20bits: Two Models of Behavior Adoption in Social Networks
Mike Sellers
· 8 months ago
Without going to physical statistical models (though they're a good place to go), I see both the threshold and cascade as variants of the same underlying mechanism as well.
The random factor in the cascade model exists as part of the model only because we do not know the weight of an individual relationship in terms of its degree of influence. Put another way, if the weight in threshold model is described as a probability [0,1] that an individual will follow the influencing person's lead, then we can aggregate all such influences (not necessarily by simple addition) to describe the threshold and cascade function.
To make that more specific, if three guys at work extol a particular idea, they will each have a variable effect (based on your trust in their opinion -- it's not random) on whether you start thinking positively about this idea as well. The aggregation matters: if you think highly of two of them and detest the third, the probability is less than if you trusted the opinions of all three. If however another far more influential person (a well-known blogger or celebrity) also extolled that position, that influence would have a disproportionate effect on your opinion commensurate with your trust in that person's opinion.
The mechanism bears a significant similarity to dendritic summation in neurons and probably other similar phenomena; it's not restricted to social contexts. Variable weight inputs aggregate in terms of their influence or effect, encompassing both what you have called cascade and threshold.
Oh, it's also worth noting that (as in neurons :) ) the *absence* of input can be important too -- this is likely part of what drives early adopters. For them, getting high-influence input from a few trusted individuals isn't sufficient to trip the threshold; there must also be a lack of ambient input. That is, if everyone else is already doing it, the early adopter loses interest. The variance in reliance on a few high-trust inputs without ambient input or many more ambient low-trust inputs describes the spectrum from early adopter to laggard in any population.
Jesse Farmer
· 8 months ago
Interesting. I'm working on a viral growth visualization project and was describing it to people as a sea of neurons. Diffusion of information or behaviors in the social network follows a lot of the same principles, as I understand it, e.g., all-or-nothing.
Do you have any information about actual formal models of these phenomena? The more math the better!
And thanks so much for the comment — really awesome.
Mike Sellers
· 8 months ago
I do have some formal models for this, but I'm not aware of any that have been published -- if you run across any I'd be interested to hear about it. The models I have are what we use to drive our "social context" software, and so we don't really give them out. :)
In both social and neural cases, there are interesting blends of all-or-nothing and smooth ramps of transmission. Any given neuron fires or doesn't, but can fire with different intensity -- and it can have a variable excitatory or inhibitory effect on other neurons. Similarly, someone can pass an opinion to someone else (or not), and then there are several other factors that come into play: how strong is the opinion, and how much does the receiver believe it. Then there are things like personality factors that moderate whether the receiver acts on the information and/or tells others about it, which starts the cycle over again.
At a simple level, you need to have people tell more than one person about a cool new idea or product to give it virality. How much more than 1 depends on the other probabilities -- but higher values increase spread quickly.
cindyalvarez
· 8 months ago
You explicitly said that this doesn't include innovators, but I think that's an important thing to consider. The very earliest adopters aren't trying a new thing because they have some percentage of friends using it; rather, the motivation is that they DON'T know anyone using it yet. They want to be able to be part of that first 1%, to be the originator of the trend.
Why is this important? Because, as the provider of the social network, it's in your interest to build in a way to recognize these innovator/pioneers. Offering something equivalent to "a low ICQ number" or marking the user's avatar can drive these initial innovators, which, in turn, creates the 5% necessary to start the Threshold condition.
Jesse Farmer
· 8 months ago
Cindy,
Good point.
The way I see most social networks (and social apps) growing is by bootstrapping through the cascade model, until they're dense enough in their parent network that they become self-sustaining and threshold psychology becomes the dominant factor.
The risk with being too aggressive with invites early on is that you never build up the density to become self-sustaining. By promoting early adopters and keeping them engaged, you can help foster the core density from which your social network can grow organically.
FWIW, although Facebook bootstrapped by spamming everyone in Harvard, they grew with the threshold model in mind from day one. As I understand it they never even considered signing up a new campus until there were at least 40 people from that campus requesting accounts. And they started with smaller campuses where density as easier to create and sustain.
Mike
· 8 months ago
Is it possible that these are the same model? The transition from one model to the other sounds a lot like the phase transition studied by statistical physicists (e.g., Ising models).
Jesse Farmer
· 8 months ago
Interesting. I don't know anything about statistical mechanics. Can you elaborate?
bgoncalves
· 8 months ago
Yes, both "models" are simple forms of an Ising system (paramagnetic and ferromagnetic). The Threshold is the coupling to an external field and Wuj are the couplings between nearest neighbors along the edges of the network. Research in similar models (mostly in the context of magnetism) has been on-going since the 20s (see http://en.wikipedia.org/wiki/Ising_Model )
jasonwatkinspdx
· 8 months ago
Good article.
One feature you may be missing is preferential attachment. Celebrities like scooble and oprah have drawn in a huge volume of twitter users. Myspace had similar dynamics due to bands in it's early days. The growth of graphs under preferential attachment is formalized and it's characteristics mostly well known:
Indeed, and thanks for taking the time to read and comment!
Celebrities and the like are an interesting phenomenon in social networks. They are always highly connected, moreso on directional SNs like Twitter and MySpace, but the extent to which they are influenced or cause influence are much more ambiguous. Their effect on behavioral and opinion dynamics is probably a research topic all in itself.
And I actually wrote a Ruby script to generate BA graphs just the other day!
JaySmith
· 3 months ago
Very confusing post. Not sure I quite soaked in all that info. Can someone elaborate?
All Comments
The random factor in the cascade model exists as part of the model only because we do not know the weight of an individual relationship in terms of its degree of influence. Put another way, if the weight in threshold model is described as a probability [0,1] that an individual will follow the influencing person's lead, then we can aggregate all such influences (not necessarily by simple addition) to describe the threshold and cascade function.
To make that more specific, if three guys at work extol a particular idea, they will each have a variable effect (based on your trust in their opinion -- it's not random) on whether you start thinking positively about this idea as well. The aggregation matters: if you think highly of two of them and detest the third, the probability is less than if you trusted the opinions of all three. If however another far more influential person (a well-known blogger or celebrity) also extolled that position, that influence would have a disproportionate effect on your opinion commensurate with your trust in that person's opinion.
The mechanism bears a significant similarity to dendritic summation in neurons and probably other similar phenomena; it's not restricted to social contexts. Variable weight inputs aggregate in terms of their influence or effect, encompassing both what you have called cascade and threshold.
Oh, it's also worth noting that (as in neurons :) ) the *absence* of input can be important too -- this is likely part of what drives early adopters. For them, getting high-influence input from a few trusted individuals isn't sufficient to trip the threshold; there must also be a lack of ambient input. That is, if everyone else is already doing it, the early adopter loses interest. The variance in reliance on a few high-trust inputs without ambient input or many more ambient low-trust inputs describes the spectrum from early adopter to laggard in any population.
Do you have any information about actual formal models of these phenomena? The more math the better!
And thanks so much for the comment — really awesome.
In both social and neural cases, there are interesting blends of all-or-nothing and smooth ramps of transmission. Any given neuron fires or doesn't, but can fire with different intensity -- and it can have a variable excitatory or inhibitory effect on other neurons. Similarly, someone can pass an opinion to someone else (or not), and then there are several other factors that come into play: how strong is the opinion, and how much does the receiver believe it. Then there are things like personality factors that moderate whether the receiver acts on the information and/or tells others about it, which starts the cycle over again.
At a simple level, you need to have people tell more than one person about a cool new idea or product to give it virality. How much more than 1 depends on the other probabilities -- but higher values increase spread quickly.
The very earliest adopters aren't trying a new thing because they have some percentage of friends using it; rather, the motivation is that they DON'T know anyone using it yet. They want to be able to be part of that first 1%, to be the originator of the trend.
Why is this important? Because, as the provider of the social network, it's in your interest to build in a way to recognize these innovator/pioneers. Offering something equivalent to "a low ICQ number" or marking the user's avatar can drive these initial innovators, which, in turn, creates the 5% necessary to start the Threshold condition.
Good point.
The way I see most social networks (and social apps) growing is by bootstrapping through the cascade model, until they're dense enough in their parent network that they become self-sustaining and threshold psychology becomes the dominant factor.
The risk with being too aggressive with invites early on is that you never build up the density to become self-sustaining. By promoting early adopters and keeping them engaged, you can help foster the core density from which your social network can grow organically.
FWIW, although Facebook bootstrapped by spamming everyone in Harvard, they grew with the threshold model in mind from day one. As I understand it they never even considered signing up a new campus until there were at least 40 people from that campus requesting accounts. And they started with smaller campuses where density as easier to create and sustain.
One feature you may be missing is preferential attachment. Celebrities like scooble and oprah have drawn in a huge volume of twitter users. Myspace had similar dynamics due to bands in it's early days. The growth of graphs under preferential attachment is formalized and it's characteristics mostly well known:
http://en.wikipedia.org/wiki/Barabási-Albert_model
Celebrities and the like are an interesting phenomenon in social networks. They are always highly connected, moreso on directional SNs like Twitter and MySpace, but the extent to which they are influenced or cause influence are much more ambiguous. Their effect on behavioral and opinion dynamics is probably a research topic all in itself.
And I actually wrote a Ruby script to generate BA graphs just the other day!
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