Where is the New Dunbar Limit?

[#1]

Michael Wu, Ph.D. is Lithium's Principal Scientist of Analytics, digging into the complex dynamics of social interaction and group behavior in online communities and social networks.

Michael was voted a 2010 Influential Leader by CRM Magazine for his work on predictive social analytics and its application to Social CRM.He's a regular blogger on the Lithosphere's Building Community blog and previously wrote in the Analytic Science blog. You can follow him on Twitter at mich8elwu.

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Last week we learned about the relativity of tie strength and the attention economy. I’ve kept the discussion at a rather theoretical level, so I didn’t discuss how any of these concepts apply to a business or an organization. Well, this time, I hope to demonstrate their utility with some applications. Let me start with attention economy.

Attention and Relationship

You will recall that people’s attention is not only a finite and limited resource, in an information-rich society, such as ours, attention is actually a scarce resource. This is because we are under a constant bombardment of information, and attention is required to process, consume, and retain the information around us. Much like a computer that has finite information processing power, the limit on our attention is direct result of our brain’s cognitive processing power. (Coincidentally, my PhD lab is actually a neuroscience lab that studies visual processing and attention.)

The attention economy limits the number of active engagement that we can hold at any given time (within our immediate engagement circle). Since strong ties will tend to win our attention and dominate our social engagement, this takes attention away from the weak ties that we create, making it harder for them to develop into strong relationships. Therefore, the attention economy will indirectly limit the number of strong relationship that we can maintain. The natural question that follows is “what is this limit?” In other words, “how many strong and stable relationships can we maintain realistically?”

Understanding the Dunbar Limit

In 1992, Prof. Robin Dunbar estimated a theoretical limit on our ability to maintain stable relationship based on neocortex size (i.e. the cognitive capacity) of human brain. This limit became what is known as the Dunbar’s number (or Dunbar limit), and it has a value around 148. That means any individual can only maintain roughly 148 stable relationships on average, where they know everything (with respect to social relationship) there is to be known about these 148 people.

There are two assumptions to bear in mind when talking about the Dunbar Number:

1. Dunbar number applies to groups that have very high incentive (e.g. survival) to maintain social cohesion. In these groups, Dunbar speculated that 42% of the time budget is devoted to “social grooming” (for non-human primates, or socializing for humans) so that everyone knows everything about everyone else’s social relationship.
2. Dunbar estimated his number with brain size data and group size data derived from 38 different primate species. Then he survey many pre-industrial villages and tribes and found their size all hover around his predicted number of 148.

That means Dunbar’s result may not be valid under the following conditions:

1. In today’s society, where the incentive and necessity for social cohesion is substantially lower.
2. In post-industrial era, where communication (an important part of socializing) is much more efficient than the pre-industrial era.

Beating the Dunbar Limit

How can we beat the Dunbar limit? Well, this has happened through the course of primate evolution. The Dunbar limits for other primate species with smaller neocortices are lower than that for human. Aside from developing a larger neocortex, how did we (human beings) beat other primates in terms of our ability to maintain social cohesion?

Dunbar proposed himself that language was developed as a form of social grooming that allowed early humans to maintain social cohesion more efficiently. The evolution of language reduces the time needed for human to socialized, bond, understand each other, and resolve conflicts. All of these activities are crucial for maintaining a social cohesion within a group. The evolution of larger neocortex, which enable language processing, ultimately lead to the larger average group size (148) compare to other non-human primates.

However, the human brain hasn’t changed much structurally over the past three hundred years from the pre-industrial to pre-social-media era. Primate neocortex size changes very slowly. The time required for this to happen is an evolutionary time scale, in the order of millions of years. So our cognitive processing power and our attention limit probably didn’t change over the past few hundred years, and it will probably remain the same for hundreds and even thousands of years in the future.

Armed with this information, there are two ways to beat the Dunbar limit.

1. We can maintain more ties at the expense of weaker tie strength for each relationship.
2. We can make socializing more efficient, so it reduces the time and attention needed to develop and maintain a relationship of equal tie strength.

Note: we will only discuss the first mechanism for beating the Dunbar limit today, and save the second mechanism for next week.

The Attention Economy and the New Dunbar Limit

Since our brain, specifically the neocortex, hasn’t change, the limits of our attention and time resources remain the same. Therefore, when we maintain more relationships, each one will get a smaller piece of the attention pie. Since the strength of a relationship is directly related to the amount of time and attention devoted to it, this usually leads to a weaker relationship (though not always, because there are other components of a relationship: intensity, trust, and reciprocity). So the important question that we should be asking is “whether or not we can get by with weaker relationships?”

We can! Although we have not dramatically evolved biologically as a species, our society has evolved. That is, even though our brain (i.e. neocortex) hasn’t  changed, our society has changed. We have developed government, law, social etiquettes, and many social infrastructures that make our world a safer place to live. Consequently, super strong relationships are probably not as vital to our survival in the modern society, unless there is a war or some natural disasters. So there is less incentive to build and maintain super strong relationships. As a result we can get by with weaker ties that require less time and attention for their maintenance. This can certainly increase the number of stable relationships that we can maintain.

So what is the new Dunbar Limit? A new estimate for the average size of personal social networks has been investigated recently by Prof. Russell Bernard and Prof. Peter Killworth. This new “Dunbar limit” is roughly 291 at the height of the information revolution (before the dot.com bust). It almost doubled the original estimate by Dunbar for the pre-industrial era. However, the Barnard-Killworth estimate was derived from data prior to the social media revolution. Now, 10 years later, could the advance in social technologies today push this limit further? This is the topic of discussion for the next post. If you are interested, stay tuned and come back next week.

Conclusion

Alright, we’ve covered a lot of concepts. So, what have we learn today? I certainly hope that I’ve given you a deeper understanding about the Dunbar’s number. We’ve discussed how Dunbar estimated it and when it is valid. But the most important thing that you should remember from today’s discussion is that there is an inherent tradeoff between the number of ties we maintained and the strength of these ties. This is because humans today are still the same humans hundreds of years ago, and the cognitive processing power of our brain is fundamentally still the same.

Next time we will discuss the second mechanism for beating the Dunbar limit. In the mean time, I welcome any kudos, comments, critiques, and any further discussion about this topic. My last post has been very quiet: no comments, and only two kudos  . I hope that doesn’t mean you readers our there are not interested in my work anymore. If there is something that you like to see, please do let me know. Honestly, I’ve been busy myself too. After coming back from my two week vacation in Japan, I barely have time to eat and sleep. I sincerely apologize for not being as engaging on twitter as I used to be. So I am working hard to catch up with my works, and before you know it, I’ll be back tweeting!

[#2]

Michael, I love reading yr articles. In every day practise we meet people that claim to maintain over a 1000 relationships. Is there a limit to the number of relationships that can be maintained at all? Regardless of strong or weak ties? How much attention potential do we need to engage in social interaction with over a 1000 others? And I would argue that weak ties tend to need more attention to keep them 'going' than strong ties. With the latter you've built up a history of interaction that created a buffer so you can be out of touch for a long time. Looking forward to yr next post. Rgrds Miriam

[#3]

"super strong relationships are probably not as vital to our survival in the modern society, unless there is a war or some natural disasters. So there is less incentive to build and maintain super strong relationships. As a result we can get by with weaker ties that require less time and attention for their maintenance"

Isn't that a seemingly pragmatic way of thinking about intimacy, trust, and authenticity?  The bar is whether it it "vital to survival in the modern society."  It sounds a little like we're assuming that Dunbar's number is just a network parameter that varies with environmental conditions.  I don't know of any evidence that supports that interpretation.  Most of the data so far seems to indicate that the number is tied roughly to brain size. 

I have to wonder whether we aren't setting the bar for relationships a little low and discounting the value of depth or interpersonal understanding and trust.  Yes, I can survive with many superficial relationships but I think I thrive only with a few deeper ones, where we understand each other well enough to know how each other thinks, where we are reliable or not, what we value. 

For me, the problem with the tradition of looking at social networks in this way is that it models individuals as just nodes in a network and mostly emphasizes that the number of connections is all that matters.  That doesn't even entirely work in neural network analysis because neurons are fairly sophisticated computationally, and I think it misses a lot more when we look at networks of humans. 

[#4]

Michael,

Welcome back!  For my part, I'm a bit behind in reading your work because most of my available time recently has gone to other channels.  Maybe that is also the case with relationships - the time investment may be aligned with mutual benefit.  We spend time with those that benefit us in some way, even if it is just making us feel good.

Certainly Facebook and Twitter interactions beg the question of how many friends or followers we have.  Does any point of connection count as a relationship?  (one could argue that "relationship" is just a term to explain how two people are relevant to one another and that there are are many degrees ore levels to that relevance)

There are probably quite a number of people who I recognize and have some affinity toward, and maybe know something about them, but there are very few who I know a great deal about and with whom I share mutual purpose and have established a high degree of personal trust.  

Did Dunbar measure the relative depth of each relationship?  You summarize his assement model.  What if we plotted number of unique relationships vs depth of the relationship (with some kind of standardized criteria for measuring the depth - say 5-10 questions that you had to be able to answer about each person, and the number that you could answer set the depth)

So say you know 100 people now, how many could you answer the 1 question about, how many 3, 7, 9 ect.  What would that distrubution look like?  Then you could look at a group of people pre and post social immersion might change this and say more accurately how social networking might change both the number and nature.

Did his model plot out some kind of a distribution - a lorenz curve for the number vs depth?

I suspect social media / social networks might increase the numbers on the low end of the scale and maybe fatten up the middle of the curve a bit, but I doubt it does much to increase the number of those relationships at the top end.

Mark

[#5]

Michael,

As a clarification on my first point before I got sidetracked making my second one...  It seems that we are often schedule, event and priority driven - so if there are immediate demands on our time for work, family, etc, our time available for electives may be limited or interrupted.  I suspect this can affect the number of relationships we can effectively maintain to the same depth - there is a certain level of maintenance - touches - to keep a relationship from declining. 

I think many of us spend time on your blog because we derive a benefit - your writing prompts us to new thoughts and insights.

Mark

[#6]

Hello Mariam,

Thank you for your comment.

"Is there a limit to the number of relationships that can be maintained at all?" This is a question that I get very often. Unfortunately, it depend on what you mean by "having a relationship."

If having someone follow you on twitter is considered as a relationship, then you can have a lot. Probably thousands, and millions are possible. This is because it doesn't require much attention and time to just get someone to follow you. But if "having a relationship" means that you will strust lending the person $1000 without legal statement, then the number would be much less. And that is because it take a lot more attention to build up a relationship exhibit the kind of trust needed to lend someone $1000.

Relationship actually do not fall into just weak ties and strong ties. They actually form a continuum all the way from the weakest to the strongest. In the modern days, different people probably have very different notion of what a relationship is. Some may consider being able to match up a name with a face is sufficient. These people can probably have thousands of friends. But some may have a more stringent criteria. For example, if they may consider having a relationship means trusting the person enough to lend them $1000. These different criteria in people's mind of what constitute a relationship is what give rise to the various different number of relationship that people claim they can have.

Prof. Dunbar simply choose a very stringent and fixed criteria in what he meant a relationship, which must be strong enough that it increase the group's survivability. That is, you almost have to trust each other with your own life. That is why his number is very exact for army units, nomadic tribes, etc.

So to answer your question of how many relationships can we realistically maintain, we must first establish a good criteria of how strong a relationship one must have to be consider a valid relationship. Then we can extrapolate back and calculate the number that we can maintain.

Finally, I agree that building relationship probably takes more attention than maitaining a relationship that already exist and is already strong. I've written a series of posts on creating a tie, building the tie strength and maitaining the tie:

1. Community vs. Social Network
2. How Do People Become Connected?
3. From Weak Ties to Strong Ties
4. Maintaining the Strong Ties

Have a look if you find these topics interesting.

Thanks again for taking the time to comment and be the first to voice your thoughts. I sincerely appreciate that. Hope to see you around again.

[#7]

Hello Todd,

Thank you for the comment and the Twitter follow.

Actually Dunbar's number is the average of group sizes extrapolated from primate anthropological data. And it is accepted in the scientific community that Dunbar's number (casually rounded to 150) is actually more accurate for subsistence farming villages, professional army units, and nomadic tribes, where survival pressure is strong. In situations where the environmental and economic pressure for survival is not as critical, group size can vary quite a bit. In that respect, Dunbar's number can indeed be viewed as a network parameter that respond to the enviromental stress.

I must say that biological system is inherently some what pragmatic, even at the cellular, and neuronal level. But I'd rather not go into that discussion here. But I will give a more social example: The evolution of civilization is testament of our interdependence, because it is a massive collaboration between many individuals that help us live and survive better with less resources. Each one of us just help the other with our strength and depend on others for their strength. I didn't farm the food I eat, nor made the clothe I wear, nor build the house I lived in. I depend on others for that. Pragmatism is not necessarily a bad thing; it is what makes us connected and more interdependent of each other.

People can choose to define what constitute a relationship anywhere they want. As in my reply to Mariam above, that is what give rise to the different number of friends people claim they have. If you definition of a relationship is to thrive rather than survive, you will have a different number of friends that you can have. But it is very difficult to quantify what does it mean to thrive. I believe that Dunbar choose survival, because that is easier to quantify (dead or alive), and it is a fixed criteria that can be applied across species of primates.

I don't think we are discounting the value of depth or interpersonal understanding and trust by looking at survival as a criteria. The strength of relationship has to be strong enough for you to trust someone with your survival means that you trust them enough to put your life in their hand. In a village, it may be a medicine man helping you to treat your disease. In an army, it maybe trusting your buddy soldiers to say "run, I'll cover your back." Or in some natural disaster, it means a parent risking their own life to save his child. That is the kind of strong relationship you should be thinking about when you talk about the Dunbar number.

Finally, I do agree that social network analysis (SNA) is probably not a good model of neurons. But that really depends on what kinds of scientific questions you want to address. A full compartmental model of neurons with precise Hodgkind Huxley dynamics is not necessary for every inquiry about neurons. Einsteinian Relativity is a much better model of the universe than Newtonian Mechanics. But for most of the problem that we need to deal with, such as building bridges, cars, airplanes, etc, Newtonian Mechanics is good enough. So most of the civil engineers and mechanical engineers don't need to consider relativity when building bridges, cars, and airplanes.

As a scientist, we must not over complicate the problem with what is necessary to explain or address the problem. So I tend to use the simplest model to exlain an observed phenomenon. If it fails, then I will go to the next more complex model and so on. So far, I find social netowrk sufficient for the kind of inquiry that most people are asking. If enough people ask questions that cannot be explain by social netowrk analysis, then I will try to use the more comoplex Dynamic Network Analysis (DNA) . And if that still doesn't explain the observe data, then I will need to formulate some new type of Netowrk analysis that is consistent with SNA and DNA, but more powerful and complex. That is how new theories are created. In fact, that is how Einstein created his Theory of Relativity. It is because he find that Newtonian Mechanics is not sufficient to explain his astrophysics data.

Ok, I maybe getting into an tangential topics now. But I love science and math, so it's easy for me to go off on a tangent with scientific discussions. So please let me know if I am loosing your attention. 

Thanks again for the comment and see you next time.

[#8]

Hello Mark,

Thank you for the nice comment and the clarification.

With Facebook, LinkedIn, and Twitter, we can certainly count every point of connection as a relationship, but that would be biased in favor of those who are more prolific on social channels. Aside from the bias, which leads to inaccurate estimate of the number of relationships that we can really hold, I personally don't think we should treat relationship so lightly. This could lead to the Social Media Bubble that Umair Haque wrote about in the Harvard Biz Rev Blog.

Dunbar did not measure the depth of relationship per se, because that is very hard to measure, specially for different species of primates, that you cannot ask them questions and get an answer back. Being an extremely clever evolutionary biologist, Dunbar use survival as a criteria. This criteria can be easily apply across species, and is actually a pretty strong criteria as I discuss in my reply to to Todd Stark above. I will not repeat that here.

Dunbar plotted the relationship between neocortex size and the average group size for various primate species, and extrapolate that line to our neocortex size to get the number 148. Basically he saying that if we assume humans are under the same kind of survival pressure that other species experience, we would expect the average group size in humans to be 148. This number has match anthropological observations for many nomadic tribes, millitary units, that are under similar survival pressure. I basically put his assumption to test and offer an alternative explanation for the observed data.

I totally agree with you that social media can definitely increase the number of ties at the low end (i.e. those that do not require much of our attention). But it probably won't change the number of relationships that we can hold with strong ties at the high end. Since this will be a topic of discussion of my next post, I will have to defer you to my next post. 

As to your clarification, that is definitely true. Most humans are urgency driven. I'm sure you heard of the 2x2 quadrant of urgent / not urgent vs important / not important. We tend to overly focused on the urgent stuff and forget what is really important but not urgent at the moment. This can definitely affect the number of relationship and the kind of tie strength that we can build.

And thanks again for the nice comment. I certainly  hope that I can continue to provide an unique and different perspectives that will continue to be valuable to my readers. Well, hope to see you again next time.

[#9]

Michael -

Another interesting and helpful post, although it may have raised more questions than it answered!  What arose for me as I read this post is that Social Network tools allow us to extend our "relationship reach" more efficiently.  However, as you say in your last comment -  tactics like over-focusing on urgent (vs important) topics or haphazard and spotty participation can get in the way of maximizing our relationship reach using these tools within our social network.   

It seems to me that being vision-directed, mission  & goal-oriented, channel-focused and  participation- disciplined can help us reach more of the right people more frequently, leading to stronger ties.   For example, your work (and a select group of others) aligns well with where I want to head with my work... so I created a twitter list called social_media_scientists to more easily following the work of that group.   Segmenting our network, organizing our content and choosing our conversations are new habits that we need to develop in order to improve our personal Dunbar limit.  Sound right?

Looking forward to your next post.

- Skip

[#10]

Hello Michael and Todd and Mark,

thanks for all yr elaborate answers! It's great for sharpening our thoughts and adds to the dilemmas I see around me.

I do value yr tips of next-to-read blogs and in your blog about From Weak Ties to Strong Ties you mention something that gives rise to the next dilemma: "The value of weak ties is in their number and diversity". It is true that we can establish our own (instrumental) goals by crowdsourcing our weak ties. They help us in finding information we're not able to access, to find a new job, new employees, new customers ... But when asking for help, one should also be willing and able to reciprocate the help. Couldn't we then foresee a situation where people might maintain 500 or 1000 or even more weak ties that make them busy answering questions of their weak ties and helping them achieving their goals, but at the same time filling their days with helping others. Where's the limit to the number of weak ties? Making the network work, only works when we are willing and able to help out others and sometimes that might fill yr days.

How can we then still achieve our own goals? When does the network change from being benificial to ties that torture?

thanks for thinking with me, Miriam

[#11]

Hello Skip,

Welcome back and thank you for the comment again.

You are on the right track. Just want to add a couple of comment as food for thought.

I certainly think that being vision driven and goal oriented can help us build stronger, deeper and longer lasting relationships. But some people might not value the depth as much as the diversity. Some people might like to have many many friends to just go hang out and have fun, but don't actually know them very deeply. And they don't care if these relationships are broken, because they are so weak anyway and didn't take them much time to build at the first place, so they just build other new weak ties. Both you and I are probably not that kind of people, but some people are.

We all have only 24 hours a day and a fixed amount of attention limited by our neocortex. Dunbar very cleverly used survival as a lowest common denominator for something that everyone (in fact every species) wants. But once we are able to survive, people start to want other things (i.e. they move up the Maslow Hierarchy of Needs and start to desire things of different values).

So if you value depth and strength of relationship, then your Dunbar number may be at the lower end, but if you don't care about depth, then your Dunbar number can be much higher. I am not proposing one or the other. I think we should aim to strike a balace, because there are values in having a lot of weak ties too. It all depends on what you want, what you find valuable, and how you allocate your limited attention and time resources.

[#12]

Hello Mariam,

Welcome back and thanks for asking a great question!

By definition weak ties are those that probably won't grab much of your attention and time. (see Figuring Out the Relationship Puzzle). That means most of the time, you will simply ignore questions from your weak ties. And in the situation you mention when they are going to compete for attention with your strong ties, the strong ties will win (see last week's post The Relativity and Economics of Relationship). You may come back to the weak ties later, but most people probably just forget or are too busy engaging with other strong ties to take notice of the weak ties at all. And that is probably OK, because your weak ties probably won't expect you to get back to them, because they know the tie is weak also. If you do get back, great! If not, no hard feelings.

You may ask then how do people get values out from weak ties. Well, a tiny fraction of the time when the weak ties ping you for help, you will be free and are not engaged with other stronger ties in your immediate engagement circle. That is when they will get your attention. Even if you are engaged with other strong ties, if the problem that the weak tie want help on is so simple, so urgent, and so relevant to you, you can take a little time out to help them out, then quickly get back to your strong ties.

But as I said in the first paragraph, most of the time you simply ignore them. But again that is OK, since there are many weak ties, you only need one that can help and reach them at the right time that can catch their attention, then they will be able to help you.

The situation you mention probably won't happen in real life, because whenever there is a competition for attention, the strong ties will usually win. Basically, you will help the weak ties when you can help. The weak ties are not going to expect you toe help them everytime they ask. Otherwise, they will be strong ties. Recall from "Figuring Out the Relationship Puzzle" the 4 component of ties strength: Time, Intensity, Trust, Reciprocity. A tie is weak because you won't always reciprocate. Otherwise, it will be a strong tie.

However, if you do maintain 1000 strong ties, then you can get into the trouble that you mention of not able to do anything for yourself. Then the network will turn into torture as you said. That is why most people just cannot keep this up for a long time, so they will reduce the number of strong ties they maintain. More realistically, some of the strong ties naturally weaken due to the lack of attention devoted to them.

Well, I hope this address your question. I think that if you grasp the key idea of the attention economy in The Relativity and Economics of Relationship, then a lot of things will fall out naturally.

Thanks again for asking such a great question and continue to participate in the discussion. See you again.

[#13]

@MikeW:  Thanks very much for your very gracious,thougtful, and splendidly detailed response.  I am learning much more from this discussion than I expected to at first, always a pleasant surprise.  Sounds like we share  lot of interests and I like the way your mind works.  A lot of good food for thought here for me to digest. 

Thanks to the other participants here also for their wonderful thought provoking comments.

[#14]

Michael,

Do you know if Dunbar's limit is effected by a person's introvert/extrovert tendencies? Introverts tend to have few but deeper interactions over the same period of time, but I'm not sure if that means they "top out" on connections at different rates.

Thanks!

Stephanie

[#15]

This isn't a "new" finding. Indeed, Peter Killworth has been dead for several years and Russ Bernard retired some years ago. It is only new to the author of this post and those who have not been following the extensive reearch in social network analysis. Indeed, 291 may well be too low according to the most recent research. And of course "291" is a mean, and not an absolute ceiling.

The 291 mean size estimate from Bernard, H. Russell, Peter D. Killworth, Eugene C. Johnsen, Gene A. Shelley, and Christopher McCarty. "Estimating the Ripple Effect of a Disaster." Connections 24, no. 2 (2001): 18-22. The larger numbers come from the same data set that Bernard and associates used, but with different, assumptions about the likelihood of names.  See: Zheng, Tian, Matthew Salganik and Andrew Gelman. “How Many People Do You Know in Prison?” Journal of the American Statistical Association 101, no. 474 (2006): 409-23. DiPrete,Thomas, Andrew Gelman, Tyler McCormack, Julien Teitler and Tian Zhang. “Segregation in Social Networks Based on Acquaintanceship and Trust.”  American Journal of Sociology 2010: forthcoming.

[#16]

Hello Todd and Others,

Thank you for the very nice comment. I learn a lot from the discussion too. Scientific discussion is always good to test the limits of our knowledge and explore new ideas. Glad you find the discussion here interesting.

Hope to see you next time.

[#17]

Hello Stephanie,

Thank you for asking the question.

I do not think that Dunbar's number is affected by the person's introvert and extrovert tendencies. It is really a cognitive capacity, not a statement about whether someone preference. So even though introverts prefer and tend to maintain fewer ties, they still have the same capacity to maintain 150 super strong ties (relationships that are strong enough that you trust each other with your life). So I believe that if these introverts were placed under severe survival pressure, they would probably be able to maintain similar number of ties as extroverts. But if not under severe pressure, then their preference kicks in.

I hope this addresses your question. Thanks again for commenting and hope to see you again.

[#18]

Hello   Bellagio99,

Thank you for the comment.

First, allow me to clarify something. I don't think I've ever said that this is a new result. I said the 291 number was published at the height of the information revolution (before the dot.com bust), which is around year 2000.

Besides, just because people are dead and retired, that is not a reason to disregard their work. Newton and Einstein has been dead too, but does that invalidate their work? I wouldn't. There are many works in history that are old and may not even be accurate anymore, but they are still valuable in the historical context, and they are useful in explaining simple phenomena that do not need the complexity of a more complete theory.

I am fully awared that there are other estimates out there. Depending on different assumption, the Bernard-Killworth estimate can range anywhere from ~300 to 3000. I simply take a more conservative estimate.

Even the Dunbar number is an extrapolation of the average group size among primate species from their neocortex volume ratio. It is not the ceiling either. Everything has a probability distribution. To say anything is the absolute ceiling and is absurd. I'm sure there is some people in this world who can maintain 151 relationship, and some that can maintain 152 also.

But if you want to talk rigorous statistics, I'm happy to do that with you. We can talk about the maximum likelihood assumptions that goes into the Bernard-Killworth estimate. Happy to talk math/stat any time. Haven't had the chance to do that much these days, so I am looking forward to it if someone can speak at that level of rigor.

And thanks for the references. Although I know some of them, one of them is new to me. So thank you for taking the time to list them.

Thanks again for commenting and taking the time to point out the other estimates.

[#19]

Mike. Best bet in learning more about current state of research in network size is to attend the International Sunbelt Social Network Conference @ St Pete Beach (near Tampa), early February. Info: www.insna.org  See you there!

[#20]

Hello Bellagio99,

Thank you for the link. I've been wanting to attend more academic conference. However, it seems that I can never find the time and resources to go being in a startup in a pretty hot industry. I will try again this year. Hope to see you there.

Thanks for coming back.

[#21]

Michael, others - are you aware of any Social Network analysis tools that use SNA and/or DNA-based solutions to help identify influencers or other critical network attributes?   Has there been any research on how effective such analysis is for "seeding campaigns with influencers"?  Michael - I seem to recall that you had a study showing that seeding a social media campaign with influencers gave up to a 50% lift on some types of desired actions.  

Thanks!

[#22]

Hello Skip,

Welcome back and thanks for the comment.

There are a lot of social network analysis tools out there. Each has its strength and weakness. The following are few that I like the most. And I listed some of their strength and weakness based on my past experience with them.

Gephi: best  visualization with temporal component, but slow with very large graph.

NodeXL: easiest to use and good for exploratory analysis, but no temporal component and too few graph metrics.

Pajek: can handle very large graph and has the most complete list of graph metrics, but not very user friendly.

I am not aware of any free or comercial tools out there that uses Dynamic Network Analysis (DNA) yet. But I know the military uses them.

I did have a research project that analyze the monetary return of WOM seeding programs and compare random seeding vs influencer seeding. You can find our whitepaper here. The result actually shows that the ROI on influencer seeding is about 50% higher than that of an random seeding program.

Alright, I hope this addresses your question. Thank you again for asking and see you next time.

[#23]

Michael,

You have had a great series of posts recently on relationship and attention constraints.  My lack of comment has been more because of my context – lately, I have been reading your posts ‘on the go’ on mobile.

I agree with most of what you talk about – the see-saw balance between strong & weak ties, the four components of TIRT (Time, Intensitiy, Reciprocity, Trust), and on dunbar.  In fact, about a year ago in a discussion around this topic, I had a tweet that overlap with your views – “Dunbar's number - agree with the essence, but thinking 'meaningful relationship' has taken on a new meaning in twitter”.

I think the single most pivotal concept is the one you mention in one of the comments above – how exactly are you defining a ‘relationship’. This will have a cascading impact on everything else downstream and on your strategies and action paths under various scenarios.

I also (personally) think the ‘Friends’ in Facebook et al. is a misnomer.  Ties do not blossom into friendships

instantaneously. Ties need to be cultivated, nurtured, tested, and exposed through TIRT before the adequate thresholds are  crossed on tie-strength.

Enjoyed the read.

Regards,
Ned

[#24]

Hello Ned,

Glad to see you back. I totally understand how everyone is busy (maybe that is a good thing, since it is usually the first indicator that the economy is slowly picking up). So I should really thank you for taking the time to comment on my blog.

Relationship is definitely one of those things that we are all familiar with, but at the same time have difficulty defining what is it exactly. That is why I like to re-examine the notion of tie strength from one of the earliest model and see how much it explains and where it fails. Although the TIRT (Time, Intensity, Reciprocity, Trust) model is simple and elegant, it is probably not the most accurate model, since it is 40 years old now. But I think these four factors can provide some interesting insights if we are willing to consider nonlinear models among them.

For example, we can construct a model where the tie strength is really a product of time and intensity (as suggested by Marsden & Campbell). But time-spent together can also build up the intensity factor, which does not fade away easily (have a long decay time constant). But the time factors decays much faster (has a much shorter time constant). Therefore, when we see an old buddy that we’ve lost touch since high school, we can quickly recall that intense relationship without having to re-build them.

People definitely drawing the line at different places (that is how strong a tie must be for people to consider it a relationship). Facebook basically set the bar to the lowest common denominator. Basically anyone that you can put a name to his face can be a friend. Moreover, Facebooks do not distinguish between strong ties and weak ties. Whether you are a family friend for 20 years, or someone just met at a bar yesterday, they are all just friends. So as you said it, “Facebook friends” is definitely a misnomer.

As always, I enjoy your comments, and hope to see you again next time.

[#25]

Wow - I fall a little (ok, alot) behind in blog reading and return to find out I'm famous! I've never been so proud to be a Dunbar

[#26]

Hello Mike,

Good to see you back again.

Yup, you are famous. I must say that I've once wonder if you are in anyways related to Prof Dunbar. Have you done any family tree or genealogy analysis of your relationship with Prof. Dunbar? It couldn't be more than a few degrees away since the whole world is only about 6 degrees apart. It would be pretty interesting to figure out.

[#27]

Michael,

Thanks so much for describing this idea. I have heard of the significance of the number 148 and how some businesses (I think Gore-Tex) organize their group size with the idea of creating strong ties by limiting their size.  I wondered about this particular concept:

"super strong relationships are probably not as vital to our survival in the modern society, unless there is a war or some natural disasters. So there is less incentive to build and maintain super strong relationships. As a result we can get by with weaker ties that require less time and attention for their maintenance"

How stable of a community, where weaker ties are the norm, would this represent? And do you see the strength of relationships ebbing/flowing? Do you think that social norms, government institutions and community groups begin to wield more significance in response to a looser social network? 

Thanks for sharing!

-Jennifer

Regards,

Jennifer

[#28]

Hello Jennifer,

First of all thank you for stopping by and commenting.

To address your question, I must emphasize that communities are not held together by interpersonal ties. A social network is held together by these interpersonal ties, so tie strength is critically important to the stability of the network. But what holds a community together is a common interest among its members. Please see the distinction between a social network and a community here. In a community, majority of the people don't know each others.

However, there are social network within communities. In fact social networks develops naturally within communities (please see this post for an explanation). So a communtity is really a place where people build and "test" their relationships, and they are supposed to be more fluid. After they leave the community, the ties (relationships) that remains is what's left over to hold them together, and those become our permenent social networks.

OK, I hope I've address your question. If anything is still unclear, please let me know. I'd be happy to discuss further. Thanks again for the question and hope to see you on Lithosphere next time.