Minority Rules: Why 10 Percent is All You Need

What does it take for an idea to spread from one to many? For a minority opinion to become the majority belief? According to a new study by scientists at the Rensselaer Polytechnic Institute, the answer is 10%. Once 10% of a population is committed to an idea, it’s inevitable that it will eventually become the prevailing opinion of the entire group. The key is to remain committed.

The research was done by scientists at RPI’s Social Cognitive Networks Academic Research Center (SCNARC), and published in the journal Physical Review E. Here’s the abstract:

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. In particular, for complete graphs we show that when p<pc, Tc~exp[a(p)N], whereas for p>pc, Tc~lnN. We conclude with simulation results for Erdos-Rényi random graphs and scale-free networks which show qualitatively similar behavior.

From a press release on SNARC’s website:

“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 percent, the idea spreads like flame.”

This has implications for all kinds of things, from understanding how religious and political beliefs spread, to why certain fashion trends catch on. And it certainly sheds new light on the seemingly intractable debt ceiling debate, and how a committed minority can drive the entire conversation. The research actually validates the entrenched strategy of the handful of House Republicans threatening to sink John Boehner‘s budget proposal. Turns out if you’re in the minority, you have less of an incentive to compromise than the majority does. Because if you stick to your guns, and reach that crucial 10%, your ideas eventually win out. Just as the graph from SNARC below illustrates:

Credit: SCNARC/Rensselaer Polytechnic Institute

[HT: Yale Fox]

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  1. Julie says:

    But what happens when 10 percent of a population holds one opinion, and another 10 percent hold the opposite view? Which one wins, and why?

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    • Suzanne Lainson says:

      That’s what I want to know. If 10% strongly support environmental causes and 10% strongly support Tea Party causes, who wins? And surely there are 10% who are committed to pro-life and 10% who are committed to pro-choice. Do we just remain in limbo?

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      • David Carroll says:

        I strongly support environmental causes and Tea Party causes. I don’t think we can have a clean and enjoyable environment if we spend our way so far into a black hole that we are forced to strip mine the environment to dig ourselves out. One big difference in a developed nation over an undeveloped nation is that we can afford to try and be clean. If we slip economically and people can no longer afford to keep themselves from freezing to death in the winter good luck getting them to switch off coal.

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    • Nosybear says:

      Hypothesis: The percentages you mention are not randomly distributed, they don’t consistently proselytize and they’re not immune from influence. In short, the populations you mention are not the same as those studied.

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    • Malcolm says:

      Nobody Wins. That or the one who cares less about the consequences of failure wins (ie. the crazier one).

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    • Alexander says:

      Whichever 10% is more zealous, committed, and adaptive that’s the one that’s gonna win.
      Also outer circumstances may play the role… So Whichever 10% is stronger to that 10% the rest is going to put their allegiance… Just a thought

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    • Krzysiek says:

      Wins the group who is more comitted. It is writen at the deginning!

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    • Matthew says:

      ”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.”

      The key point there being ‘immune to influence’. This would suggest a strong tendency for the most efficient/true view to win out, as it would be the most resistent to compromise. Ofcourse this would be without the inclusion of extraneous variables, i.e. alternate interests conditioning and forcing one view.

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  2. Christopher says:

    I find the claims dubious in the extreme, due to the magic power of ten. This sort of claim only holds up in mathematical models, not real life.

    To illustrate, if 43 of Congress persons (roughly 9.9%) hold an opinion, “It would literally take the amount of time comparable to the age of the universe for this size group to reach the majority.” But if they convince one Congress person, it is inevitable and “the idea spreads like flame.” But what if, as is not unlikely, 44 Congress persons hold the exact opposite idea?

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    • Steve Bennett says:

      Clearly that part was not well expressed. Presumably there is some subtle meaning in “visible progress”. Or maybe there is a distinction between general spread of an idea and the spreading of an idea through proselytising. That is, perhaps once more than 10% of the population accept the idea, it grows through sheer force of numbers, rather than the merits of the idea itself.

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  3. James Martin says:

    Wait, wait, this “10%” figure is for one specific toy model of opinion formation (the binary agreement model), on one specific graph (the complete graph). I could come up with equally plausible models, or different graphs, for which the figure would be 2% or 50% or anything you like. At best, you should take away from the paper the idea that there is some threshold: below it, the opinion spreads, above it, it doesn’t. This is a very familiar phenomenon from all sorts of models of epidemics and the like. Really, it’s not appropriate to say that “according to a new study by scientists at the Rensselaer Polytechnic Institute, the answer is 10%” as if that number 10% says anything about the real world.

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    • Christopher says:

      Exactly.

      The study uses a model where there exists a small percentage of “committed agents” who consistently proselytize the opposing opinion and are themselves immune to influence while the others are not “committed” or “immune”.

      The authors themselves admit there are open questions, including a network with non-trivial
      community structure. Yet one of them, SCNARC Director Boleslaw Szymanski, makes the quoted claims about “always” vs, “the age of the universe”.

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  4. Yoshi says:

    What is the tipping point?

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    • RogerP says:

      I think I am quoting correctly from “The Management of Power” by R J Swingle, that it takes about 3% of the population to organise an effective civil disobedience campaign and about 10% to start a civil war. If so, you can take 3% as being the absolute minimum tipping point.

      For those who abhor the tyranny of ten, the tipping point for the capitulation of minority regimes in Southern Africa was when the ratio of oppressors to oppressed got to about 1:8.

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      • James says:

        “…the tipping point for the capitulation of minority regimes in Southern Africa was when the ratio of oppressors to oppressed got to about 1:8…”

        Of course this is making some unsupported assumptions about which were oppressors, and which the oppressed.

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      • RogerP says:

        The term “oppressors” and “oppressed” are the modern PC terms. At the time, the former were bulwarks against the spread of communism and the latter were terrorists.

        What I wanted to add, though, was that the ruling party in South Africa is today struggling to get its membership numbers up to 1 million, or 2% of the population. Even allowing for the doubling of the South African population over the past 30 years, 1 million members were barely sufficient to get a decent civil disobedience campaign going at that time, let alone overthrow the government.

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  5. Joshua says:

    Hidden due to low comment rating. Click here to see.

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  6. AaronS says:

    Alas, this is meaningless. Why? Because it is irrefutable.

    Consider that you cannot measure “committed.” You can measure 10%, but if their beliefs do not indeed ripple out to the rest, then you can just backtrack and say, “Well, I guess they weren’t very committed.”

    This is not to say that there’s not some truth here. I think we all realized that small, committed group can make great headway. But in TRUTH it starts with ONE committed person…who wins another…who in turn wins another…on and on until we reach, I suppose, the 10% mark, and then it’s all gravy from there.

    In some ways this is exciting. In others, it is a shame. The early Church turned the world upside down with their message. Yet today, in America, where the vast majority claim to be Christians, we are out-committed by small groups of atheists and anti-religion groups. We have the numbers; they have the commitment. A complete reversal from 33 A.D.

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    • Yoshi says:

      On your “TRUTH” of it starting with “ONE committed person,” that is patently false. People can simultaneously and independently arrive at the same ideas.

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      • AaronS says:

        Yoshi,

        How about I rephrase that to say, “But in TRUTH it CAN start with one committed person…?”

        Because I agree that things can sprout up independently, so I think the rephrasing captures both of our notions.

        At the same time, even if one person here and one person there get the same idea at the same time, it is rippling outward from these single persons…until the ripples meet and join.

        Fair enough?

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  7. Prashant Patel says:

    More than 10% of the US population believes in Young Earth creationism (and they are pretty damn adamant about it). I highly doubt this figure will ever reach more than 50%. I doubt even further that if they did gain 50%, all 50% would be as adamant as the current 30% or so. This whole 10% idea would be more interesting if people would actually “stick to [their] guns.” That tends to not be the case.

    The reason it is not the case is because people are not as loyal as we think they are. This brings me back to a marketing class I took. When discussing customer feedback to a business, many studies find that those who rate a service/product 5 out of 5 are very likely to be loyal and become fierce advocates in their own right. Stepping down just one level to 4s would mean the customer was still highly satisfied. Our assumption (as naive students) was that the 4s would still be rather loyal and even decent advocates. However, the same studies showed that their loyalty and advocacy was substantially reduced from that of the 5s. The lesson was that we should seek 5s when marketing our product/service and we should tailor our entire customer service and satisfaction thinking to getting as many 5s as possible. Yes, 4s are nice in the short run, but 5s are the ones who truly bring life to a product/service (think of how many Apple fanboys are running around and what they are basically doing to our technological marketplace).

    I think this same logic will apply to beliefs. If you have a fierce base of 5s that make up 10% of the population, they will spread their ideas quickly, and I do not deny this. However, the likelihood is that they are spreading their ideas to people who will be 4s and 3s. Politically, I am of course speaking of independents and aligned “moderates” who do not “stick to their guns” as often as true leftists and rightists. So, though the minority may have more power in the short run, in the long run the only way they will maintain a high amount of support for their belief is by recruiting more 5s. And it tends to be pretty hard to recruit 5s when you come from a standpoint of extremism and basically deny mountains of evidence that stand contrary to your point. Hell, if I didn’t know so many people who denied evolution myself, I wouldn’t even believe that their extremism and painful denial would get them many 3s.

    Then again, maybe I assume too much of people. Maybe they are so feeble as to fall in line with a bunch of fierce advocates simply because those people are more dedicated.

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    • James says:

      “More than 10% of the US population believes in Young Earth creationism…”

      Which leads to a pretty good counter-example to the 10% theory. At some date – in fact, we can pinpoint this pretty closely as July 1st, 1858 – only a handful of people – Darwin, Wallace, and the handful of people that Darwin had shown his preliminary work to – believed in Darwinian evolution. Within a year or so, after the publication of “On the Origin of Species”, this had grown to a large number, and in the following century and a half the number rose fairly quickly, then plateaued, as it included basically everyone except the YECs and others committed to a religious worldview.

      The same seems to be true of many scientific theories – relativity, quantum mechanics, plate tectonics, and more. When introduced & supported with evidence, they spread fairly quickly from a handful of believers to encompass most of the educated population.

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    • Antiphon says:

      Plus distribution seems to be the key they’re talking about. Proponents of Young Earth creationism may make up 10% or more of the population but they all reside in one niche of society so the rule doesn’t apply. By placing all the proponents in one group it becomes much easier to dismiss the idea as simply as you might dismiss the group. The ten percent rule makes more sense for a believe in evolution because people from many different sections of society could independently come to support the idea.

      Think about it this way: if all of your friends support a cause and you all made up 10% of a group it might be difficult convincing everyone else because others could dismiss your views as something unique to your friend group. However if you took the same number of supporters but distributed them throughout the sample population it would make it much easier for you to convince others (your friends in particular) since you could describe the idea as supported by many different types of people including yourself (who I’m assuming they respect at least moderately).

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  8. Rodrigo says:

    Ok, but once the 10% population expread their idea, there will be again another 10% against it, does this means it will always be a fight between this two groups?

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