You may have seen one of those science articles in the news, about opinions. It was not an experiment with people, but a computer experiment modelling three types of social network with different properties concerning how the nodes were connected to each other.
The summary at Livescience reflects all the others reported elsewhere.
In all cases, a few people within the network held an unwavering, but uncommon, belief; everyone else held a traditional view but was open-minded. They found that, regardless of the type of network, 10 percent remained the threshold required to shift the majority opinion once the true believers began to speak with everyone else.Now, I was a bit sceptical of this - if you dig for the actual journal article this kind of report is based on, it often turns out to say absolutely nothing of the kind. So I did the digging, and Google Scholar found me the article. It doesn't seem to be in the journal that Livescience said it was, but the authors have previous articles in that journal, so perhaps it will be. You can nearly always find them, anyway, if you have the authors' names and the year.
Social consensus through the influence of committed minoritiesFor the time being you can actually download the whole thing in PDF, I had to skip over the mathematical parts but I know some readers won't need to, and might be interested.
J. Xie, S. Sreenivasan, G. Korniss, W. Zhang, C. Lim, B. K. Szymanski We show how the prevailing majority opinion in a population can be rapidly reversed by a small fraction p of randomly distributed committed agents who consistently proselytize the opposing opinion and are immune to influence. Specifically, we show that when the committed fraction grows beyond a critical value p_c \approx 10%, there is a dramatic decrease in the time, T_c, taken for the entire population to adopt the committed opinion ...
The acknowledgement of military funding at the end is interesting, and tells me that this research was seen, at least by the US military, as possibly useful in practice. But then, I've heard they felt the same about staring at goats. My question would have been "what happens if you have 10% committed agents to each opinion?" But they don't discuss that.
Anyway. It's not clear to me that they're saying anything about anything outside a computer. But socially speaking, based on my personal experience within various little communities, I find the story plausible.
Obviously, they're not asking whether it matters if the 'opinion' has any merits. But on reflection, I wouldn't be very surprised to discover that, in as far as real life reflects this, the merits of the case made little difference after persuading the first 10%.
My first thought was, 10% seems fairly low. But on reflection, 10% seems very high for true commitment - for people who are really certain, won't shut up, and can't be persuaded. That's not so common.
If you get to 10% of some community really committed to some idea, that probably means you've already persuaded enough relatively normal people that it stops mattering if some of the first 1% were sociopathic loons who constantly went around making people want to avoid sharing their opinions. Indeed, the role of cocks, bores, witterers, malicious obsessives, and the variously deranged in disseminating both bad and good ideas surely deserves some careful empirical study, along with the different roles of other familar social types such as the Nice Person.
The digging process led me, incidentally, to two social-psychology articles about the process of persuasion and the relationship between the merits of the arguments, the qualities of the source, and whether people think it is a majority or minority opinion:
When credibility attacks: The reverse impact of source credibility on persuasion
The effects of majority versus minority source status on persuasion: A self-validation analysis
But, having read them, I won't trouble you with their arguments. They didn't convince me that their experiments meant anything.