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07 March 2010 @ 09:52 am
"Six degrees" debunked  

I ran across this in one of the books I’m currently reading and thought it rather interesting. Interesting enough, in fact, that I decided to pass it along to you:
  How is it that such unexpected connections [between people] seem to happen as often as they do? In the 1950s, a Harvard University psychologyist named Stanley Milgram wanted to answer this question by determining, on average, how many links it would take to get from any person to any other person in the United States.
( … )
In his most famous study, Milgram found that, for the letters that made it to their target, the median number of intermediate acquaintances from starter to target was five. This result was widely quoted and is the source of the popular notion that people are linked by only “six degrees of separation.”
Later work by psychologist Judith Kleinfeld has shown that the popular interpretation of Milgram’s work was rather skewed—in fact, most of the letters from starters never made it to their targets, and in other studies by Milgram, the median number of intermediates for letters that did reach the targets was higher than five. However, the idea of a small world linked by six degrees of separation has remained as what may be an urban myth of our culture. As Kleinfeld points out,
  When people experience an unexpected social connection, the event is likely to be vivid and salient in a person’s memory…. We have a poor mathematical, as well as a poor intuitive understanding of the nature of coincidence.   
Complexity: A Guided Tour, Melanie Mitchell, Oxford University Press, New York, 2009, pages 227–228.

 
 
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(Deleted comment)
dd-bdd_b on March 7th, 2010 04:09 pm (UTC)
Yes.

I was surprised to discover he'd been involved in 6 degrees too.
DrS: Percy OKdocstrange on March 7th, 2010 04:21 pm (UTC)
Indeed. I think Milgram ultimately was a master at making initial studies delving into complicated topics, using unconventional (and sometimes ill-advised) methods. That gave him memorable results where the study turned out to be (and apparently where it did not turn out to be) on the track of a significant finding. Perhaps that's true of many true ground-breakers.

Thanks for posting that, Fred. The 6-degrees bit is a long-standing irritant in Cultural Anthro circles, where it's clear the terminology and notion comes from conflating that study with other cultural terms, into the kind of self-evident bogon the book you quote describes.
Fred A Levy Haskell: Fredcritter eyes onlyfredcritter on March 7th, 2010 04:49 pm (UTC)
You're quite welcome, doc. I do try to be useful…
Fred A Levy Haskell: Fredcritter eyes onlyfredcritter on March 7th, 2010 04:47 pm (UTC)

The omitted material describes his experimental design and first study and leads a reader to the inference that "most famous" in this context refers to this particular suite of studies and not to his entire body of work.



Edited at 2010-03-07 04:48 pm (UTC)
Fred A Levy Haskell: Fredcritter eyes onlyfredcritter on March 7th, 2010 05:49 pm (UTC)
It also occurs to me that to the general public, the "small world experiment" may well be more famous than the "behavioral study of obedience," even when we're not being pissy about the distinction between "famous" and "infamous." That is, I suspect more people "know" the six-degree meme and that an experiment by "some researcher guy" is at the root of it than know about, you know, "that study where some students shocked some other students." Although I will admit that the latter has also penetrated into the folklore to an extent. We educated folk, of course, know immediately and exactly what is meant when someone speaks of "The Milgram Experiment."
dd-bdd_b on March 7th, 2010 04:30 pm (UTC)
I think the urban legend version claims that a path of that length exists; whereas his study tested actual forwarding paths, which there was no reason to believe were optimal. The low completion rate could well have been because the obvious paths are through famous people, who are perhaps less likely to forward random letters they get.

I wouldn't go so far as to say I do think it's true necessarily. But if we each just know about 40 people, the numbers work out, at the rawest level.
Fred A Levy Haskell: Fredcritter eyes onlyfredcritter on March 7th, 2010 04:52 pm (UTC)
I wonder how much our life in fandom skews our perception of how likely "six-degrees" is to be true. I mean, I'm personal friends with, for example, Jim Young, Bruce Schneier, and Jon Singer, each of whom alone is about four degrees worth of connections…
dd-bdd_b on March 7th, 2010 05:19 pm (UTC)
The academic world is the same way, and I have some connections there still. When I was in college, I was two links from Mao Tse-Tung. And Chiang Kai-shek too.

But yeah, it's almost certainly much harder to link a grocery bagger in Gary Indiana to a farmer in India.

Celebrities of various types serve as marker beacons, visible from a long distance. But lots of people have relatives living far away from them, and that network must be pretty dense; it's just harder to find.
Carol Kennedycakmpls on March 7th, 2010 08:11 pm (UTC)
Since B had his internship at the School of Advanced International Studies Korea Institute, I am two and three links away from an ASTONISHING number of people around the world.
dd-bdd_b on March 8th, 2010 02:17 am (UTC)
Yes, I imagine!
sethb on March 9th, 2010 05:36 pm (UTC)
Grocery bagger in Gary Indiana -> customer (local college professor) -> classmate from India -> . . .

So probably not that many steps.

People have mentioned the major problems with the results: non-optimal paths (which increases the study's results relative to the true result), and ignoring failures (which would tend to decrease the study's results relative to true).

Guessing at the overall structure of the relationships (many tightly-connected groups, with many people participating in several), some such result seems reasonable.

I would guess that the answer nowadays is about two links shorted than 50 years ago.
Carol Kennedycakmpls on March 7th, 2010 08:10 pm (UTC)
I recently discovered that three people (B, C, D), one of whom I know well and two casually through fandom, are Facebook friends with someone (A) my brother knows very well, who has only a peripheral connection with fandom--about as much as my brother has just by being my brother. I suspect that B, C, and D know A in other contexts. I do not know A and my brother does not know People B-D.
Carol Kennedycakmpls on March 7th, 2010 08:14 pm (UTC)
I think the urban legend version claims that a path of that length exists; whereas his study tested actual forwarding paths, which there was no reason to believe were optimal.

I think that's correct. The urban legend maintains that the links exist, not that each person would know the best route from the first person to the final person.
et in Arcadia egoboo: banana genesapostle_of_eris on March 8th, 2010 02:25 pm (UTC)
I recall that the “hundredth monkey” is similarly mythic.

But here's a sourced one from my sig collection:
If there are two or more ways to do something, and one of those ways can result in a catastrophe, then someone will do it.
-- Edward A. Murphy, Jr., one of the engineers on the rocket-sled experiments, 1949
Before too many years had gone by variants had passed into the popular imagination, changing as they went. Most of these are variants on "Anything that can go wrong, will"; this is sometimes referred to as Finagle's Law. The memetic drift apparent in these mutants clearly demonstrates Murphy's Law acting on itself!
-- Murphy's Law