, junk e-mail is a weird thing, wholly
unwanted.” But there is no real origin story.
One person I talked to, a colleague of mine said, “Well no we use the term spam because
Google’s junk e-mail folder is called the spam folder.” The paradox here of course is that the
reason that Google uses the term spam is because people use the term spam. So it’s always easy
for any of these examples to look back over and say, “Well this institution codified, that’s why
we do it.” But it obscures the actual true historical process by which the norms emerge. So
that’s what we are going to try and get at.
So in order to do this we need a new method. We can’t just use observational data. So I am
going to use a method that borrows sort of principles from Durkheim, Simmel and Homans,
which is this intuition that we can think about societies as sort of independent observations. We
can take an entire society and hold it next to an entirely different society and say, “In one society,
because of some structural property, we expect this behavior to emerge, but not here.” And if we
can compare them and get sort of all the controls right we can say, “This one feature the society
generates this collective behavior and we can predicatively assess whether or not it will occur
and [indiscernible] is suicide. He says, “Look this one feature of social interactions is more
likely to generate suicide when it’s absence and as a result I can structurally predict when there
will be greater patterns of suicide in a society.”
So I am going to argue that we can talk about social norms the same way and it’s independent of
the cleverness of the solutions or the options that are available. It has nothing to do with the
content of the norm. We can simply say that by changing the structure of a social network, by
changing the connectivity of a population we can generate spontaneous coordination on global
norms in once case and have systematic failure in another case. This will show us how the
structural features of a population govern this process of global emergence.
So I’m going to give you a little bit of theoretical background and talk about the experiment
design and get into the findings. So the background here, there is sort of generations of
modeling, it’s really staring in the 90s. They looked at these sorts of cognitively simplistic
agents. This kind of grows out of the game theory tradition, agents playing these games they are
trying to coordinate with one another. And the main question has been to look at how this sort of
pattern of connectedness affects this. People will be familiar with these graphs. This is the
lattice. This individual has 4 neighbors, 2 on the left, 2 on the right and those neighborhoods are
overlapping. This is a randomized version, everyone still has 4 neighbors, but the network ties
are across the network. This is a small world topology. Then over here, this is homogeneous
mixing. This is a mean field model that we are used to from economics and physics.
The interesting thing about these networks is that none of them are realistic. Real world
networks don’t look like this, but actually the dynamics and here the formal models have been
very helpful, the dynamics that occur across this space of networks, this topology going from a 1
D lattice, to an infinite dimensional random, to full mixing, actually encompassed the full space
of interesting network dynamics. So if you say, “Well what about a small world network,” well
the dynamics of that network occur in an un-interesting way, in a linear way, between the
dynamics of a lattice and a random. If you say, “Well what about a scale free?” Again, in a
linear fashion, uninteresting fashion, the dynamics occur between a random and homogenous
mixing, which means if we can bookmark the entire dynamical space with these two results we
actually know everything that happens in between because it is uninteresting and that’s very
useful for us.
What’s that?
>>: Is it meant to represent like there is a complete graph on a single vertices?
>> Damon Centola: Yeah, so the kinds of interaction sequences we are looking at here are
something like pairwise interaction. So in a pairwise interaction model this person would select
randomly from her 4 neighbors with replacement and then just continue selecting randomly. So
here again you select randomly from your 4 neighbors and here you select randomly from the
population with replacement. Any other questions?
So there have been some predictions about how these kinds of structures would effect the
dynamics. And one intuition is, because well people here have clustered neighbors they will be
able to coordinate with one another and that coordination will make local critical mass possible,
which will make global coordination much more easy. Whereas over here people are still
interacting with the same neighbors, but there is no local clustering that makes coordination
harder. Then over here you are just picking people at random over the population. What will
that do to the dynamics of coordination?
So Ellison has a really nice model of this which we can look at. Each node is an individual and
you will see the lengths light up as people interact with each other, but essentially the network
connectedness is the same as what we just looked at. This is a lattice and this is the homogenous
mixing case. I am just going to play for you the dynamics of actors trying to sort of coordinate
and if they coordinate they both turn red and you can see what happens over the course of the
coordination process. So the lengths fill in as they interact and when they have successful local
coordination you see sort of that area of red starting to spread around the graph.
Over here on the right you have interactions all over the network, however because each person
interacts on the next round with a new person it is very hard to get a local norm off the ground.
It’s very had to get coordination off the ground. And very quickly you get coordination in the
lattice, but not in the full mixing case. And this has been kind of the default intuition about how
these kinds of coordination dynamics emerge and how structure affects it. Yeah?
>>: [inaudible].
>> Damon Centola: Yeah, it’s an AB model. It’s very much like in the [indiscernible] and
[indiscernible] tradition. This is kind of risk dominance. So the intuition has been the local
clustering and repeated interactions accelerate global coordination and increasing connectivity
actually slows it down.
So what I want to push on this is with the concept of innovation. These models are actually,
[indiscernible], and [indiscernible], these guys at Stanford and they actually work on this too,
kind of extending the Ellison. So they call this innovation diffusion and I think that’s interesting
because there actually are no innovations in this space. These are just two options that are
competing with each other. And I started thinking about this really behaviorally and wondering
what would happen if individuals actually could engage in some sort of co-evolutionary process,
where if someone chooses a behavior and another person responds completely in an unbounded
way where they can either choose the same thing or choose something different and they can
adapt to one another’s behavior and really introduce new innovations into the space.
Well intuitively once this happens the dynamics now have a different sort of character to them
because it means that new options can show up anywhere in the network at any time. And this
means now that the network structure in terms of the smallness of the world actually should
matter for effecting global coordination because it is not just a matter of local coordination that
matters, but also the ideas that are present in the population need to be able to reach everyone
else in the population. So having greater connectivity might actually facilitate the process.
So I want to re-formalize it with a couple of principles: one is that there is no a priori limit on the
number of alternatives. So basically now instead of having two options you have ecology. You
have people introducing options continuously. And they may not, they may decide to just
choose one, but they could in principle keep introducing options. And that’s not just sort of at
the beginning of the study, but continuously means that even at the end of the study the
population of options can increase instead of decrease. The expected payoffs are the same for all
options, that’s important because again before the fact we have no idea what’s going to be a good
song or a bad song; what’s going to be a good show or a bad show. So we don’t know ahead of
time what the payoffs for the options are. We have to learn that through social interactions.
Individual attempt to coordinate locally: this is important because the classic example of this is
like driving on the right, driving on the left, you don’t care what people are doing in a different
city in terms of driving on the right or on the left. You care what people are doing on the parts of
the highway that you are driving on. Coordination is a fundamentally a local process. So you
want to think of it that way, which means that no one has any information about the rest of the
world and they don’t care quite frankly, they are just trying to coordinate locally and our
question is under this very sort of difficult assumptions, with no limitations to what people can
do they only care about that local interaction, and they can change at any time, under those
assumptions can we really get global coordination without any institution? Is it really possible
for it to just emerge indigenously?
So we formalize this in terms of naming. This is based on a Wittgenstein naming game in which
he has this idea that basically 2 people are looking at an object and one person points and says
something and simultaneously the other person points says something and the question is: Will
they wind up saying the same thing? And of course they are able to learn from each other, they
evolve in answer and then through trial and error ultimately coordinate. Our question is: Well
two people can figure this out, but how does a population figure this out? As I am trying to
coordinate with one person, I am also coordinating with other people, who are coordinating with
other people and so on and so forth and what does this do in terms of the global population?
So people have been trying to work on this empirically, this is work out of Sony labs. I used to
put this slide up and say, “This is top secret,” but some one in the audience once was like that’s
no longer top secret, everyone know about that. So everyone knows about this, but this is
essentially two robots playing the Wittgenstein naming game. They are looking at the objects,
they are trying to name them, and they are pointing and its interesting stuff. You learn
something about these dynamics and maybe about how computers can mimic language learning
in humans, but it doesn’t tell you much about our question, which is it doesn’t tell you about the
global dynamics of coordination emerge, because this is just binary interaction.
So I am going to talk about the strategy I have been using with the experiments and there have
been a couple of sort of challenges historically in doing this kind of work: one is that this is a big
deal actually. Most of the work that has been done on this is in small laboratory groups, sizes of
like between 2 to 6 people, sometimes up to 10 and it is actually really interesting work. They
put people into kind of a room and give them a game, but give them no language to use to
communicate with one another and they have to invent a language to coordinate in solving some
problem and people are actually really good at this. And it’s quite interesting to see how the
language has evolved.
The problem with studying those kinds of real evolutionary dynamics is that even with 6 people
it takes a long time and it’s hard to do. What the models are useful for here is they show that if
you look at populations that are smaller than some critical threshold, and this case the critical
threshold is about 20, the dynamics are exactly the opposite below 20 as above 20, which means
that if you study small group dynamics it tells you something about small groups, but those
results systematically do not generalize to large populations and this can see like bad news
because that means we have to wipe all this research off the table. It doesn’t mean that, it just
means if we want to understand how these things generalize we have to study larger populations,
but there’s also really good news here. If you want to understand 61 million people you don’t
need a data set of 61 million people, in fact you just need to have a dataset that larger than that
critical point and in theory those results are generalized to large populations.
So people have tried to do large sort of scale experiments, but the real time decision making
usually typically involves a kind of game theoretic setup. People have an AB choice, the payoffs
are know, there are incentives for global coordination, which is interesting stuff, but it brings us
back into the space of not really being able to really study the evolutionary dynamics in sort of a
free and unbounded way. Yeah?
>>: A quick question, don’t spend too much time on it: When you said the dynamics are exactly
the opposite in groups over and under 20 what precisely do you mean by that?
>> Damon Centola: Sure, what I mean by that is there are conditions I am going to show you
where there is divergence in the conditions, below a certain size that the two converge. So that
divergence only shows above a certain population size and that divergence generalizes from 100,
to 100 thousand to 100 million.
So if you want to study the real time evolutionary dynamics of people making real decisions and
you want large scale people will say, “Well that’s what big data is for, that’s what we use, that’s
the whole point of big data to be able to do that.” Sure, it’s true, you have those data, but the
problem is now the data are uncontrolled, which means if there were institutional influences you
couldn’t eliminate them from these data sets nor could you understand the systematic way how
the pattern of connectedness was effecting it, because these are just observational data. So if you
want to get causality you need some way of studying a controlled and reproducible fashion how
different structures of a population are going to affect these different collective outcomes.
This is where reproducibility comes in. This is a standard, a criterion for social science research
that has rarely been worried about. The reason is because even like getting any of these is hard,
but then saying, “I’m going to get a data set that’s perfect along all these lines and also I am
going to get it 3 times in a row, or 4 times in a row, or 10 times in a row,” that’s an impossible
thing. How are you going to control those sorts of things? But, it’s really important to do and
here’s the reason why: if you have 100,000 people connected in a data set and they are all
interacting in a social network and they are by construction influencing each other’s behavior,
right it’s a social evolutionary process, how many data points do you have? You don’t have
100,000 data points because people are not IDD; they are all inner connected in one process,
which is a culture evolutionary process. You have 1 data point of 100,000 people.
So if you want to understand what’s happening in a systematic way you need to reproduce at the
level of the population and that gives you multiple observations and that’s going to be the
standard of evidential reasoning I’m going to present today. And the way we do that is by
creating essentially these online social Petri dishes. And the logic here is really very much the
same logic as biology, which is to say that if you can take 2 populations and make them
indistinguishable, in the sense that this is not a psychology experiment, I’m not saying if I give
you a different world, you would behave differently. I am saying that I give you a universe that
looks pretty much the same in both cases, but I changed something in the background that’s
invisible, which is the structure of the network, but you have no immediate awareness of it.
Does that therefore grow a systematically different collective behavior in one world than another
world even though you don’t know that there should be a difference? And this to me is really
important because in our daily lives I know people are excited about the fact that Facebook has
like some kind of hairball image that’s the network, but the truth is that you pretty much know
who you are connected to and you kind of know who they are connected to, but beyond that you
have no idea what the network looks like. So the point is the real connected structure of society,
how its diameter looks like or what its clustering looks like, you really don’t know. But those
features, presumably even though we don’t know them, affect our collective behaviors and that’s
what I want to evaluate here. We should be able to see systematic changes in a collective
behavior or population in one condition that just don’t show up in the other one.
So what we do is study actually the same exact thing as the model, it’s a naming game. People
enter an online environment, we give them an object to name, they both point at it, they come up
with a name for it, they see each other’s options and then they are able to revise and keep
playing. The object here is a face and that was important because we wanted to choose an object
that had no kind of a priori boundaries. You can type in any name you want and in fact you can
type in any character string you want. So it is an unbounded text box. And I ran this initially
when I was at MIT and people just typed in –. Well a couple of people actually just pasted in
code, like trying to hack the system. I didn’t work, but our question is: As people intact with one
another trying to coordinate locally will this generate global coordination on a social norm, in
this case a naming convention?
So when people arrive to the study they see this. You are going to get this game screen and
what’s going on in the background is important just from a mythological point of view. So as
people arrive here there are these 3 networks I showed you; the lattice, the random and the fully
connected. They are sitting in the background and they are empty. So people are essentially
being randomized across these and it’s not until all 3 networks are full the experiment starts,
because we are randomizing, randomizing and randomizing. Let’s say each network has 25
people so after 75 people show up all 3 networks are full and then at that point we start the
experiment.
This is the experiment interface. This is pretty much the entire experience. The game starts,
there’s a face, there’s a text box, you can type in any name, hit enter, there’s a timer of 20
seconds and then on the right there is a number of rounds. You see you are going to play 20
rounds and you are currently in player round 1 and then the winnings are on the right. So if you
and your partner type in the same name then you win 25 cents and if you don’t type in the same
name you don’t win anything. I added a feature to this which is interesting, which is that if you
fail to coordinate I actually take money away from you. Now I can’t go below 0 because that
would be called gambling and the state of Massachusetts frowns on that, but if you win money I
can take that money away. So your winnings actually go up and down based on your
coordination level.
Here on the left hand side you see a list of players. This is important because this list of players,
if I showed you who you are interacting with, you could easily infer what the structure of the
network was. You would see clustering and you would see repeated interactions and more
importantly the size of the network. You would know how many people were interacting in the
world. But, of course you don’t know those things about the world. So what I did was keep this
list constant across all the network conditions. So regardless of what condition you are in and
regardless of what the size of the network is you just see this list, right. And this allows us to
really evaluate the effects of network structure independent of any information you may have
about the world.
So when you type in the name you hit enter and then you get a screen that shows you the name
the other person typed in and your name, which let’s you now first of all that you can increment
your memory. You have in memory the name you typed and the name the other person types,
but you also know the other person sees the same thing. So you know they have in their memory
the name you typed and the name they typed. So you are starting to develop kind of beliefs
about the other people in the world and you are also creating this kind of history, this memory
list and using this to evolve what the options are in the population. You have no information
about the population or what the sorts of popularity of options are.
I am going to show you the results now, but before I do that are there any questions about this
interface, because if there are it will be useful?
>>: Are they allowed to type in instructions, like let’s call this girl out.
>> Damon Centola: Yeah and it’s literally unbounded. I mean I guess it’s bounded by the
number of atoms in the universe, but you can type in anything you want in there. And people
did, people said, like “Copy me: Simone.” Then the interesting question is like if people do
these kinds of cheating tactics how does it affect the dynamics?
>>: Is there anything to prevent gaming [indiscernible]? I would think there could be some prior
agreement or agreement that [inaudible]. Every bit is going to be called Randy; everybody types
Randy all the time.
>> Damon Centola: Yeah, well that goes to the question of: How did I select subjects? So
people were selected from the World Wide Web. So it wasn’t like I just got a bunch of grad
students to come and play. I mean for testing purposed, but not for data. For data I actually took
out adds in a commercial journal, which is a really expensive way of recruiting subjects. But
you basically get people from all around the planet. And there is a kind of workload intensive
recruitment system that I use that wind up, because part of the challenge here is to coordinate.
You have to have 75 people online, at the same time, in the same 5 minutes, actually caring and
engaging in this game and that’s actually hard to do.
>>: For those 5 minutes it’s just those people, in just this one [indiscernible]? Then they go there
separate ways and play again?
>> Damon Centola: They go their separate ways and there’s no personal identifying information
and if they did happen to know someone in the space they wouldn’t –.
>>: So we have a problem, we have like a thing here, UHRS, which is like our internal Amazon
Mechanical Turk and one of the big problems that we have is that people coordinate with each
other that are like certain Mechanical Turk people, in particular around like finding easy
experiments or communicating ways to like game experiments. Was this something that you sort
of worried about or thought about?
>> Damon Centola: It wasn’t because of my recruitment strategy. I think if you are recruiting
from the same pool again and again that becomes a problem and we did find this later on. There
was another set of experiments that I will talk about at the very end, stuff that we are doing now
in collective intelligence, and we ran a bunch of trials across this large population and then we
were curios and wanted to go back and redo one of our trials because we had a question about
what happens if we change this or that and it was just kind of a robustness test that didn’t really
matter.
But, we ran it in one of our same populations, like we recruited from the same place and the
behavior was really different. We were like, “Is this because of something we did?” Then we
actually saw, because there was chatter, I think we used Reddit or something, and you actually
see there was Reddit chatter about, “Oh I have played this game before,” and we were like, “Oh,
okay so this is why you don’t re-recruit.” You just like use a different population each time and
it allows you to do that. But, I think that is a consistent problem. You get people playing the
same game over and over again or the same population being recruited over and over again.
>>: Our problem in particular is that people, real life people, are coordinating because they know
each other, to do our experiments.
>> Damon Centola: Yeah no, I know.
>>: But I guess the strategy in place helps.
>> Damon Centola: So my strategy for solving that problem has been to target as many different
recruitment environments as possible and just mix it up and try to get sometimes all of them
together, right if we do a big recruitment get this whole together, because they are going to be
randomized. So that makes it much, much harder for anyone to coordinate with anyone else.
But the only time I actually had a problem with that was when I was doing the beta testing. So
when I was just getting it working I ran it with some undergrad’s at MIT and you could tell that
people, on the very first round put the same thing in and just coordinated the whole time. You
are like, “Okay, those people are probably like roommates,” but it was just beta testing so it
didn’t matter.
Okay, there are no more questions? Yeah?
>>: So after I send my choice how many neighbors do I see?
>> Damon Centola: So you are interacting now in pairwise fashion. So basically from your
neighborhood in the network, this is either lattice, or random, or homogenous mixing.
>>: But it is chosen at random, right?
>> Damon Centola: We are choosing at random one person that you are connected to. Then of
course when fully connected you are connected to everyone. But choosing one person you are
connected to and saying, “Okay, you are in a pairwise interaction with them.” You see what they
put in; they see what you put in. You either win money or you don’t and then you start over.
Now you are in another pairwise interaction –.
>>: [inaudible].
>> Damon Centola: No, you don’t, because if you did right here –. We random [indiscernible],
you just highlight the bar and say this is the person you are interacting with. The problem is if
you do that then you have information about the network. For example you can see who they are
interacting with; you are like, “Oh this person, these two people, or these people are interacting
with each other, so on and so forth.” That would confound the idea that it is not the topology
doing the work, but information about the topology doing the work. So we eliminate
information about the topology and just say, “The topology itself, what kid of work does it do?”
>>: So you don’t know whether you are interacting in round 2 with the same person as in round
1 or with a different person.
>> Damon Centola: That’s right, that’s right.
>>: Do you ever see people volunteer their own ID, or own name, or own identifier together?
>> Damon Centola: My own name? No. There is a lot of really interesting behaviors, but no one
says, “My name is.” People do the kind of thing you are saying where they are saying, “Let’s
coordinate on.” And there are other kinds of cheating things, which I will show you when I
study the results. You will see people try little cheating things like they type in categories
instead of names, like blue eyes. But no one ever says, “Hey my name is Damon.” Was there
another question?
>>: Yeah, I was wondering if you ever put a list of players. If was playing a game like this I
would infer that there were 10 people in the network, incorrectly, because there were 10 players.
I was curios about why you did that.
>> Damon Centola: Well because we ask at the end. This was an important check both on the
soundness of the design, but also on exactly that intuition, which is if I show you this list do you
make an inference now about how many people are in the population? Then the question was:
Across different conditions, and I will show you some of the different conditions we run, how
different were the answers in the sort of exit survey? And the exits survey questions were: Was
there a coordinated answer? What was it? How many people did you interact with and how
many people were in the population?
And by the way to just sort of fast forward the results were robust. In fact across all different
conditions you got the same answers and some people guessed wildly. The answers were as wild
as you could expect. Some people said hundreds, some people said one, and some people said
nobody, like everyone just typed in all kinds of stuff. My favorite was there were a couple of
people who just typed in, “How could I possibly know?” And I was like, “Well yeah, of course,
you can’t.”
So, one of the advantages of doing online experiments are that at this stage most people would
show you a regression table. Yeah?
>>: Sorry to keep asking you, but do I have to wait for my partner basically. If I am quick, do I
have to wait?
>> Damon Centola: Yeah, so this is something we did design. This took a couple of months of
building because it’s in a network, there is this pairwise system of matching and then you can
imagine all kind of funky things happen, like someone get’s left out. They just happen by
random chance not to get matched or they are very slow. So other people played, other people
finished and they are left by themselves, in which case the game hangs. So we actually had to
build the system, and the engineers that I had working with me at one point were like, “You
know we should publish a paper on this,” because it’s extremely robust.
>>: So the premise of my question is: If I had to wait, maybe that waiting time gives me
information of the partner I have. So like I remember this quick guy or that is the slowest guy. I
always somehow see this guy.
>> Damon Centola: If I had to wait? It could be the case that you had a slow person, but some of
these networks, like if you are interacting with 20 people, or 24 people, or even more than that,
these games only take about 4 minutes. It’s hard to imagine you would develop that much of an
inference over that short of a period of time.
>>: So there is a possibility for leakage, but you don’t think it’s significant?
>> Damon Centola: I think that inference is a bit strained, but I can also just invoke the
methodology and say, “Right, but because of experimental randomization it is going to happen
equally in all conditions. So we are no worried about it with these results.”
>>: But don’t all systems, like you are unlikely to see a person for a second time?
>> Damon Centola: Well no, if you are in a lattice and you only have 4 neighbors, then you will
see them more than once. So I am going to show you the results for the lattice, the random, the
fully connected and what I am not going to do is present to you, like I said a social science thing,
where I give you a regression table with starts. I mean the beauty of the internet experiments is I
can just show you that you are supposed to not do this. I am going to show you the raw data. I
am literally just going to play for you what happened and it’s one of the beauties of this kind of
data I think because the actually time series has so much rich information, way more than you
can present in a paper. And you can actually just see it unfold. Yeah?
>>: The middle one, the standard graph, you still only has a few neighbors.
>> Damon Centola: The numbers of neighbors you have in the random and the lattice is the
same. The only thing you have to change is the diameter.
>>: So you are re-sampling neighbors in both of those 2, but not in the 3rd case?
>> Damon Centola: Well in the 3rd case you are also, but your neighbors are everyone.
>>: Right, I mean the third case [inaudible].
>> Damon Centola: That’s right. So what we are doing is it’s kind of, well it’s not exactly a
multi-arm chart, but it’s almost like that. You are saying, “All right, what happens if we hold
degree constant, but vary topology?” And it’s like, “Okay, diameter is about the same and we
are now we are changing these things.”
So this is kind of like the simulation I showed. So each node is a person and as they interact the
nodes light up, but now they have an unbounded set of options. So what’s going to happen is
when they choose an option they are going to light up a color and on the right hand side you are
going to see a histogram show up and the histogram has a bar associated with a color and then
the actual name? So you can read the names that people are using. It’s a real histogram. So as
more people use Sue and Sue is blue in fact then the histogram will become larger and it will
shrink if people start changing and moving away from Sue.
So it’s like this dynamic process and you can see the name list increase. You can also get a
sense of what the ecology looks like, how many names are in the population. Finally when
people interact the link lights up, but the link will light up the color of the interaction. So if they
coordinate, say they both choose Sue and Sue is blue, the link will be blue. If they don’t
coordinate, they choose different colors, the link will be white. These are real data. I show these
to people and afterwards they are like, “You know those simulations you showed at the end?”
It’s so frustrating.
So you can see very quickly –. Can people see this by the way? Do we need to dim the lights?
Yeah, okay. So, people start to coordinate very quickly. You can see the name Sarah is getting
popular over here, the name Alana is popular down here, Samantha is here, the other is a Julie
group and you can see what’s happening is that people are changing, they are coordinating and
they are failing to coordinate. Like ideas and names are percolating into a neighborhood and
then they are being sort of pushed back out again. Then there is some sort of dominance here
and it looks like that sort of area is going to grow, but then it get’s invaded.
And what’s really interesting here is what happens on the boards. The people on the boards are
in this sort of really difficult position where they are seeing some of their neighbors choose an
option and they are seeing other neighbors choose another. So basically they are seeing A on
one side, B on the other, A on one side, B on the other and something happens here which
doesn’t happen ever in the model, which is people do something spontaneous. Instead of just
trying to choose between A and B people get frustrated and they are like, “A, B, A, B, I don’t
know F,” and they just sort of try something new. Then sometimes F starts to percolate to the
network and people adopt that, but then these people wind up coordinating back with their
neighbors. So then they are back to A and B, meanwhile F has percolated across the network.
So unlike a diffusion process where there is this sort of swath behind a spreading contagion that
everyone has adopted. Here a contagion can spread through the network, but then its path or
show get’s eliminated by the coordination of the intervening people. Then it can show up far
away in the population. This is exactly how innovation diffusion works. You find independent
innovations showing up in these places and in between those two places we have not trace of it,
but it sort of takes hold in these different regions. What’s so interesting is that this is a very
organic and real process, it’s a real life process and we can replicate it in this kind of clustered
environment.
The most interesting thing that happens of course is that we fail. We fail to get global
coordination on the population. In fact what we get are these group, these competing group
structures, this group, that group, that group, that group, with these boundaries. This is very
much like what we see in real geographic networks. We see things like soda, and pop and Coke
being used regionally and across these boundaries people typically have to either try to
coordinate with one or the other or they stay on one side. This is party interesting because a lot
of scholars, when they look at these kinds of boundary effects in like ethnic diversity, and
linguistic practices and also in cultural practices, tend to assign group identity to people.
And they say, “Well the reason people do this kind of thing, the reason we see these boundaries
is because people have some sort of sense of belonging.” But of course here people have no idea
what these boundaries are and they have no idea that they are members of a group. Nevertheless
these group structures just sort of emerge as a function of the social network. Is there a
question?
>>: Yeah, what order are these listed in?
>> Damon Centola: Originally they were just showing up and then they get reordered based on
their popularity with the most popular ones that the top.
>>: So popularity within that order in which they appear?
>> Damon Centola: The sequence, yeah.
>>: Okay.
>> Damon Centola: And this is what I was taking about. You see like this section: gorgeous,
sexy, beautiful and blue eyes.
>>: It appeared in a row and didn’t catch on.
>> Damon Centola: It didn’t catch on.
>>: One must have caused the next.
>> Damon Centola: Well there is probably a sequence of responses and there are some here
where people really did kind of create a thing, like someone said, “Frances” someone said,
“Sherona,” and someone said, “Ferona”. They did sort of synthetic combinations of phonemes
trying to sort of coordinate with one another and one of them someone literally typed “copy me:
Simon”. Then someone else typed, “Simone” and then someone else typed “Simmone” spelled
differently and then someone else. So it kind of evolved a little bit. But what’s important about
this is that regardless of their attempt to out smart the system the structure dominated the
dynamics.
So it’s not as if, and this is the key point, it’s not as if is a particularly cleaver solution that could
solve the problem. The structure wouldn’t let the problem be solved.
>>: Did anybody every offer multiple choices, like A or B, I’m seeing them both?
>> Damon Centola: Oh, can it say like choose Francine or Sherona? I am sure at some point. I
mean the guy who typed in code, like when I displayed it took up 8 lines here, it was basic. I
don’t recall ever seeing that in particular, but I think that it would go to the point here which is
that it wouldn’t affect the dynamics in those kinds of choices. So our question then is: By
putting people into a network with a lower diameter where it is easier to sort of communicate,
does that make the problem easier to solve? It’s harder to see the structure here because there is
no geographic structure to the network, but if you look on the right you can see the histogram
and the size and the number of groups tells us something about the ecology and what that
ecology looks like as compared to the spatial network.
And what we see is pretty interesting because all of this topology is as different as can be and
from a diffusion perspective we say, “Well lattice and a random network are like the opposite
extremes for diffusion.” Actually, we see the same thing happening here; we see the same basic
ecological dynamics emerging, which is there is a small number of groups and those groups are
competing with one another and those groups have about the same size as they had in the spatial
network.
So it’s interesting because it means that essentially having this reduced topology, this sort of
reduced diameter in the network, didn’t affect the ecological co-evolutionary dynamics of norm
formation. So our question then is: Well does homogenous mixing solve the case? This one is a
man space. You can see we are getting men’s names. We did it with both men and women and
we varied this in all these conditions. There is gender parity across all. What you can see
happening here first of all there is a lot more names and there’s a lot more names because people
are interacting with strangers each time and with less repetition means the ecology explodes
more quickly, but also you have one name taking off. This is something we didn’t see in either
of the other two conditions. And it gains so much popularity so fast that it winds up swamping
all the other options in the population and going to global convergence very quickly.
So we look at these dynamics in terms of a time series and the x-axis of the time series and the yaxis is the popularity is the market share of any given norm. This is basically like a marker
ticker and if something goes to 1 everything else goes to 0, which is like this fraction of the
population that any given name has. So here you have a bunch of options competing, the most
successful one get’s up to .4, but then dives back down again. The other ones get to .4, but
nothing ever takes off in the spatial network. In the random network we see, as we saw
dynamically, we see exactly the same thing; options are competing, interestingly you see the
same think not just qualitatively, but quantitatively. The maximum size is about .4 and it dies
back down. Then of course you go over to the mixing case and you see something qualitatively
different where all of a sudden, very quickly one option takes off and reaches saturation.
Now one thing that is interesting to note about this is that people talk about critical mass
dynamics and when they do that the question almost always is, “How large is the critical mass?”
But if you notice this one get’s to .4 and never takes off, this one get’s to .4 and never takes off
and this one get’s to .3 and then takes off. If you just saw this you would say, “Oh .3 is the size
of the critical mass, it’s all you need,” but what that would be is a conclusion that is totally
insensitive to the structure of the network and how that governs these processes of critical mass.
The most interesting thing for me about this is that if we compare these dynamics to the
dynamics from our theoretical model they look identical, again not just qualitatively, but
quantitatively. You get groups of about .4 in both case, and no take off and here you get very
quick takeoff of the population to convergence.
>>: So what’s the model?
>> Damon Centola: The model is basically the naming game model. Two agents are playing this
game and they are trying to coordinate. The only difference between what humans probably do
and what they do in naming game model is if you do coordinate you delete your memory and if
you fail to coordinate you add something to your memory. So basically each round you try to
coordinate with one of your randomly chosen neighbors from the network and you pull from
your history of past plays. Then you use one of those and you dominate it and the nodes play
this game with each other. If they ever have success they delete their memory of past plays and
start over. But of course if they now have a failure then they start re-incrementing their history.
>>: Do they add the name that their partner plays to their history?
>> Damon Centola: That’s right, yeah. So it’s this incredibly simple sort of minimal model and I
will talk about it in a minute. We did some things to like elaborate it, but –.
>>: Is this theory plus simulation or theory plus theory?
>> Damon Centola: No the top level is the experiment –.
>>: No the bottom one, like the bottom one is theory and then you stimulate?
>> Damon Centola: Yeah, these are numerical. These are all basically taking an agent based
model that implements those rules and iterating ecology. And I’m showing that the ecology here
looks identical to the ecologies that we see. And in terms of the behavioral dynamics actually,
like the times that people repeat the same name, those actually look the same too. So it’s a fairly
good approximation of what humans are really doing in these kinds of coordination processes.
Now I told you before there were this sort of critical point in the dynamics, which means that
above a population size of 20 these dynamics generalize to populations of unbounded size. And
we know that from the theory and the theory is a pretty good fit for the data. With that said there
is still kind of an empirical curiosity, which is to say that fine, we got this, but what’s cool about
this is that got it so fast and in such a reasonable, empirical time scale, is it really true that if we
start increasing the population size these dynamics are the same?
So we doubled the size of the population. So we looked at basically 48 people. Now think about
this, you have to get 50 people sitting in a room essentially, but sitting at their computers, online,
all at the same time, engaged in playing this game, actually like actively trying to coordinate with
their neighbors and you want to see whether that produces global emergence on a short time
scale.
Remarkably that was as effective as it was for a population size of 24. So then we got excited
and we thought, “Okay we probably have something publishable.” But, then our question was,
“Well just out of curiosity, what if we doubled the population size again?” So now we have 100
people sitting in this sort of homogenous mixing space, interacting, will they also, in these same
dynamics be able to coordinate again? And the answer is, “Yeah, in fact the dynamics
coordinated on the same time scale.” This is remarkable because in the lattice people couldn’t
figure this out for 24, but you increase the population size by 4 times and in the fully connected
they are still figuring out on the same time scale. So it really drives home the point that network
structure is doing what the majority of the work in these coordination dynamics.
For those of you with like a physics or math background the underlying phenomenon here is
called symmetry breaking. What that means is that you have got a bunch of options bouncing
around and they are all symmetrical in the sense that any of one them can win and that’s signaled
here by basically this “if” distribution. So anyone of them, even the low ones, can kind of pop
up and take dominance. What happens here at this really special point, where this is this sort of
breaking, where all these options are down here and this option starts to trend up is you can see a
shift in this distribution.
Now a shift in a distribution which becomes steeper and steeper means that one option has a
larger and larger fraction of the sort of global market share. These other options start to go to
extension and it becomes less and less likely. And at a certain point is reaches 100 percent
certainty that the one option is going to go to fixation. So this is not like a voting model where it
can kind of go back and forth at all times. All right. What happens here is that even though the
options haven’t all gone to extinction, it’s a mathematical certainty that they are going to. And
symmetry breaking is a very cool thing. A couple of people have won a Nobel Prize for this at
the subatomic level. It’s phenomenal to see this is exactly what the models predict, but we see
the same symmetry breaking dynamics in human populations and we compare them side by side
and we say, “Here’s our spatial and our random networks compared to our homogenous mixing
networks.” It’s a demonstrably clear and causal pattern, right.
We published these proceedings in the national academy and this is one of those few papers that
were like you know in PANS you can make a major classification and a minor classification. So
the major one was social science and the minor one was physics. That rarely happens, but I was
obsessed with putting a “P” value in and my colleague in this paper, Andrea [indiscernible] is a
physicist and was like, “A ‘P’ value, why do you need a ‘P’ value, just look at it. What do you
need a ‘P’ value for?” And he is right, just the evidence has manifest that there is a clear,
underlying effect of network structure on generating this to create a winner take all society.
Yeah?
>>: Is critical mass defined to be a mass such that when you reach it you are unlikely to go back
down?
>> Damon Centola: Well people misuse the term. I mean Everett Rogers misuses the term, but
the actual technical term would just mean it would be an unstable fixed point. It would be an
unstable fix point below which you collapse down to the stable attractor and above which you
grow up to the stable attractor. That would be a technical, critical mass. So that wouldn’t be
detectable on a time series.
>>: So if that’s your definition that would seem to imply that when you haven’t played enough to
have anybody have reached critical mass, that whatever is the biggest thing at the moment is
actually unlikely to develop into the eventually winner. Probably everything is going to fall back
down and somebody is going to get lucky, but it’s going to take a long time.
>> Damon Centola: At some point, yeah.
>>: But that doesn’t seem to be exactly what happens. It seems like within a fairly short amount
of time, even when you increase the system size, something pops up to this level. So maybe
critical masses happen a lot earlier or something.
>> Damon Centola: Well, critical mass, I mean the right way to think about critical mass is when
the size of the group saying one option is large enough then you have kind of shifted the basin of
attraction. You are now in the upper basin and you are going to grow. The interesting thing
about this is this is a time scale issue. So look if you run this for infinite time with noise then
yeah, the lattice will ultimately converge an infinite time with noise, because it’s infinite time.
The point is on a reasonable, tractable time scale you are getting this breaking process.
And the reason that critical mass is not the most helpful concept for looking at this figure is
because even in the lattice, if you run it for millions of iterations and it get’s to 99 percent 1
option and 1 percent the remaining option, even at that point it can reverse, because symmetry
isn’t broken. It is always possible to reverse in the lattice, whereas what’s happening here is
something really different. It is irreversible; once it breaks it breaks. That option goes to
saturation.
>>: Yeah, maybe the breaking criteria are that you are a lot bigger than the second biggest or
something like that.
>> Damon Centola: Yeah, exactly that’s this “if” distribution. Once the distribution becomes
skewed enough, right then –.
>>: Just looking at the graphs, once there is separation between the top and the next one –.
>> Damon Centola: Well I mean this is the more helpful one for talking about symmetry
breaking. I am going to quickly finish up though, sorry.
Do people remember this? So then this goes to the question of critical mass. One of the things
to think about is, “Well if you do get systematic dominance of one option in a world you know
this was a world in which no one was trying and it just happens all by itself endogenously ever
time. So it’s a causal claim. Then the question is, “Well geeze, doesn’t that mean that people
can hijack the system really easily?” If it goes to a fixation endogenously what if someone
wanted to do that?
So I was out at [indiscernible] last year and so I was at one of these like Silicon Valley cocktail
parties and someone was like, “Isn’t this related to your research?” And I was like, “What, that
no, of course not,” but then of course it is. And I was like anytime you get like large scale
coordination that’s polarized on an option there has got to be some underlying social process
going on there. It’s not as if everyone’s eyes either see one color or another color. There I some
kind of social coordination going on. So our question was, “Could we hijack this coordination
process and control it?”
So I had my grad students run this where we played the name game with that and gave them a
list of options they get to type in. So unlike the previous one it wasn’t open text, it was just you
had a list of 6 or 7 options, but black and blue and white and gold of course were the popular
ones. So we drove it to coordination on black and blue and the question was, “Now if we have
got 100 percent coordination on this can we overturn the norm?” So we started typing in white
and gold, getting a small group, this is the committed minority of the critical mass to try to
overturn it. Then you have got this flipping effect and then white and gold wound up taking
over.
And what’s interesting about this is that you have a bunch of people here saying one option and
then over here saying another option and there fundamental goal is to coordinate so they are
driven by this idea of what people are saying, but it took a minority to get it off the ground. So
with the smaller group kind of being active enough in pushing an option it was successful in
changing the norm. Now of course the question then is how general could this be? What kinds
of norms could we overturn? What kinds of things could we change?
>>: What was the network structure for that?
>> Damon Centola: That was fully connected. That’s important because first of all global
convergence really only happens there. So getting shifting also is important for that
connectedness.
So I gave this talk at IPAN, it’s for applied mathematics at UCLA and someone in the audience,
who looked like that guy and said, “You know you can get this for names, but you are getting
names that look like the people. You can never get the name like –,” and he said like a minority
female name for himself. And I thought, well this is perfect because it is exactly the point I am
making, like just how dead wrong he is. He has got this intuition that the norm of a name is
somehow fixed in the universe, even though it is endogenously emerging here, there is some
kind of way in which norms are in principal bias by these sorts of things.
So we ran this and our question was, “If we put in other names into the population could we get
it to evolve in a different way?” So if you look at a face like that and you say, “Okay well the
red option is bouncing around, then the green option, then the blue option and they are all kind of
tied around here.” Then the red takes off and red and green are tied and then red ultimately wins,
the question is well what’s that red option or what could it be? And these were the names: so
we had Nia, Eric, Sean and Hans and if you look at a face like that you say, “What’s the most
likely name?” But, Nia is the one actually won.
And this tells us something about these spaces, which is that norms are flexible, people can
actually be encouraged to adopt or change their beliefs based on what the other people in the
ecology are doing. And even though there is sort of some resistance, maybe initially, these
actually can evolve in surprising ways. And this gives us some intuitions about the applications.
I think that there is really interesting work done by Cecilia Ridgeway at Stanford, she is a social
psychologist, on how certain traits that are thought about as influential or status characteristics
aren’t just fixed in the universe, aren’t just fixed biologically, but they emerge socially. I think
that’s one of the really interesting things we can explore in this kind of space. How status and
social dominance can emerge and shift based on online interactions.
Of course one of the major applications that people always think about is in health, because in
health, again these things aren’t binary. You don’t just diet or not diet. You have to choose a
diet, you have to stick to it, and you have to adjust it. You don’t just exercise or not exercise.
You have to choose an exercise for T many times a day, what kind of intensity, etc. These things
all have sort of a qualitative free form nature to them and they are all calibrated based on what
other people are doing.
So our question is, “Well if we put people into environments like in a health environment, can
we actually evolve these norms in ways that are based on people’s endogenous interactions?
And the answer is yes. We published a couple of projects this fall that have been doing this in
online health networks. And of course I think one of the most interesting things to think about is
thinking about collective coordination not just on any social norm, but on an accurate social
norm. On a social norm that actually is beneficial. And the space of collective intelligence and
collective problem solving is really interesting here because we have these social processes
evolving in a lot of different places and we want to know whether one pattern of connectiveness
can actually affect the quality of the decision that people come to and of course finally whether
or not this matters for effecting social change. I think one of the interesting implications here is
that even if people don’t know that they are coordinating on a global scale their coordination
nevertheless can wind up being a sort sweeping change in behavior which means that a small
number of people who have an agenda can actually shift a very large population in terms of their
opinions and norms. So the question I still have to answer is, “Can social norms or conventions
emerge endogenously without any institutions governing the process?” And the answer is yes,
but it depends decisively on the connectedness of the population.
When people can innovate independently and coordinate locally actually greater connectedness
facilitates this, which means that in traditional spatial geographic networks you would find
clustered groups with competing views. But in the highly connected space of online interactions,
where people are interacting more and more with strangers, more and more with on these one off
interactions actually you have the capability, and in fact in some sense, the certainty of large
scale shifts in beliefs, attitudes, and norms just emerging endogenously and also capable of being
hijacked by small groups.
So I will take your questions. This is the thing we are running now, the application to collective
intelligence. The Annenberg Data Science Competition, which is going to be going live. We are
actually starting to run it now, which is basically running these kinds of experiments, but looking
at people solving hard data science problems. Okay, thank you.
[Applause]
Yeah?
>>: So what would happen if you replaced the lattice graph with just the ring graph? Is that too
simple?
>> Damon Centola: No it’s fine, they are both one dimensional. The dimensionality of the graph
is what governs the dynamics. So if you are saying a ring –. Well I mean that was actually a
ring graph in the sense that it’s two on the right and two on the left, but that was a one
dimensional lattice. So the dynamics are the same in one dimensional and 2 dimensional lattice.
But if you are just saying one neighbor on each side the dynamics are the same as having 2
neighbors on each side, and so on and so forth. Yeah?
>>: So your one dimensional thing, your ring thing, actually random [indiscernible], in your 24
first data set, those behaved very similar. So I think that’s because they are similar when the
neighborhoods are that small, but if you have a bigger, when you look at 100, we saw what
happened in the third condition. It was very different, but do the first 2 start to distinguish
themselves from each other at that point?
>> Damon Centola: Not because of scale, but because of time. So the big difference here is
between the lattice and the four connected. In fact the random network is interesting because it
is kind of a hybrid case. Because of the point that you are making, because of local connectivity
it has similar dynamics to the lattice, up to a point. Now up to the point isn’t a scale question,
it’s a temporal question. So the real question is like, “How does the time to convergence scale
with size?” And it’s like N with the lattice, but it’s like root N with the fully connected and it
winds up being like root N with the random as well, because you actually can get symmetry
breaking out of the random network. So the small connectivity is actually fighting against the
diameter. So as the diameter get’s smaller and smaller you actually tend towards dynamics that
look more like the fully connected network. Are there any other questions? Well thanks guys,
thanks for coming.
[Applause]