Introduction to Mathematical Sociology by James S. Coleman

By James S. Coleman

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Inkeles and Rossi, 1956). 4 P r e s t ig e S c o r e s of V a r io u s O c c u p a t io n s in t h e United States Score Physician 93 State governor 93 College professor 89 Scientist 89 County judge 87 Head of dept, in state government 87 Minister 87 Architect 86 Lawyer 86 Member of Board of Directors of large corporation 86 Civil engineer 84 Owner of factory employing about 82 100 people Accountant for a large business 81 Captain in regular army 80 Building contractor 79 Instructor in public schools (teacher) 78 Farm owner and operator 76 Official of international labor union 75 Electrician 73 Trained machinist 73 Reporter on daily newspaper 71 U n it e d St a t e s Score United States 68 Bookkeeper 68 Insurance agent Travelling salesman for wholesale 68 concern 67 Policeman 66 Mail carrier 65 Carpenter 60 Corporal in regular army Machine operator in factory 60 59 Barber 58 Clerk in a store Fisherman who owns own boat 58 Streetcar motorman 58 Restaurant cook 54 54 Truck driver 50 Farm hand 49 Coal miner Restaurant waiter 48 Dock worker 47 Bartender 44 Street sweeper 34 Shoe shiner 33 obtained in comparable surveys in these other countries.

The above discussion is left as it was to show the different directions which mathematical formalization might go. For Bernard Cohen (1963) has built a mathematical model for the Asch situation which conceives of the behavior as a stochastic “learning” Introduction to Mathematical Sociology 34 [Ch. i process. ” His past behavior in conforming or nonconforming, together with the felt rewards or punishments from the group, leads toward a “learning” of the group-reinforced response. 36Yet still remaining to be investi­ gated are most of the suggestions above: effects of group size, individual variables, environmental variables, and a psychophysical definition of the stimulus to free the mode!

A one-dimensional scale can be tested with two items (only responses yes-yes, no-yes, and no-no are allowable; yes-no responses are inconsistent with the scale). Similarly, by direct extension, a two-dimensional scale can be tested with three items, only seven of the eight possible responses being allowable (see Coleman, 1957b). However, multidimensional scales of several kinds have been developed (see Shepard, 1962; Torgerson, 1958), and different restrictions are implied by each. Another technique for locating “underlying” attributes of the individual, and one more widely used than any of these, is Thurstone’s (1947) factor analysis (the ordinary JR technique).

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