The following chart represents a network of the entire population of a fictional and very small town. Each circle represents a person. Two people who know each other are connected by a line. People who are not connected by a line have never met.

The day’s political issue: whether baseball caps are fashionable. Each circle is colored to indicate that person’s stance on the issue. Blue circles think they are fashionable. Orange circles think they are not. (On this issue, everyone has an opinion.)

The town will be voting on whether to officially consider baseball caps fashionable. A polling firm recently asked whether each person thought baseball caps would get a majority of support.

Assume each person based their vote solely on how the people they know would vote (excluding his or her own view).

Did the polling firm find the measure was expected to pass or fail?

Pass
Fail

Select an answer above to learn about the experiment and how it can affect changes in public opinion.

That’s right. Based solely on their friend networks, most people think the measure would pass.

Actually, that’s incorrect. Based solely on their friend networks, most people think the measure would pass.

Taken at face value, the result seems odd. Only three people think baseball caps are fashionable. But, as shown in these charts, most people think almost everyone else is for baseball caps.

The first chart cycles through what the network looks like to each person. Remember, each person only knows about part of the network.

The second chart lays out each of these individual views. As you can see, most people think baseball caps are not fashionable (represented by orange circles). But most have a majority of friends who are for baseball caps (blue circles).

The majority think they’re in the minority. Or, “the few shaping the opinions of the many,” as network researcher Kristina Lerman described it.

Lerman calls this the “majority illusion.” It’s our flawed perception of some networks that relies a logical proverb: We just don’t know what we don’t know.

And in some networks, the information we do have, our sliver of local knowledge, can lead us to the false conclusion.

Whether this fictional town endorses baseball caps is rather innocuous. But paradoxes like the majority illusion apply concretely to our world, from the way we fight drug epidemics to how quickly public opinion sometimes flip flops. Understanding the theory behind them gives essential insight into why people form the opinions and make the decisions that they do.

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In the example above, the people who think baseball caps are fashionable tended to know more people. Networks with this property – those with a correlation between popularity and a specific opinion – are susceptible to the majority illusion, according to Lerman’s research.

Earlier research into a simliar paradox has repeatedly shown statements that seem to contradict themselves are mathematically true: Most of your friends on average have more friends than you, tweet more frequently than you and even drink more alcohol than you.

This quirk is caused by a diverse network with ultra-popular hubs. The @justinbieber’s of the world skew the results for the rest of us. (Math nerds: Lerman’s research group has shown this holds in some networks even when taking medians, not means.) This conundrum, called the “friendship paradox,” is closely related to the majority illusion.

This illusion may have been behind the swift change in public opinion on the issue of same-sex marriage.

Republican pollster Glen Bolger told The Fix’s Chris Cillizza in June he thought the opinion change happened at the interpersonal level.

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“I think the shift is because as more and more gays came out of the closet, people realized they know gays personally, and that makes a huge difference in attitudes,” Bolger said.

This personal persuasion effect is well-known. But Lerman’s research pushes it further, examining how different configurations of networks can catalyze such a change of opinion.

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A person with a large audience spreads his or her opinions much more widely than the average person does. By definition, he or she has many more connections, which means more people are on the receiving end of the opinion. This gives a celebrity’s opinion outsize influence, affecting the local perspectives of many.

If same-sex marriage proponents tend to be more popular in a network, then, by the same logic, their opinion would seem more prevalent than it actually is.

Since people base their decisions on the behaviors of others, as Lerman’s research notes, this can cause mass changes in opinion over time.

Polling is an effective antidote to the majority illusion. If people have an accurate sense of where an entire population stands on an issue, the influence of a biased local network is lessened. One may not personally know any Republicans who would vote for Donald Trump, for instance, but polling shows many would.

But not all issues have as much polling as presidential races – or any polling at all. And without that global knowledge, the majority illusion can be a factor.

Lerman suspects the majority illusion and related paradoxes were factors in the same-sex marriage opinion shift, noting the change was likely well underway before pollsters started providing global knowledge.

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The applications of these discoveries are subject only to imagination. Lerman floated these ideas as potential research areas:

  • Fighting HIV in Africa: Instead of vaccinating a random group of people, vaccinate their friends. The “friendship paradox” states their friends will most likely have more friends and are therefore more center to the overall network.
  • The role of mass media: Lerman thinks the Arab Spring movement gained traction at least partially because mass media, by definition, is a “hub” in many networks. By covering demonstrations, the many people connected to media organizations saw others demonstrating and joined in themselves.
  • Alcohol abuse on college campuses: Since the “friendship paradox” holds that on average your friends drink more than you do, raising awareness of this quirk could give understanding to those who feel pressured to increase their own drinking.

“Right now, connections to the real world are few, but we are just now starting research,” Lerman said.

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