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]


Julie

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?

Suzanne Lainson

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?

David Carroll

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.

Christopher

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?

Steve Bennett

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.

James Martin

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.

Christopher

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".

Yoshi

What is the tipping point?

RogerP

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.

James

"...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.

RogerP

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.

Joshua

Have you all heard the good news about Jesus Christ, Incarnate God and Resurrected Man?

AaronS

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

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

AaronS

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?

Prashant Patel

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

"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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Rodrigo

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?

KevinH

it seems to me that one critical real world factor they are missing is changing the social graph with belief over time. If someone is committed to a particular belief, it is also more likely that they will loose ties with people not as strongly committed, and gain ties with other committed people.

It seems to me that adding such a behavior could easily lead to a fractured social graph, more akin to what we see in current times.

That would also explain why small towns, where is is much harder to change your social graph, are more likely to end up in a situation where everyone goes to the same church, shares similar political beliefs, etc.

164

Kind of depressing to think that we are all just a heard of sheep waiting to the next 10% fad to come along. There are a lot of 10%'s holding crazy ideas that fortunatly will never make it to the mainstream. Surely the 10% theory has to attach to a good idea or opinion.

Josh

Can you guys please add a Google+ +1 option? Thanks!

LG

This is absurd on its face. If <10% would take "the age of the universe" to catch on, then how do you ever get 10% to begin with? Wouldn't that imply that the only ideas that would ever dominate the culture are the ones for which at least 10% held that belief since time immemorial? But that's clearly not the case, we frequently have new ideas -- sometimes starting with a single person or very small group -- that come to dominate the culture in a short amount of time.

Michael

Exactly. Large numbers grew from small numbers, so a point-in-time measurement of less than or greater than 10% doesn't make sense.

AaronS

This probably needs to be further qualified to say that this works only if those 10% believe something that is not strongly contestable (e.g., Young Earth Creationism). For instance, what holds Young Earth Creationism back--even though at least 10% of Americans believe it, I suppose--is that it is strongly contested by scientists.

On the other hand, a religious belief that is resonates with people, or is otherwise not disprovable, has a much better chance than something that is strongly contested.

It is not only commitment that matters, but the force of evidence (i.e., does it appear to be the actual truth?). Otherwise, it would be kind of hard to explain how Darwinism overcame so many difficult obstacles to its acceptance. The reason it did was because it has what is (or is at least perceived to be) the weight of the evidence on its side.

I'm sure we can also find some notable exceptions to this "rule" of 10%. Certainly, 5% with commitment and arms and organization vs. 95% without no particular commitment and few arms and less organization (think of 1917) can drive change. Of course, exceptions just showcase the rule.

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VH

The author, Mr. Philips, indicates that the minority opinion will "inevitably" become the majority opinion, once the 10% threshold is crossed. When I read the abstract, hwever, that is not what it says. It only says that it is nearly impossible for the minority opinion to become the majority without 10% commited agents. It says that the time constraint is seriously reduced by the presence of 10%. Infact, and this maybe flawed logic like a Zeno paradox, but the study makes no mention of how long it takes to get 10%, so if the initial goal of the minority is to acheive the threshold 10%, then it turns to the majority, there may be time for that. In any case it isn't certain the minority opinion will become the majority even with 10%.

T'Jere Todd

I am not quite convinced that it is 10% of the population that can change the attitude of the group as much as it is what standing that 10% holds within the population. I believe that the more successful and known the people are the smaller the amount that needs to believe in the idea. If you have 10% of the population that is lower class then the idea is not as easily taken to as if the 10% were upper class and influential. It seems like an easy feat to convince 10% of the population but what we have to remember is what 10% need convincing.

JD Will

I think this works for a time, as in the case of communism, then reality intrudes and unexpected consequences erode the momentum of the movement. Kind of like what is just now happening to the AGW push to de-carbonize our economies.

Mark

If there is a group of 10, could 1 persistent person make the belief the prevailing belief? And if that group of 10 is in turn a sub-group of a group of 100, then could that group of 10 could make the belief the prevailing belief of the larger group, and so on?

Eric M. Jones.

I remain unconvinced.

One day it dawned on me that the reason for limiting the lifespan of humans is that it effectively limits the growth of nutty ideas.

Every birth of a child represents a new possibility for humanity....not necessarily a good one, but at least not the old one.

MinnItMan

There are a lot of worms in this can. I don't intend this to be pro or anti-religion, but rather an indication of the types of questions I would ask, more-or-less along the lines of the customer satisfaction survey scale.

1) I believe in god.
2) I believe in God, whose name I shall not speak.
3) I believe in God and shall have no ther gods before me.
4) I believe in God and shall have no ther gods before me, and shall seek the destruction of those who do.
5) I believe that there is but one way to God, through the Son.
6) I believe that there is but one way to God, through the Son, and that the Holy Sacrament is literally his flesh and blood.
7) I believe that there is but one way to God, through the Son, and that the Holy Sacrament is more-or-less his flesh and blood.
8) I believe I should go to church, regardless of what I believe, because I really don't know, and it's good for the kids.
9) I hate Apple products and how they represent a black box, albeit deceptively designed with exceeding pleasant aesthetics, yet constantly a reminder to me of the requirement to pay tolls for eternity to do the simplest things.

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Joshua Northey

"immune to influence. " is the premise that is doing all the work here.

That is a huge assumption and caveat in the day to day world. Saying we only need to get to 10% with no faltering, and then hang on with no faltering is kind of silly. People falter all the time, even among mormons, and cultists, and muslims.

Much less among shoe wearers...