Accounting as a mathematical measurement theoretic discipline

Abstract

The major purpose of this dissertation is to consider and discuss a mathematical measurement theoretic foundation for financial accounting. First, certain of the philosophical writings in measurement theory are reviewed. In particular, it is emphasized that measurement entails identifying selected attributes of a set of objects (or events) and then assigning numbers (or vectors) to these objects so that the properties of the attributes are preserved by the assignment. Second, previous works by accountants in the measurement area are reviewed. Vickrey's "theorem"--accounting is a measurement discipline if and only if there exists an extensive economic property possessed by accounting phenomena-- is reformulated by modifying his definition of "extensive." In addition, the possible limitations of Ijiri's axiomatic structure of historical cost are considered. Finally, Chambers' insistence of a temporal requirement for accounting measurement is discussed. Third, using Debreu's work as a model, a mathematical, measurement theoretic foundation for financial accounting is provided. The relevant empirical economic attribute that commodity bundles possess in competitive markets is formally defined. A triple <G,N,Q> is established, where G is an empirical relational system, N is a numerical relational system, and Q: G --> N is a measurement homomorphism. Therefore, accounting is modeled as a measurement system. Fourth, G is shown to be naturally related to a set G (two tilde lines over G) which is proved to be a linearly ordered topological group. As such the examination of linearly ordered spaces is relevant for the foundation provided; certain topological properties of linearly ordered spaces are examined.