Scientists at Rensselaer Polytechnic Institute have found that when just 10 percent of the population holds an unshakable belief, their belief will be adopted by the majority of the society. The scientists, who are members of the Social Cognitive Networks Academic Research Center (SCNARC) at Rensselaer, used computational and analytical methods to discover the tipping point where a minority belief becomes the majority opinion. The finding has implications for the study and influence of societal interactions ranging from the spread of innovations to the movement of political ideals.

“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,”

“Once that number grows above 10 percent, the idea spreads like flame.”


The findings were published in the July 22, 2011, early online edition of the journal Physical Review E in an article titled “Social consensus through the influence of committed minorities.”

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.

To reach their conclusion, the scientists developed computer models of various types of social networks. (...)
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 pc ≈ 10%, there is a dramatic decrease in the time Tc taken for the entire population to adopt the committed opinion. (...)

Human behavior is profoundly affected by the influenceability of individuals and the social networks that link them together. Well before the proliferation of online social networking, offline or interpersonal social networks have been acknowledged as a major factor in determining how societies move toward consensus in the adoption of ideologies, traditions, and attitudes [1,2]. As a result, the dynamics of social influence has been heavily studied in sociological, physics, and computer science literature [3-7]. In the sociological context, work on diffusion of innovations has emphasized how individuals adopt new states in behavior, opinion, or consumption through the influence of their neighbors. Commonly used models for this process include the threshold model [8] and the Bass model [9]. A key feature in both these models is that once an individual adopts the new state, his state remains unchanged at all subsequent times. Although appropriate for modeling the diffusion of innovation where investment in a new idea comes at a cost, these models are less suited to studying the dynamics of competing opinions where switching one’s state has little overhead. Here we address the latter case. From among the vast repertoire of models in statistical physics and mathematical sociology, we focus on one that is a two-opinion variant [10] of the naming game (NG) [11–15] and that we refer to as the binary agreement model. The evolution of the system in this model takes place through the usual NG dynamics, wherein at each simulation time step a randomly chosen speaker voices a random opinion from his list to a randomly chosen neighbor, designated the listener. If the listener has the spoken opinion in his list, both speaker and listener retain only that opinion, or else the listener adds the spoken opinion to his list (see Table I). The order of selecting speakers and listeners is known to influence the dynamics, and we stick to choosing the speaker first, followed by the listener. (...)


Minority Rules: Scientists Discover Tipping Point for the Spread of Ideas

Social consensus through the influence of committed minorities