Caltech class sizes and the "Rule of 150"

Colleges and Universities A-Z California Institute of Technology
21

<p>One property is that Caltech houses are contained within a larger social group that exceeds the size of 150. There an external group that members of the house must interact with on a daily basis, so to speak, and the external group that it must interact with on a daily basis exceeds 150.</p>

<p>This is also true for small military companies, however.</p>

<p>However, the size of the external group may also affect outcomes such as informally bottom-up enforced protocol vs. formally top-down enforced protocol.</p>

22

<p>Hi all. Sorry for ducking out for a day -- but I'm very pleasantly surprised by the turn this discussion has taken.</p>

<p>SilvaRua asked whether the "Rule of 150" (in particular, that precise number) has much relevance in actual social science research. You are right that the answer is no. Gladwell is cheerleading -- that's his job. The faux precision colorfully raises the hope that laws governing large-scale social interactions might be akin to laws of physics (with precise constants!), although of course the real statements in this science of social interaction would probably not include the number 150.</p>

<p>With books like Gladwell's, and with Freakonomics, I think the important thing for intellectually serious readers to remember is that hyperbole and imprecision form the essence of those works and that this is not so bad. The best scientists I know still get excited by that type of cheerleading despite -- or perhaps because of -- understanding the caveats better than anyone else. I think the reason is that it does a good job of capturing the fundamentally exciting hope of the field at the cost of a few pesky facts. Responding to a book like that by complaining about robustness is like responding to a fable of Aesop's by saying that foxes don't talk. It is true but misses the point.</p>

<p>I maintain vigorously that Caltech houses are almost perfect examples in the essential ways. SilvaRua said:
[quote]
It's neither highly person[al] nor are there informally enforced rules,

[/quote]
but I think both of these statements are off. I'll only take on the rules for now. Each house clearly has such rules. In Fleming, it is a serious social faux pas to talk much about academics at any house social event. At dinner this rule is enforced explicitly, while elsewhere it is enforced very informally. Everyone knows this and everyone obeys the rule. I am sure this happens also in other houses -- with different rules, of course. </p>

<p>But we could argue forever about whether the houses are or aren't good examples. Obviously Gladwell's exposition wasn't precise enough to give very clear criteria to settle the debate. If we give a little more leeway, I do think it's relevant that Caltech's small community allows a more personal and informal system of governance than any other major university and that this is a big component of Caltech's success. Would you guys disagree?</p>

23

<p>
[QUOTE]
With books like Gladwell's, and with Freakonomics, I think the important thing for intellectually serious readers to remember is that hyperbole and imprecision form the essence of those works and that this is not so bad. The best scientists I know still get excited by that type of cheerleading despite -- or perhaps because of -- understanding the caveats better than anyone else. I think the reason is that it does a good job of capturing the fundamentally exciting hope of the field at the cost of a few pesky facts. Responding to a book like that by complaining about robustness is like responding to a fable of Aesop's by saying that foxes don't talk. It is true but misses the point.

[/QUOTE]
</p>

<p>I almost completely agree with this, except I simply considered "Freakonomics" more exciting, since its conclusions and applications were more unexpected and more solidly supported by empirical evidence. </p>

<p>Obviously, it's a genre of books (social science popularization/sociological commentary) that aren't supposed to be rigorous, but within that, you have both the good and bad; "Freakonomics" being one of the absolute best, and something like "The World is Flat" being one of the absolute worst. </p>

<p>Gladwell's was in-between for me, but the rule of 150 in particular seemed quite hollow and boring. </p>

<p>


</p>

<p>Combined with the disclaimer about Gladwell's unclear criteria, you're absolutely correct here. But in that case, the rule of 150 just seems worthless; what interesting conclusions can we draw from it, aside from observations about House dinners, which I could argue are as much a factor of mandatory board for anyone living on campus as anything else? Furthermore, a bunch of people, including both of us, didn't attend those dinners much after frosh year, so what long-lasting effect did it honestly have, and did it truly impact the entire group? </p>

<p>On a slightly related note, I'm disliking the House system the longer I spend at Caltech.</p>

24

<p>
[quote]
SilvaRua asked whether the "Rule of 150" (in particular, that precise number) has much relevance in actual social science research. You are right that the answer is no. Gladwell is cheerleading -- that's his job. The faux precision colorfully raises the hope that laws governing large-scale social interactions might be akin to laws of physics (with precise constants!), although of course the real statements in this science of social interaction would probably not include the number 150.</p>

<p>With books like Gladwell's, and with Freakonomics, I think the important thing for intellectually serious readers to remember is that hyperbole and imprecision form the essence of those works and that this is not so bad. The best scientists I know still get excited by that type of cheerleading despite -- or perhaps because of -- understanding the caveats better than anyone else. I think the reason is that it does a good job of capturing the fundamentally exciting hope of the field at the cost of a few pesky facts. Responding to a book like that by complaining about robustness is like responding to a fable of Aesop's by saying that foxes don't talk. It is true but misses the point.

[/quote]
</p>

<p>Interesting points as always. :)</p>

<p>
[quote]
something like "The World is Flat" being one of the absolute worst.

[/quote]
</p>

<p>Why do you think "The World is Flat" is one of the absolute worst books? While it's not based on social science research, I still think that its hypotheses are thought-provoking, to say the least. </p>

<p>
[quote]
Combined with the disclaimer about Gladwell's unclear criteria, you're absolutely correct here. But in that case, the rule of 150 just seems worthless; what interesting conclusions can we draw from it, aside from observations about House dinners, which I could argue are as much a factor of mandatory board for anyone living on campus as anything else? Furthermore, a bunch of people, including both of us, didn't attend those dinners much after frosh year, so what long-lasting effect did it honestly have, and did it truly impact the entire group?

[/quote]
</p>

<p>I think the only interesting conclusion would be drawn if there was a comparison made between a 100-member house and a house with over 150 members. Since no arrangement exists, and there seems not to be a reason to motivate such an arrangement, it's impossible to really draw any conclusions from the specific number of 150, apart from the already well-known observation that # of people correlates inversely with in-group intimacy. The point of such hypotheses, anyhow, is not to draw any rigorous conclusions, but to more or less encourage the reader to be more aware of how significant group sizes can be in social interaction.</p>

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<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>

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<p>That was an excellent post; in fact, it's motivated me to try to find some research papers on the subject. </p>

<p>It certainly makes sense that it's non-linear, especially if we model the social group as a system of differential equations. Thanks for the insight; I'm really hoping to see Ben's own version of "Freakonomics" ten years from now.</p>