Axiomatic justification for a geometric quality aggregation function

A central issue in many decision-making situations is the need to consider multiple factors. A special case of multifactor modeling is the quality aggregation problem, which is to derive an overall quality measurement from a set of component quality-measurements. Although much research has been published regarding the components of a quality construct, alternative methods for aggregating quality components have been largely ignored. The function generally used for this aggregation is an arithmetic weighted average. This article proposes four axioms that are intuitively desirable in a quality aggregation function. Concepts are drawn from related disciplines such as utility theory, decision theory, and microeconomics. Empirical evidence is presented to support the axioms. The arithmetic weighted average function is found to be inconsistent with all four axioms. A geometric, or multiplicative, function form is presented as a superior alternative, consistent with the four axioms. Model specification issues and other implications are discussed.