Deluding the majority on denier blogs like @wattsupwiththat

You'll often see comments like these at WUWT, suggesting that people think that everyone just knows that climate science is a scam or a fraud or a hoax or global cooling is about to start. Many deniers are under the illusion that fake sceptics constitute the majority. They are wrong. There is a phenomenon that might go part way to explaining the delusions of deniers. (The comments below are all from just one article at WUWT):

Chris Marlowe says:

January 16, 2014 at 4:29 am
The smartest of these guys will be looking for an exit strategy and will eventually look the other way if anyone suggests they were once on the bandwagon beating the drum.

Stephen Richards says:

January 16, 2014 at 4:36 am
What I don’t want is for these guys to remain in place when this whole scam is exposed. Like Erlich they will just keep coming back with another scare for money scheme.

Henry Galt. says:

January 16, 2014 at 5:05 am
The Cl(imate/imatology)(P/C)ause.
My take on “The Clause”:
CS due to 2xCO² is ≤ 0.000°K à la Ferenc Miskolczi.
Back-pedalling grant seekers are barfing up lower and lower guesswork for CS as time passes, we get colder and the 0.000°K part becomes increasingly obvious.

How delusions spread

There's a new paper lodged at arXiv.org, which may help explain the apparent delusion of some climate science deniers. Those who wrongly think that they are in a majority, when the reality is that it's a minority of people who reject climate science. The paper is also discussed in the MIT Technology Review from a marketer's perspective.

The Friendship Paradox

There is a paradox known as the friendship paradox, which says that on average your friends will have more friends than you do. That's because people having lots of friends (or seen to have them) are more likely to be numbered among the friends of any one person. Or, in the words of Scott L. Feld (1991):

The basic logic can be described simply. If there are some people with many friendship ties and others with few, those with many ties show up disproportionately in sets of friends. For example, those with 40 friends show up in each of 40 individual friendship networks and thus can make 40 people feel relatively deprived, while those with only one friend show up in only one friendship network and can make only that one person feel relatively advantaged. Thus it is inevitable that individual friendship networks disproportionately include those with the most friends.

Extending the paradox to The Majority Illusion

This phenomenon has been generalised to other things. Kristina Lerman and her coauthors explain in their new paper:

For example, your co-authors are cited more often than you [13], and the people you follow on Twitter post more frequently than you do [19]. In fact, any attribute that is correlated with degree will produce a paradox [13, 23]. Thus, if heavy drinkers also happen to be more popular, then people examining their friends’ drinking behavior will conclude that, on average, their friends drink more than they do. 

The paper makes what they call a novel observation, extending this phenomenon to what they call contagious behaviours. They describe any attribute (or behaviour) that is binary, such as "has red hair" or denies climate science (though they didn't use that last example). They explain that under some conditions, this can create what they term a "majority illusion".

The paper includes a diagram to illustrate the "majority illusion". In the two diagrams below, the two networks are identical, except for which three nodes are colored. These are the “active” nodes and the rest are “inactive.” Let's say the red nodes represent people who deny climate science.

In the first network below, all “inactive” nodes observe that at least half of their neighbors are “active" - or at least half their neighbours think climate science is a hoax.

All “inactive” nodes observe that at least half of their neighbors are “active”

In other words, looking at the network above, despite the fact that only three out of 14 people in their network believed that climate science is a hoax, each person in the network would think that half the people think it's a hoax.

In this second network, identical to the one above except for which nodes are active, no “inactive” node sees that many "active" nodes. In other words, the most that any inactive node sees is that maybe two people think that climate science is a hoax, and lots don't even see one denier.

Threshold to adoption

The paper goes on to discuss the impact on behaviour in terms of thresholds. In the top two diagrams, after a time interval, people will change their behaviour if a certain threshold is reached. For example, if the threshold is a (perceived) majority, then when each person thinks that more than half the people in their network think that climate science is a hoax, then they'll adopt that position as well. What that means is that over time, all the people in (a) above will eventually adopt the position that climate science is a hoax. That's because as each person sees the majority is a "climate hoax" conspiracy theorist, they will become a denier as well. I've animated the top diagram to illustrate this:

This can only happen with diagram (a). It can't happen with (b) above because the 50% threshold is never crossed for any of the "inactive" nodes. (Fifty per cent is an arbitrary cut-off. The threshold could be lower or higher.)

The authors spend some time on the maths, and on empirical observations in the real world. In the discussion they write about how local prevalence can be very different from the wider world, but can trigger an avalanche:

Local prevalence of some attribute among a node’s network neighbors can be very different from its global prevalence, creating an illusion that the attribute is far more common than it actually is. In a social network, this illusion may cause people to reach wrong conclusions about how common a behavior is, leading them to accept as a norm a behavior that is globally rare. This may explain how global outbreaks can be triggered by very few initial adopters, and why people overestimate how much their friends engage in risky behaviors, such as alcohol and drug use.

The power of high degree nodes in disassortive networks

Linking it back to the friendship paradox, the authors write how the "'majority illusion' can ultimately be traced to the power of high degree nodes to skew the observations of many others".  As I understand it, high degree nodes are like the people with lots of friends in the "Friendship Paradox" described above. However it depends on the networks. They write about the difference between disassortive and assortive networks.

• In disassortative networks, nodes prefer to link to dissimilar nodes.  An example is a star composed of a central hub and nodes linked only to the hub. Political networks were cited as disassortative. 
• In assortative networks, nodes were said to have a tendency to link to similar nodes ie high-degree nodes to other high-degree nodes. 

The authors state:

Specifically, we showed that the paradox is much stronger in disassortative networks, where high degree nodes tend to link to low degree nodes. In other words, given the same degree distribution, the high degree nodes in a disassortative network will have greater power to skew the observations of others than those in an assortative network.

The WUWT illusion

Given that political blogs, like WUWT, would be considered a disassortative network, you can see how the crazy ideas posted there spread easily through the deniosphere.

I'll take the liberty of extending beyond the paper. Below is what a normal person would see when they visit WUWT - with the red dots representing some crazy new idea, like that NOAA has "fudged" the temperature data. All Anthony Watts has to do is seed the idea and almost everyone at WUWT picks it up as the gospel truth. Anthony is in the centre - he's the "hero" to thousands after all. It could equally well be the potty peer or conspiracy theorist Tim Ball:

From there the fake story spreads through the deniosphere. You'll notice that I've left just one node white. Anthony has to keep one normal person commenting on his blog so his fans have someone to flame. Let's call him Nick Stokes :)

My take-away: Shattering the Illusion

What I take from this idea is that it's important to show the illusion for what it is. People who venture into hostile denier territory like WUWT to scatter a few seeds of reality are the real heroes. It also demonstrates the importance of papers like Cook13 - the 97% paper.

References

Kristina Lerman, Xiaoran Yan, Xin-Zeng Wu. "The Majority Illusion in Social Networks." arXiv:1506.03022 [cs.SI] (open access)

The Social-Network Illusion That Tricks Your Mind - article about the paper in MIT Technology Review.

Feld, Scott L. "Why your friends have more friends than you do." American Journal of Sociology (1991): 1464-1477. (open access on registration)