This question is not just interesting in the age of social networking tools and the quest for universal popularity, but has tremendous historic value, for example in situations when governments were replaced and the general population simply agreed with it.
A new study published by Rensselaer Polytechnic Institute 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 behind the study consider the 10 percent mark the tipping point where a minority belief becomes the majority opinion.
“When the number of committed opinion holders is below 10 percent, there is no visible progress in the spread of ideas. It would literally take the amount of time comparable to the age of the universe for this size group to reach the majority,” said SCNARC Director Boleslaw Szymanski, the Claire and Roland Schmitt Distinguished Professor at Rensselaer. “Once that number grows above 10%, the idea spreads like flame.”
The scientists used computer models applied to social networks to reach their conclusion. One of the networks had each person connect to every other person in the network. A second model included certain individuals who were connected to a large number of people, making them opinion hubs or leaders. The third model gave every person in the model roughly the same number of connections. Each of the individuals in those networks "held a view, but were also, importantly, open minded to other views."
The scientists then added "true believers" to 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."