The more a team depends on the joint brainpower, the smaller it has to be (up to the minimum size for the complexity of the ideas sought, or rather multiplied by a term for that).
We see that in software teams that are usually limited to a size of around 7.
The highly productive lightcone teams seem to be even smaller.
At equal size, teams with more women should be more stable. To test this a domain is needed where there are roughly equal men and women, i.e., not engineering but maybe science or business administration.
What is the number at the limit of what people can do? I tried to look up the team size of the people working on the Manhattan project, but couldn’t find details. It seems that individual top scientists were working closely with teams building stuff (N=1), and there were conferences with multiple scientists (N>10), e.g., 14 on the initial bomb concept conference.
What does it actually mean to do things in a group? Maybe different actions scale differently. I can quickly think of three types of action: Brainstorming an idea. Collecting feedback for a proposal. Splitting work among multiple people who do it separately.
Brainstorming and collecting feedback seem like they could scale almost indefinitely. You can have thousand people generate ideas and send them to you by e-mail. The difficult part will be reading the ideas. Similarly, you could ask thousand people to send feedback by e-mail. Perhaps there is a psychological limit somewhere, when people aware that they are “one in a hundred” stop spending serious effort on the e-mails, because they assume their contribution will be ignored.
Splitting work, that probably depends a lot on the nature of the project. Also, it is a specific skill that some people have and some people don’t. Perhaps the advantage of a good team is the ability to select someone with the greatest skill (as opposed to someone with the greatest ego) to split the work.
More meta, perhaps the advantage of a good team is the ability to decide how things will be done in general (like, whether there will be a brainstorming at all, whether to split into multiple teams, etc.). This again depends on the context: sometimes the team has the freedom to define things, sometimes it must follow existing rules.
I am just thinking out loud here. Maybe good teamwork requires that (1) someone has the necessary skills, and (2) the team is able to recognize and accept that, so that the people who have the skills are actually allowed to use them. Either of these two is not enough alone. You could have a team of experts whose decisions are arbitrarily overriden by management, or a team of stubborn experts who refuse to cooperate at all. On the other hand, if you had a team of perfect communicators with e.g. zero programming skills, they probably couldn’t build a nontrivial software project. (There is also the possibility of unknown unknowns: a team of great communicators who are all missing some important skill, and are not even aware that such skill exists. So all they do is clearly communicate that the project is difficult for mysterious reasons.) Leadership is also one of those skills.
All your thinking out loud makes sense to me. Brainstorm as you suggested probably doesn’t scale well as many ideas will be generated again and again, maybe even logarithmic distincti results. I once read that husband wife teams do better on joint tasks than randomly paired people if equal skill. This indicates that splitting is possible.
But I you seem to go more in the direction of looking for specific mechanisms while I am more interested in data on scaling laws. Though indeed what are the scaling parameters? I guess I can be happy if there is any data on this at all and see what parameters are available.
I guess I can be happy if there is any data on this at all and see what parameters are available.
Yeah.
Well, taking your question completely literally (a group of N people doing an IQ test together), there are essentially two ways how to fail at an IQ test. Either you can solve each individual problem given enough time, but you run out of time before the entire test is finished. Or there is a problem that you cannot solve (better than guessing randomly) regardless of how much time you have.
The first case should scale linearly, because N people can simply split the test and do each their own part. The second scale would probably be logarithmic, because it requires a different approach, and many people will keep trying the same thing.
...but this is still about how “the number of solved problems” scales, and we need to convert that value to IQ. And the standard way is “what fraction of population would do worse than you”. But this depends on the nature of the test. If the test is “zillion simple questions, not enough time”, then dozen random students together will do better than Einstein. But if the test is “a few very hard questions”, then perhaps Einstein could do better than a team of million people, if some wrong answer seems more convincing than the right one to most people.
This reminds me of chess; how great chess players play against groups of people, sometimes against the entire world. Not the same thing that you want, but you might be able to get more data here: the records of such games, and the ratings of the chess players.
Sure, it depends on the type of task. But I guess we would learn a lot about human performance it we tried such experiments. For example, consider your “many small tasks” task: Even a single person will finish the last one faster than the first one in most cases.
That would imply some interesting corollaries:
The more a team depends on the joint brainpower, the smaller it has to be (up to the minimum size for the complexity of the ideas sought, or rather multiplied by a term for that).
We see that in software teams that are usually limited to a size of around 7.
The highly productive lightcone teams seem to be even smaller.
At equal size, teams with more women should be more stable. To test this a domain is needed where there are roughly equal men and women, i.e., not engineering but maybe science or business administration.
What is the number at the limit of what people can do? I tried to look up the team size of the people working on the Manhattan project, but couldn’t find details. It seems that individual top scientists were working closely with teams building stuff (N=1), and there were conferences with multiple scientists (N>10), e.g., 14 on the initial bomb concept conference.
What does it actually mean to do things in a group? Maybe different actions scale differently. I can quickly think of three types of action: Brainstorming an idea. Collecting feedback for a proposal. Splitting work among multiple people who do it separately.
Brainstorming and collecting feedback seem like they could scale almost indefinitely. You can have thousand people generate ideas and send them to you by e-mail. The difficult part will be reading the ideas. Similarly, you could ask thousand people to send feedback by e-mail. Perhaps there is a psychological limit somewhere, when people aware that they are “one in a hundred” stop spending serious effort on the e-mails, because they assume their contribution will be ignored.
Splitting work, that probably depends a lot on the nature of the project. Also, it is a specific skill that some people have and some people don’t. Perhaps the advantage of a good team is the ability to select someone with the greatest skill (as opposed to someone with the greatest ego) to split the work.
More meta, perhaps the advantage of a good team is the ability to decide how things will be done in general (like, whether there will be a brainstorming at all, whether to split into multiple teams, etc.). This again depends on the context: sometimes the team has the freedom to define things, sometimes it must follow existing rules.
I am just thinking out loud here. Maybe good teamwork requires that (1) someone has the necessary skills, and (2) the team is able to recognize and accept that, so that the people who have the skills are actually allowed to use them. Either of these two is not enough alone. You could have a team of experts whose decisions are arbitrarily overriden by management, or a team of stubborn experts who refuse to cooperate at all. On the other hand, if you had a team of perfect communicators with e.g. zero programming skills, they probably couldn’t build a nontrivial software project. (There is also the possibility of unknown unknowns: a team of great communicators who are all missing some important skill, and are not even aware that such skill exists. So all they do is clearly communicate that the project is difficult for mysterious reasons.) Leadership is also one of those skills.
All your thinking out loud makes sense to me. Brainstorm as you suggested probably doesn’t scale well as many ideas will be generated again and again, maybe even logarithmic distincti results. I once read that husband wife teams do better on joint tasks than randomly paired people if equal skill. This indicates that splitting is possible.
But I you seem to go more in the direction of looking for specific mechanisms while I am more interested in data on scaling laws. Though indeed what are the scaling parameters? I guess I can be happy if there is any data on this at all and see what parameters are available.
Yeah.
Well, taking your question completely literally (a group of N people doing an IQ test together), there are essentially two ways how to fail at an IQ test. Either you can solve each individual problem given enough time, but you run out of time before the entire test is finished. Or there is a problem that you cannot solve (better than guessing randomly) regardless of how much time you have.
The first case should scale linearly, because N people can simply split the test and do each their own part. The second scale would probably be logarithmic, because it requires a different approach, and many people will keep trying the same thing.
...but this is still about how “the number of solved problems” scales, and we need to convert that value to IQ. And the standard way is “what fraction of population would do worse than you”. But this depends on the nature of the test. If the test is “zillion simple questions, not enough time”, then dozen random students together will do better than Einstein. But if the test is “a few very hard questions”, then perhaps Einstein could do better than a team of million people, if some wrong answer seems more convincing than the right one to most people.
This reminds me of chess; how great chess players play against groups of people, sometimes against the entire world. Not the same thing that you want, but you might be able to get more data here: the records of such games, and the ratings of the chess players.
Sure, it depends on the type of task. But I guess we would learn a lot about human performance it we tried such experiments. For example, consider your “many small tasks” task: Even a single person will finish the last one faster than the first one in most cases.
I like your chess against a group example.