This thesis revisits the axiomatic foundations of Statistical Activity Cost Analysis (SACA). This entails discussing the applicability of Representational Theories of Measurement to accounting with the view of revising SACA’s interpretation of the empirical attribute represented by accounting numbers. It is shown that a reinterpretation of the accounting attribute is possible and desirable such that it expresses input-output relationships among physical resources within a set of accounting transformations that refer to trading, production or both. The additive representation is retained. An alternative is introduced that expresses the representational theorem in multiplicative terms. It is argued that the additive representation is preferred by accountants while the multiplicative one is preferred by economists. The underlying attribute, input-output relationships, is additively represented by costs and multiplicatively represented by prices.
SACA relies on two axiomatic structures which complement each other, cost and production, along with axiomatic statements concerning a currency standard. This thesis focuses on production only. It proposes statements that are different from the original ones and such that the resulting formalism is made probabilistic at the very axiomatic level. This theoretical outcome had not been developed previously. With the probabilistic formalism the nature of the attribute is subjective information held by decision-makers about input-output relationships. The collection of subjectively interpreted input-output relationships is associated with the term ‘strategy’.
The thesis makes two additional contributions to the accounting measurement literature. It clarifies what an accounting process-based measurement is supposed to mean. This helps to understand the existing dichotomy between the balance-sheet and market based approach to value measurement as opposed to the income statement approach. Further, it renders SACA in the formalism of linear algebra. This is expected to help spreading SACA-based analyses among theoretical accountants, managerial accountants, economic theorists, and production managers.
The thesis also opens new venues for investigating the connections between accounting and economics at the level of the formalism.
