<p>SilvaRua – I agree with you that in the cases we’ve been talking about, these observations about group size and social behavior aren’t going to yield incredible insights. We’re essentially examining them for plausibility. But I think InequalineKea is right in the most recent post – the value of such a theory would be in deciding between competing policies.</p>
<p>The reasonably robust fact lurking below this 150 silliness is that the relationship between group size and group cohesion is highly nonlinear*. Naively you might think that in increasing the size of your group by 10 people, you win something (more people in your group) and lose something commensurate (a little closeness in your group). Contrary to this simple intuition, the social scientists seem to be finding a “phase transition” where, at some point (which differs based on the setting) adding only a few people can be quite severely detrimental to cohesion. </p>
<p>So the take-away caution is that if you have a small “150ish” group that you like, and you are voting on expanding it to 170, you should be careful and you should not use the last expansion from 130 to 150 as a reliable predictor of the effect (even though comparing that expansion to 110 –> 130 seemed to give good results). Currently a lot of work in the economics of social networks is focusing on questions like how to use simple data to determine the actual location of such phase transitions.</p>
<p>I think that result is reasonably interesting. I couldn’t have predicted it, but it seems plausible and simple in hindsight, and it does help us with serious choices we have to make sometimes. What do you think?</p>
<hr>
<ul>
<li>Toy model: imagine a “tight” organization maintains at least half the links that could exist: i.e. at least half the pairs of people who could be acquaintances actually are. With n people, there are n(n-1)/2 total pairs and so such an organization would be maintaining at least n(n-1)/4 social ties. This number is of order n^2, and so the costs of maintaining such a tight group go up quadratically in group size.</li>
</ul>