Treating Data Collected by the “Small World” Method as a Markov Process

This article uses data gathered by the "small world" technique to estimate the distance between social categories, the diffuseness of connection within a category, and the relative isolation of various categories. The critical questions for the data are the adequacy of the categories and the distribution of the chains of booklets which fail to reach the target. If the population can be divided into n categories, the natural model for the data is an n+2 state Markov process where the two additional states are "lost" and "target." The discussion centers around the use of the transition matrix as a description of social structure and the comparison of observed and predicted average chain lengths as a test for the adequacy of the categories as a descriptive system. If the categories are "good," the "lost" column of the transition matrix can be eliminated and the new matrix can then be used to "correct" the observed average chain lengths to estimates of the average chain lengths, had all chains been completed. Milgram (1967; 1969), Korte and Milgram (1970), Shotland (1970; 1971), and Travers and Milgram ( 1969), have used a technique that extends classical sociometry to the study of very large preexisting groups such as nations and campuses. Milgram (1967) called the method the "small world' technique. A booklet is given to a "starter" person with instructions This content downloaded from 207.46.13.86 on Sat, 15 Oct 2016 04:26:25 UTC All use subject to http://about.jstor.org/terms 322 / SOCIAL FORCES / vol. 52, mar. 1974 to move the booklet to a person designated as the target. If the starter does not know the target according to the established criterion (for example, knowing the person on a first name basis) then he is instructed to pass the booklet to a person he does know (according to the criterion) who has a better chance of knowing the target. This process is repeated until it reaches the target. If the booklet reaches the target, the number of intermediaries or passes is an index of the social distance from starter to target. Thus Milgram gives an estimate of about five intermediaries as the average social distance of two randomly chosen people in the United States. If the population can be partitioned into exhaustive categories, the average distance from persons in category A to persons in category B can be taken as an index of the distance from class A to class B. The distance from A to B can be estimated from a sample of chains where the starter is randomly selected from A and the target is randomly and independently selected from B. Finally we note that this procedure can be applied to a single class A. However, the average length of chains from one person in A to another person in A will not be zero and is thus not a "distance" measure. Rather this number assesses the diffuseness of social structure in a category and if categories are of the same size it is a measure of average social isolation. For example, the social distances betWeen the students, faculty, and administrators of Michigan State University were measured by Shotland (1970; 1971). His distances are shown in Table 1. Table 1. The Mean Number of Intermediaries Required for a Booklet to Go from People in One University Category to People in Another (Shotland, 1970). Each cell mean is based on 110 booklets