Invariance and structural dependence (Q1189545)

This book is a formal study of the concepts of dependence and independence as they occur in applied mathematics in a deterministic, as opposed to statistical, sense. An example of structural dependence arises when a variable quantity \(y\) is a function of a variable quantity \(x\). If \(x\) is an inverse function of \(y\), then dependence is symmetric. Dependence in this functional sense of determination is distinguished from another sense of structural dependence, based on relevance. Measures of both of these forms of dependence are introduced, from complete determination to complete indeterminacy, and from complete relevance to total irrelevance. These two measures may differ. One chapter (ch. 5) applies this formalism to social choice theory. The study of structural dependence in the sense of determination requires the formalization of the concepts of conformity and subordination. One major result is that the subordination relation generates a lattice in a natural way. A second major result relates subordination to invariance under a set of automorphisms. A final result grounds the concept of relevance on the concept of determination.