Mathematical Modeling in the Social and Life Sciences

CHAPTER 7

Foundations of Measurement Theory

It is a scientific platitude that there can be neither precise control nor prediction of phenomena without measurement. Disciplines as diverse as cosmology and social psychology provide evidence that it is nearly useless to have an exactly formulated quantitative theory if empirically feasible methods of measurement cannot be developed for substantial portions of the quantitative concepts of the theory.

—Dana Scott and Patrick Suppes

I. The Registrar's Problem

Middlebury College divides its academic year into three major components: two 12-week semesters sandwiching a 4-week “winter term.” During the winter term each faculty member offers, and each student enrolls in, one course. Because of the experimental nature of many of the courses offered, enrollment is often restricted to 20 or 25 students in each class. Since a typical Winter Term will find 1,800 students on campus and only 70 courses, it is clear that not every student will be able to take the course she most desires.

When a student registers for winter term, then, she lists five courses in descending order of preference. The registrar assigns each student to a course, using these preferences as a guide. At the present time, the registrar uses a procedure based on the desire to maximize the number of students who receive their first choice. There has been considerable discussion lately about the fairness and desirability of this particular priority scheme. An alternative method ...