The power of bloody-mindedness

There's a surprising amount that's already known about how ideas spread in different circumstances, both theoretically and observationally. For example, it's been found that if 10-15% of sources contradict an established belief, there's a strong backfire against believing them (e.g. one local lunatic down the pub) - but if the number exceeds around 30%, then the backfire effect drops away (the idea has become mainstream). Similarly, if around 25% of the population believe something, there's a good chance it can completely overturn the existing prevalent idea. We also know that expectation influences belief in a Bayesian-like fashion, that the presence of even a few individuals who are immune can stifle the spread of an idea, and that if 3.5% of a population take part in a non-violent protest, they're virtually certain to be successful.

This new study makes a different claim. It says that the tipping point for a minority belief can be as low as 10%. Why the difference ? Does this overturn the previous findings ? Is this another example of a replication crisis ?

No. Remember, all scientific statements carry with them implicit assumptions. This is especially true for press releases, which in general like to paint a ridiculous black and white picture, neglect any and all assumptions, and degrade research to the status of right or wrong. Not this one though. It's very explicit about what the authors did :

Scientists at Rensselaer Polytechnic Institute have found that when just 10 percent of the population holds an unshakable belief, their belief will always be adopted by the majority of the society. An important aspect of the finding is that the percent of committed opinion holders required to shift majority opinion does not change significantly regardless of the type of network in which the opinion holders are working. In other words, the percentage of committed opinion holders required to influence a society remains at approximately 10 percent, regardless of how or where that opinion starts and spreads in the society.

This is quite clearly not describing the general case. I'm not sure it's true that, "In general, people do not like to have an unpopular opinion and are always seeking to try locally to come to consensus", but it's obvious that a core of zealots is not a general rule. But it's not unimportant by its rarity either. I only skimmed the actual paper (it's not an easy read) where they note :

There are several historical precedents for such events, for example, the suffragette movement in the early 20th century, and the rise of the American civil-rights movement that started shortly after the size of the African-American population crossed the 10% mark.

And these results are model-dependent simulations (that is, they may not depend on the network structure, but they may depend on the model of interactions and persuasion used) :

Each of the individuals in the models "talked" to each other about their opinion. If the listener held the same opinions as the speaker, it reinforced the listener's belief. If the opinion was different, the listener considered it and moved on to talk to another person. If that person also held this new belief, the listener then adopted that belief.

Once the networks were built, the scientists then "sprinkled" in some true believers throughout each of the networks. These people were completely set in their views and unflappable in modifying those beliefs. As those true believers began to converse with those who held the traditional belief system, the tides gradually and then very abruptly began to shift.

I guess this is a simplified approximation, but the obvious question is how someone reaches a truly unshakeable belief. Everyone starts off life believing nothing much of anything, so all beliefs are formed. How and why do they sometimes become irreversible ? Does this ever truly happen in reality, or are the models simply saying that these agents have such strong convictions that overturning them is effectively impossible in the conditions they experience in the simulations ? It's also unclear to me if their model accounts for individuals varying in how easy they are to persuade (they speak of "binary agreement models" and "opinion dynamic models", but I don't know anything about these) or if it's a case of agents being either open to persuasion or not, or if the agents could ever lose confidence in their beliefs.

Still, the result strikes me as a credible one, providing we remember the assumptions. If you have a group who are mostly open-minded but 10% are absolutely convinced, it seems reasonable to me that that could be enough to convince the majority. Of course, if you also had 10% who are absolutely opposed, then the result might be different. And they note in the paper :

The binary agreement model is well suited to understanding how opinions, perceptions or behaviors of individuals are altered through social interactions specifically in situations where the cost associated with changing one’s opinion is low, or where changes in state are not deliberate or calculated, but unconscious.

Or in other words this result may not hold in the case of changing a belief having a (social) cost associated with it, or being so complex that it requires careful thought. Keeping all those factors in mind, this is still a very interesting result - one which sounds relatively easy to test.

Minority rules: Scientists discover tipping point for the spread of ideas

Scientists have found that when just 10 percent of the population holds an unshakable belief, their belief will always be adopted by the majority of the society. The scientists used computational and analytical methods to discover the tipping point where a minority belief becomes the majority opinion.