Why are conversations limited to about four people?(sciencedirect.com)
sciencedirect.com
Why are conversations limited to about four people?
https://www.sciencedirect.com/science/article/pii/S1090513818301491
73 comments
Because otherwise you have to wait too long for your turn to speak, and you start whispering to the person next to you.
More than 4 people in a hunting party will scare any game. Small groups have evolution advantage.
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To emphasize the point, you end up needing to listen to other people instead of having other people listen to you. This is a big problem with discussions, the need to show your own worth easily overrides the value in having an actual discussion.
Another way of looking at it is if people aren't listening to you, it's not a discussion. I was at a small party a week ago, and all 12 people in the room listened to me tell a story. None of them interrupted and felt the need to show their worth. But, I wouldn't call that a discussion.
This is true, though not everyone is worth listening to, and not on $RANDOM subject.
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I've always preferred groups of 2-6 people. Many board games are made for groups of this size.
On one side, humans can mentally cope with 4-6 objects at most - as though we have 4-6 memory slots, which is reasonable given that we have 4 limbs.
On another side, network effects of nodes on a grid become unmanageable above about 6 nodes - a group of 6 people will have 36 one-on-one interpersonal relationships to manage.
On one side, humans can mentally cope with 4-6 objects at most - as though we have 4-6 memory slots, which is reasonable given that we have 4 limbs.
On another side, network effects of nodes on a grid become unmanageable above about 6 nodes - a group of 6 people will have 36 one-on-one interpersonal relationships to manage.
Coincidentally, the idea of this natural conversational limit at Four surprises me. Sure, it is challenging, if you intend to participate (without just being a spectator). I'm used to Six as the described hard limit for this phenomenon.
The professor would then muse down a tangent about "six archetypal roles". But remembering this about human active memory and reasoning capabilities flushes things out a bit more.
The professor would then muse down a tangent about "six archetypal roles". But remembering this about human active memory and reasoning capabilities flushes things out a bit more.
a group of 6 will have 5 + 4 + 3 + 2 + 1 = 15.
It's directional. The calculation is 6x6 = 36.
The simplest example is with two people. John is a different person from Mary, so both John and Mary have a relationship with each other. 1x2 = 2 relationships.
The simplest example is with two people. John is a different person from Mary, so both John and Mary have a relationship with each other. 1x2 = 2 relationships.
Shouldn't that be 6x5=30? Unless you count everyone's relationship with themselves.... [this also aligns with the 5+4+3+2+1 version, it's just n*(n-1)/2 ]
He probably meant to say 30, since he did set the diagonal elements to zero in his N = 2 answer (otherwise he would have said 4).
yes
You get 36 if you count the relationship in each direction (e.g. crush one way, disinterest the other way), and if you also count each person on their own (e.g. a quick temper).
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Tangential, but I noticed the same thing with visual information when testing data visualizations: people have a hard time processing information beyond 4-5 variables.
The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information
https://en.m.wikipedia.org/wiki/The_Magical_Number_Seven,_Pl...
Most humans can only really understand 2D (2 variables). That is why visual representation of data are almost always 2d. Graphs, charts, scatter plots.
What are you claiming?
That in a picture with line graphs varying X, Y, people can't understand if the lines are different colours or the same colours (a third dimension)?
That people can't play 3D games because they can't understand that the image is depicting length, width and depth?
That people can't use windowing GUIs with overlapping windows, because they can't understand the Z-order of which window is "in front"?
It seems intuitive that people can cope with more than 2 variables and more than 2 "dimensions" spatially or otherwise.
What do you mean when you say they can't - what, specifically, can't people do?
That in a picture with line graphs varying X, Y, people can't understand if the lines are different colours or the same colours (a third dimension)?
That people can't play 3D games because they can't understand that the image is depicting length, width and depth?
That people can't use windowing GUIs with overlapping windows, because they can't understand the Z-order of which window is "in front"?
It seems intuitive that people can cope with more than 2 variables and more than 2 "dimensions" spatially or otherwise.
What do you mean when you say they can't - what, specifically, can't people do?
I think they're claiming that people have enormous amounts of trouble reasoning formally about graphs with 3 or more dimensions. Anecdotally this is bourne out by my experience, where it's easy to read an X-Y plot and speak to how the X value influences the Y value(EG linear, cubic, quartic, grows to infinity in one direction, etc). Add a third or 4th dimension and I start to have a lot of trouble making general statements because I have to juggle the impact of the third dimension on the X-Y plot slices.
Please note that I'm not saying it's impossible for people to intuitively understand 3 or more dimensions. Indeed as you say we do it every day. This is not the same as reasoning about it in a general way, which is much harder.
Please note that I'm not saying it's impossible for people to intuitively understand 3 or more dimensions. Indeed as you say we do it every day. This is not the same as reasoning about it in a general way, which is much harder.
There’s a confound here between an extra “spatial dimension” (x, y, z) and an extra “feature dimension” (x vs y for plain and star-bellied sneeches). Very few people have trouble with the latter, but the former is tricky to plot and interpret.
And the dimensionality becomes hard to manage when you go from interpreting it as a spatial dimension to interpreting it as a feature dimension.
Certainly 3 variables is common place? https://i0.wp.com/flowingdata.com/wp-content/uploads/2018/08...
4 is pretty common too, but I agree that 4-5 is tricker to make sense of.
4 is pretty common too, but I agree that 4-5 is tricker to make sense of.
> On another side, network effects of nodes on a grid become unmanageable above about 6 nodes - a group of 6 people will have 36 one-on-one interpersonal relationships to manage.
Network effects grow surprisingly fast. Between 2 people there's only 1 bidirectional edge. Between 3 it's 3 and between 4 it's 6.
Network effects grow surprisingly fast. Between 2 people there's only 1 bidirectional edge. Between 3 it's 3 and between 4 it's 6.
| people | edges |
|--------|-------|
| 2 | 1 |
| 3 | 3 |
| 4 | 6 |
| 5 | 10 |
> this is important because in a conversation, each member must project and rationalise each other communicator's response to a message
Do they, though? Maybe I participate in conversations differently, but trying to unravel how A interpreted B's comment is not something I would do.
Do they, though? Maybe I participate in conversations differently, but trying to unravel how A interpreted B's comment is not something I would do.
It's all I do. It's the only way I can understand if my next comment will offend or work as a joke or if I'm posing an interesting topic. It's what makes conversations so draining to an introvert I feel. The more people, the more I have to figure out what I can say to be ok with the group at hand.
As I posted below, there is a difference between observing how different people react to a particular comment (O(n)) and observing how different people react to a particular comment based on who it's from (O(n^2)). I'm mostly trying to question the idea that there's anything quadratic in the number of participants going on here. Are you sure you're saying that the work you do is quadratic?
That's fascinating, thinking about this, I've realised that I only do this when I'm in a conversation with new people or for whatever reason am specifically considering the interplay of what's being said.
Otherwise I have a broad set of heuristics I apply which I adjust as needed.
I never considered that a tendency to do this might have an impact on introversion/extroversion. Something to mull over, thanks!
Otherwise I have a broad set of heuristics I apply which I adjust as needed.
I never considered that a tendency to do this might have an impact on introversion/extroversion. Something to mull over, thanks!
I think you (and everyone else) does this implicitly. It makes sense for a survival perspective to be able to assess how people react to certain comments & actions in conversation. If other people support a comment it's a signal that you can reiterate the comment or build upon it.
There's a difference between observing how a comment was generally received and remembering exactly how each person reacted. I'm not saying nobody does the latter, but I don't.
And the other way, one can notice how a person reacts to a comment without necessary needing to remember the source of it. Both of these are going to scale linearly (obviously).
I might pick up on something like "A seems to respond to B uniformly negatively" and make a note of that, but remembering one notable thing doesn't require me to "allocate" memory for all of the other non-memorable things. I'm not literally building and labeling a graph, like some commenters are implying. Or if you insist, it's a sparse data structure.
I might pick up on something like "A seems to respond to B uniformly negatively" and make a note of that, but remembering one notable thing doesn't require me to "allocate" memory for all of the other non-memorable things. I'm not literally building and labeling a graph, like some commenters are implying. Or if you insist, it's a sparse data structure.
I guess this has something to do with why communication is so different in collectivist cultures. Maybe it's the different nature of communication itself that allowed collectivism by allowing to manage larger groups of people without getting into overwhelming numbers.
Care to elaborate on elaborate/enlighten on the difference nature of collectivist culture communication?
There have been tons of research and nobody seems to fully understand it.
Collectivist, most messages are intended for the whole group, with ocassionally talking to a specific person, but it's expected the message will be understood by other people who are present. There is very little "code talking" within the group.
In individualist cultures, it's expected that most messages are targeted to specific people, and there can be whole dialogues meant to be only understood by the two people. Or a message may be superficially said to one person, but is actually meant to be overheard by another person. Very often what is said isn't actually true, but it was only said as a means to an end (to make somebody do or say something) and the people involved are expected to understand that. Very litle detail and deeper information is shared, things are rarely said that are not strictly necessary to know.
Collectivist, most messages are intended for the whole group, with ocassionally talking to a specific person, but it's expected the message will be understood by other people who are present. There is very little "code talking" within the group.
In individualist cultures, it's expected that most messages are targeted to specific people, and there can be whole dialogues meant to be only understood by the two people. Or a message may be superficially said to one person, but is actually meant to be overheard by another person. Very often what is said isn't actually true, but it was only said as a means to an end (to make somebody do or say something) and the people involved are expected to understand that. Very litle detail and deeper information is shared, things are rarely said that are not strictly necessary to know.
It truly is a cognitive burden for people who care about how their words are perceived and understood. Logically, I see two ways to succeed in communicating to large groups.
One way is to tune down your level of awareness of, or your psychological attachment to, how your message is being perceived; i.e. turn off the filter and just talk, public perception be damned.
The other way would be to improve your mental approximation of how people are perceiving and emotionally responding to your message, taking the integral of emotional response like some kind of social calculus. Perhaps this consists of bucketing people into groups, the way politicians do, only in more of a real time fashion? I'm not sure, but I do find it interesting.
One way is to tune down your level of awareness of, or your psychological attachment to, how your message is being perceived; i.e. turn off the filter and just talk, public perception be damned.
The other way would be to improve your mental approximation of how people are perceiving and emotionally responding to your message, taking the integral of emotional response like some kind of social calculus. Perhaps this consists of bucketing people into groups, the way politicians do, only in more of a real time fashion? I'm not sure, but I do find it interesting.
It helps to be aware that anyone could hear it and to account for that. It's not perfect, but it reduces problems.
It also helps to be aware that some parts of what you are saying will be entirely missed by some people and this not only isn't a problem, it can be a feature.
It also helps to be aware that some parts of what you are saying will be entirely missed by some people and this not only isn't a problem, it can be a feature.
That is thought provoking. But it almost seems like accounting for everyone (infinite nodes) could make things even more complicated. I have noticed that, as I've gotten older, I've become more aware that people can break into conversation by overhearing something at almost any time. Sometimes it makes me just want to say less so avoid that possibility.
There are typically three things you need to think about:
1. The intended audience, whether an individual or group.
2. Anyone who could generically presume you somehow meant them or were commenting on their life.
3. Actual people you personally know that you actually are speaking about or that might legitimately assume you meant them when you didn't.
Group 3 is probably the biggest source of trouble for most people. It's the one I make the most effort to account for.
My brother-in-law is (or was) a programmer. Though his hourly rate is certainly something I envy, he has a history of working part-time and intermittently and is more talented at spending money than at making it.
That strongly shapes my failure to live in awe of programmers and my failure to presume them to all be wealthy and powerful types. But I believe this is the first time I have said such on HN because it's challenging, at best, and potentially impossible to express that without sounding like I am putting him down. So I just never said anything about it. Most people didn't really need that information anyway, so not saying something potentially offensive to my sister, her husband and other relatives was the easy solution.
Basically, before you tell that cutesie anecdote about your own life, contemplate what it says about people connected to you and how they might feel if they heard you telling that story. Does it cast them in a bad light? Could it be construed as such, even if that wasn't your intention? Is there some means to tweak it to make it less problematic?
The other thing I worry a lot about are acquaintances that will think I meant them when I didn't. I try to not make comments that could be taken to mean I am talking about them when I'm actually not. This is often a matter of tweaking it slightly. It might be as simple as saying "a curly haired person I know" instead of "a blonde person I know" to make sure a blonde acquaintance with straight hair doesn't assume I mean them.
Group 2 is best addressed by finding a sympathetic framing and going ahead and giving some provisos. Don't assume that folks will just know that, of course, you would make allowances for X.
Your friends and relatives may know that, but other people won't. It helps to view it as simply an artifact of clear communication.
The mistake most people make is only thinking about the intended audience and stopping there. You do need to think about that. But you should also think about anyone you are "talking about" or could be construed as talking about.
Edit: To be perfectly clear, I'm not putting my brother-in-law down. His work history is due in part to supporting my sister's career, a thing she doesn't appreciate enough.
1. The intended audience, whether an individual or group.
2. Anyone who could generically presume you somehow meant them or were commenting on their life.
3. Actual people you personally know that you actually are speaking about or that might legitimately assume you meant them when you didn't.
Group 3 is probably the biggest source of trouble for most people. It's the one I make the most effort to account for.
My brother-in-law is (or was) a programmer. Though his hourly rate is certainly something I envy, he has a history of working part-time and intermittently and is more talented at spending money than at making it.
That strongly shapes my failure to live in awe of programmers and my failure to presume them to all be wealthy and powerful types. But I believe this is the first time I have said such on HN because it's challenging, at best, and potentially impossible to express that without sounding like I am putting him down. So I just never said anything about it. Most people didn't really need that information anyway, so not saying something potentially offensive to my sister, her husband and other relatives was the easy solution.
Basically, before you tell that cutesie anecdote about your own life, contemplate what it says about people connected to you and how they might feel if they heard you telling that story. Does it cast them in a bad light? Could it be construed as such, even if that wasn't your intention? Is there some means to tweak it to make it less problematic?
The other thing I worry a lot about are acquaintances that will think I meant them when I didn't. I try to not make comments that could be taken to mean I am talking about them when I'm actually not. This is often a matter of tweaking it slightly. It might be as simple as saying "a curly haired person I know" instead of "a blonde person I know" to make sure a blonde acquaintance with straight hair doesn't assume I mean them.
Group 2 is best addressed by finding a sympathetic framing and going ahead and giving some provisos. Don't assume that folks will just know that, of course, you would make allowances for X.
Your friends and relatives may know that, but other people won't. It helps to view it as simply an artifact of clear communication.
The mistake most people make is only thinking about the intended audience and stopping there. You do need to think about that. But you should also think about anyone you are "talking about" or could be construed as talking about.
Edit: To be perfectly clear, I'm not putting my brother-in-law down. His work history is due in part to supporting my sister's career, a thing she doesn't appreciate enough.
Interesting - so with 5 people, your memory slots are clearly exceeded, even without considering the possibility that edges might not be the same in each direction.
An abstract is to summarize the results of research not to tease the reader. That's why I flagged it.
Yeah, feels like the editors dropped the ball on that. Hopefully they'll fix it before the final version.
Anyway, here's a link: https://sci-hub.tw/10.1016/j.evolhumbehav.2018.09.004
Anyway, here's a link: https://sci-hub.tw/10.1016/j.evolhumbehav.2018.09.004
thanks. was wondering how could something upvoted this high be behind a paywall without anyone asking for the paper itself. It's like people read the abstract and choose to discuss what they will.
I also couldn't be bothered to read on after that.
In some contexts the abstract has a bibliographic rather than reporting function. E.g 'is this paper relevant to my research', not what was the outcome of their research. I agree it is annoying when the abstract is only a tease to get you to look behind a paywall. However in defence and other contexts it is possible to have an unclassified abstract announcing but not summarising a piece of work whose results are classified.
The problem I see with larger group discussion is that the idea permutates far enough from the original idea after 4 turns that a participant's response to the topic may no longer be valid in the new discussion context. It can be very frustrating to have to unwind the progress to an early point for the input to be valid.
This is usually my experience, where if I'm with more than 3 people I stop talking because the idea I have is no longer relevant by the time there's an opening for me to say something.
I always thought about this in terms of individual conversational coefficients. Each separate conversation consumes a total conversational coefficient of 1.0 from all sources. Go above 1.0, and some people don't get to have their say. Go below 1.0, and there may be uncomfortable lulls.
Each person has a range of conversational contributions that they may feel comfortable with. A good university lecturer, radio show host, or stand-up comedian, for instance, might be able to sustain a maximum of 1.0 all alone for hours at a time. Someone with an inflated ego might not feel comfortable dipping below 0.5 for any length of time, whereas an introvert might range between 0.0 (pure listener) and a peak value they cannot sustain for long outside of a narrow range of topics.
So establishing the most efficient number of conversations, and their participants, becomes a form of the backpack problem. A conversation group can only achieve its highest efficiency of some people aim to fulfill different roles. Some participants are bulky and heavy, some are spongy and flexible, and others are small and light.
There's the baseline talker. This is likely the person with the highest sustainable coefficient. They drive the conversation. Then there are responders, who need to have a wide, tunable range of coefficient. They top off the conversation to 1.0 by adjusting their output to an appropriate value. There may be interjectors, who pipe up with a witty quip or relevant factoid every now and then, aiming for high return on low coefficient. There may also be swappers, who participate at a low level in multiple conversations, flipping to whichever one seems to have a lower coefficient, but less able to sustain higher coefficients than a responder. Sometimes there is even a gestural participant, who mainly contributes to the conversation with non-competing visuals rather than interruptable speech.
So having a single conversation with more than six people is easy. You kick out the baseline talker, get two responders to drive the conversation instead, and fill up the rest of the group with interjectors. This happens all the time in tabletop gaming groups, where the game itself adds a baseline coefficient, and the typical participant has a low maximum sustainable coefficient. Some people just don't want to talk much, and the game can create a structured conversation that pulls lower-coefficient players up enough to make the group reach 1.0 .
Each person has a range of conversational contributions that they may feel comfortable with. A good university lecturer, radio show host, or stand-up comedian, for instance, might be able to sustain a maximum of 1.0 all alone for hours at a time. Someone with an inflated ego might not feel comfortable dipping below 0.5 for any length of time, whereas an introvert might range between 0.0 (pure listener) and a peak value they cannot sustain for long outside of a narrow range of topics.
So establishing the most efficient number of conversations, and their participants, becomes a form of the backpack problem. A conversation group can only achieve its highest efficiency of some people aim to fulfill different roles. Some participants are bulky and heavy, some are spongy and flexible, and others are small and light.
There's the baseline talker. This is likely the person with the highest sustainable coefficient. They drive the conversation. Then there are responders, who need to have a wide, tunable range of coefficient. They top off the conversation to 1.0 by adjusting their output to an appropriate value. There may be interjectors, who pipe up with a witty quip or relevant factoid every now and then, aiming for high return on low coefficient. There may also be swappers, who participate at a low level in multiple conversations, flipping to whichever one seems to have a lower coefficient, but less able to sustain higher coefficients than a responder. Sometimes there is even a gestural participant, who mainly contributes to the conversation with non-competing visuals rather than interruptable speech.
So having a single conversation with more than six people is easy. You kick out the baseline talker, get two responders to drive the conversation instead, and fill up the rest of the group with interjectors. This happens all the time in tabletop gaming groups, where the game itself adds a baseline coefficient, and the typical participant has a low maximum sustainable coefficient. Some people just don't want to talk much, and the game can create a structured conversation that pulls lower-coefficient players up enough to make the group reach 1.0 .
for me it is an NP-hard-like reasoning. I'm not only concerned with my effect on the 3 other participants, i'm concerned with each participant's effect on each participant.
I agree with this. I also believe this is why socially normal (i.e. not socially awkward, not shy) people can have problem talking in crowds. Needs more cognitive overhead to analyze what words may cause what on certain people.
The article does mention the recursive nature of theory of mind like you note.
There's a reason why Roberts Rules, and other parliamentary procedures exist.
Once you get to ~10 people who all want to input something into the discussion, its completely and utterly impossible to move a discussion forward without a set of rules. Normally, one person who yells the loudest and ignores the most people eats up the entirety of conversation space.
As such, basic rules are invented. In Roberts Rules, its one-at-a-time, and at most contribute 2-times per any particular subject, at roughly 10-minutes maximum per person. The "Chairperson" controls the discussion to ensure the rules are applied equally to everyone, so that everyone gets a turn. If possible, the Chairperson is supposed to choose an order of people's speaking turns so that both sides of a discussion alternate back and forth (pros, then cons, then pros again. Etc. etc.).
Its slower, but it scales better. The unfortunate effect is that most people don't understand the point of Roberts Rules or Parliamentary procedure (there are many sets of rules, Roberts Rules are just the most common in the USA), so most people just see it as unnecessary set of rules that slow down a conversation.
Once you get to ~10 people who all want to input something into the discussion, its completely and utterly impossible to move a discussion forward without a set of rules. Normally, one person who yells the loudest and ignores the most people eats up the entirety of conversation space.
As such, basic rules are invented. In Roberts Rules, its one-at-a-time, and at most contribute 2-times per any particular subject, at roughly 10-minutes maximum per person. The "Chairperson" controls the discussion to ensure the rules are applied equally to everyone, so that everyone gets a turn. If possible, the Chairperson is supposed to choose an order of people's speaking turns so that both sides of a discussion alternate back and forth (pros, then cons, then pros again. Etc. etc.).
Its slower, but it scales better. The unfortunate effect is that most people don't understand the point of Roberts Rules or Parliamentary procedure (there are many sets of rules, Roberts Rules are just the most common in the USA), so most people just see it as unnecessary set of rules that slow down a conversation.
When I have a conversation, I like it to be back-and-forth: I say something, they react, I react to that, and so on, with reactions being things like asking a question, making an evaluation, saying I have had something similar happen to me, making a funny comment, and so on, so we go further and maybe deeper, a process I find rewarding.
The more people, the less often I get to react, and so it gets less enjoyable. On the other hand, with some groups we are on the same wavelength enough that a third person's reactions to the second person are enjoyable to me, too, so I am happy to just listen to their back-and-forth, at least for a while. Ditto if it is a subject being discussed that is really interesting.
The more people, the less often I get to react, and so it gets less enjoyable. On the other hand, with some groups we are on the same wavelength enough that a third person's reactions to the second person are enjoyable to me, too, so I am happy to just listen to their back-and-forth, at least for a while. Ditto if it is a subject being discussed that is really interesting.
While yes, you have to get your turn to speak, there are sometimes situations where you don't need to speak to communicate. For example in my TS raid group while there are always speakers, I prefer to write on chat and can communicate even when somebody is speaking - while I can follow the conversation that is happening between 4 speakers I can partake in the discussion and can communicate with other verbal/nonverbal participants. While my points might get omitted in the discussion, or can have a delay to get picked up it allows people that didn't get their turn to speak to get into the "conversation". In that sense the problem is not communicating with 4 people - the problem is getting your turn.
I got halfway through, which I think gets you to the answer to the money question of what's special about four. Here's my attempt to summarize:
There are bunch of possible reasons conversation size might be limited or optimal at certain numbers. They choose to focus on mentalizing -- your ability to maintain a mental model of another person. (I don't know if they have a strong claim for why they chose this.) One interesting observation that HN will love is that mentalizing is recursive. When I have a mental model of your mind, that model includes why I think your mental model of me is, and so on. If I say something to Fred while George and Harry listen in, I can reason about what Fred will think of what I say, what George will think of what Fred will think of what I say, and what Harry will think of what George will think of what I will think of what Harry will think of... ad infinitum.
By focusing on mentalizing, what matters more is the pairs of people in a conversation more than the number of people. It's about the relation between one person and their reaction to another. Pairs grow faster than linear as the number of participants increases. There are "n(n-1)/2" pairs in a conversation with "n" people.
Then they make a distinction between "inclusive" and "exclusive" pairs. An inclusive pair is one that includes you. So in a three-person conversation, there are three pairs: you-A, you-B, A-B. So two of those pairs are inclusive.
The number of pairs increases quadratically. The number of inclusive pairs increases linearly. At larger group sizes, most pairs of people don't include you.
They claim four is the magic number because that's the largest conversation size before the exclusive pairs outnumber the inclusive ones. With four people, there are three inclusive and four exclusive pairs. With five people, there are four inclusive and six exclusive.
It's a neat observation, but they note themselves that they are basically doing a post-hoc analysis. They started with four and then tried to find some math that makes it special, and eventually found two lines that cross at that point.
I do think there might be something to it. If you assume that the most valuable interactions are ones that involve you (versus deriving value from seeing what two people say to each other), then it stands to reason that you want to avoid conversations where most utterances aren't from you or to you.
But that also presumes (1) people don't derive much value from watching others talk to each other and (2) all participants are communicating to each other equally. Neither of those is true in practice.
I think a smarter way to look at it is that people strive to maximize the total value they get from all pair-wise communications. One way to do that is in a small even-handed conversation. But you can also get that by:
1. Giving a speech where you get to do almost all of the utterances. So even though there are many many pairs, most of those channels are silent, and most of the communication does involve you.
2. Watching a debate where even though your aren't participating, you get a lot of value from what the other two are saying to each other.
3. Less formal approximations of the above. All of us have probably experienced a conversation that grew to larger than four people because a minority of them had more dominant personalities so you end up with a couple of "performers" and some "audience" though people occasionally change sides.
Anyway, fun paper.
There are bunch of possible reasons conversation size might be limited or optimal at certain numbers. They choose to focus on mentalizing -- your ability to maintain a mental model of another person. (I don't know if they have a strong claim for why they chose this.) One interesting observation that HN will love is that mentalizing is recursive. When I have a mental model of your mind, that model includes why I think your mental model of me is, and so on. If I say something to Fred while George and Harry listen in, I can reason about what Fred will think of what I say, what George will think of what Fred will think of what I say, and what Harry will think of what George will think of what I will think of what Harry will think of... ad infinitum.
By focusing on mentalizing, what matters more is the pairs of people in a conversation more than the number of people. It's about the relation between one person and their reaction to another. Pairs grow faster than linear as the number of participants increases. There are "n(n-1)/2" pairs in a conversation with "n" people.
Then they make a distinction between "inclusive" and "exclusive" pairs. An inclusive pair is one that includes you. So in a three-person conversation, there are three pairs: you-A, you-B, A-B. So two of those pairs are inclusive.
The number of pairs increases quadratically. The number of inclusive pairs increases linearly. At larger group sizes, most pairs of people don't include you.
They claim four is the magic number because that's the largest conversation size before the exclusive pairs outnumber the inclusive ones. With four people, there are three inclusive and four exclusive pairs. With five people, there are four inclusive and six exclusive.
It's a neat observation, but they note themselves that they are basically doing a post-hoc analysis. They started with four and then tried to find some math that makes it special, and eventually found two lines that cross at that point.
I do think there might be something to it. If you assume that the most valuable interactions are ones that involve you (versus deriving value from seeing what two people say to each other), then it stands to reason that you want to avoid conversations where most utterances aren't from you or to you.
But that also presumes (1) people don't derive much value from watching others talk to each other and (2) all participants are communicating to each other equally. Neither of those is true in practice.
I think a smarter way to look at it is that people strive to maximize the total value they get from all pair-wise communications. One way to do that is in a small even-handed conversation. But you can also get that by:
1. Giving a speech where you get to do almost all of the utterances. So even though there are many many pairs, most of those channels are silent, and most of the communication does involve you.
2. Watching a debate where even though your aren't participating, you get a lot of value from what the other two are saying to each other.
3. Less formal approximations of the above. All of us have probably experienced a conversation that grew to larger than four people because a minority of them had more dominant personalities so you end up with a couple of "performers" and some "audience" though people occasionally change sides.
Anyway, fun paper.
Paper seems paywalled. How are you reading this? Any mirror?
Did you try Sci-Hub? Always try Sci-Hub.
The Discord engineering blog post this week has a fascinating sentence on this topic, perhaps much more interesting to me than the engineering itself:
> Every audio/video communication in Discord is multiparty. Supporting large group channels (we have seen 1000 people taking turns speaking)
https://blog.discordapp.com/how-discord-handles-two-and-half...
> Every audio/video communication in Discord is multiparty. Supporting large group channels (we have seen 1000 people taking turns speaking)
https://blog.discordapp.com/how-discord-handles-two-and-half...
More than 4-5 people simply gets impractical, but that's not such a big deal. With some restrictions you can have meetings with more people and e.g. at a long table it's simply a balance of distance (for voice and non verbal clues) and frustration of not being able to talk (at some point you just tell it your neighbor, splitting the group when it gets too big).
We have the terms monologue and dialogue, but I'm not aware of words for 3 speakers or more specified by number. (They may exist, but presumably aren't in common usage.)
So I'm a little surprised to learn that four-way conversations are a thing, actually. Or an important thing, I guess. Not that they exist per se, but that they are an important demarcation.
So I'm a little surprised to learn that four-way conversations are a thing, actually. Or an important thing, I guess. Not that they exist per se, but that they are an important demarcation.
Four way conversations are only relevant as a concept in this case because of the effects on what would be considered a discussion at that number (or more) of participants.
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Not on the internet ...
> we present one novel possible explanation for the four-person conversation size constraint.
But we're not going to tell you in the abstract.
But we're not going to tell you in the abstract.
This is really not rocket science - is a mathematical model required, and even reflective, of reality here?
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id suggest that there is no inherent need for mathematical models at all, unless there was a specific desire in the first place to produce said models for some reason. while certainly one would hope that formal models and analysis is performed in the pursuit of some noble/practical end, sometimes it's just fun to research things for the sake of it, because there's always the possibility that in researching one concept, you get exposed to an expanding universe of other concepts that depend on that original one which you never would have considered without the context of the research being performed.
that being said, i think having a formalized way of speaking about the limits of social discourse could be highly beneficial in several different contexts, such as providing effective group therapy, the representation of social interaction in film/literature/etc, and beyond that it can also be used to reason better about the nature of that squishy device that evolved to the point of being able to even comprehend the idea of "conversations" in general, no less the concept of having multiple of them simultaneously
that being said, i think having a formalized way of speaking about the limits of social discourse could be highly beneficial in several different contexts, such as providing effective group therapy, the representation of social interaction in film/literature/etc, and beyond that it can also be used to reason better about the nature of that squishy device that evolved to the point of being able to even comprehend the idea of "conversations" in general, no less the concept of having multiple of them simultaneously
that means webRTC can be quite useful
The dynamics of a good conversation are almost identical to those of a good game of hacky-sack.
6 ways from the Mythical Man Month, right?
Have you ever played the game telephone?
Behind a paywall :/