4 - The essential mathematics of inputs

Summary

INTRODUCTION

This chapter attempts to conceptualize formally the decisionrelated inputs that were discusssed in the previous chapter, and to specify the interrelations among those inputs. This effort is stimulated by three points I raised at the end of chapter 3. First, I attempt to show how the domain of decisional inputs can be made more parsimonious by developing composite measures of seemingly distinct variables. Secondly, I show that these concepts are not only substantively meaningful but also mathematically precise and operationally tractable. Thirdly, I show how these individual level inputs can be transformed into group level inputs.

Three comments about the contents and structure of this chapter are in order. First, the discussion will be purely abstract. I do not go into details regarding operationalization procedures of the various concepts, though the examples I use should give some ideas regarding empirical measurement. To be sure, there are a lot of problems requiring resolution when one transforms purely abstract concepts into empirically observable variables, and I definitely do not wish to ignore them. However, in order not to confuse abstract concepts with their empirical referents, I will stick to mathematics rather than to statistics. The puzzled empiricist is referred to some of my earlier work (Maoz, 1981, 1986) for a discussion and illustration of measurement procedures and solutions to problems of validity and reliability.