Comment on Kleinfeld's "Could it be a big world after all?"


Thomas Blass
of Maryland, Baltimore County
Baltimore, MD

Judith Kleinfeld argues, on the basis of her research, against the validity and reliability of Milgram's "small world" phenomenon i.e., that two strangers in different parts of the country could be linked by about 5 or 6 intermediaries who knew each other.


Kleinfeld deserves credit for helping renew interest in a fascinating phenomenon. My purpose in writing this note is my concern that people reading her article might come away with the erroneous conclusion that her analysis is the last word on the subject.


As someone who has been immersed in Milgram's research for quite a few  years, I can tell you it is not. Kleinfeld raises some interesting questions. However, the problem with her analysis is that she goes out on a limb to draw firm, critical, conclusions on the basis of ambiguous evidence.


Specifically, she bases her argument on three things:


1) Most of the  letter chains were not completed. In Milgram's main study only about 30% of the letters reached their target. Actually, Milgram was quite "up front " about this ,saw this as a shortcoming that might give "the illusion that the chains are shorter than they are". But just how problematic this is for the small world phenomenon  depends on how one  accounts for the low completion  rates. Kleinfeld chooses to interpret this as damaging : that people tried  to pass the letter on but could not find the right intermediaries, hence no "small world". That is possible. Milgram ,however, believed that "chains die before completion because on each remove a certain proportion of participants simply do not cooperate and fail to send on the folder." That interpretation is also possible ,and there is really no way to know what is the best explanation. Milgram went on to note that his colleague at the Social Relations Dept in Harvard, the mathematical sociologist Harrison White, developed "a mathematical model to show what the distribution of chain lengths would look like if all chains went through to completion. In terms of this model, there is a transformation of data, yielding slightly longer chains". [quotes are from Milgram's article "The small world problem" in Psychology Today, May, 1967.]


2) Kleinfeld claims that Milgram's subjects were from the high-income upper-class. They  may well live in a world of small-world connectivity but  not others. Hence, according to her, Milgram demonstrated a limited phenomenon.  How does she know that  Milgram's subjects were from the upper class? Many of Milgram's subjects came from mailing lists that one can buy. The people on these kinds of lists, she claims ,are typically high-income. This is pure speculation.


3) In searching the literature, Kleinfeld found very few between-city replications of Milgram's "small-world"  findings. I have no doubt that she did a thorough search and  the results of her search are accurate. What I disagree with are the conclusions she draws. She sees this situation as being due to the fact that many  may tried to carry out "small world " experiments but were not able to replicate Milgram's findings. While this is possible, it is speculation. Another likely, and perhaps more likely, possibility is that very few others even tried to conduct such an experiment. Others may not have shared Milgram's fascination with the phenomenon. His fellow social psychologists, who were used to conducting single-point-in-time lab experiments, were not likely to be attracted to a tedious, longitudinal study. And even those who may have been interested may have found the task too daunting. Milgram had the energy, drive ,perseverance ,organizational ability, and attentiveness to detail that an exp like the "small world" required. Milgram thrived on the challenge of coming up with new techniques to study a phenomenon -- he referred to it as "experimental invention"-- no matter how much time and energy it took. He was always like that. When he was a doctoral student at Harvard, he proposed to Gordon Allport, his mentor, a cross-cultural experiment on conformity which would involve conducting an Asch-type conformity experiment in two different countries ,as his dissertation project. Allport, who was always supportive of Milgram's efforts, tried to dissuade it him as being too unrealistic. Milgram was not deterred, however. He spent one year in Oslo setting up and conducting his experiment and the following year doing the same thing in Paris, involving nearly 400 subjects .


A final point. Kleinfeld refers to Milgram's small-world "theory". Actually, Milgram did not have a theory, formal or informal, about the small world. Like most of his other  research, it was atheoretical -- something he would be criticized for throughout his career. He developed the small world method simply to provide an empirical test of a mathematical model of small-world connectivity formulated by Ithiel de Sola Pool and Manfred Kochen.