Search

The history of the past four decades of the theory and application of additive conjoint measurement (ACM) is characterized by vivid developments of its theoretical foundation (cf. Luce and Tukey, 1964; Krantz et al., 1971, 2006; Narens, 1974), industrious developments of statistical and computational implementations (cf. Karabatsos and Ullrich, 2002; Karabatsos and Sheu, 2004; Karabatsos, 2005; Myung et al., 2005) and heated debates about its applicability and significance in psychology (cf. Michell, 1997, 2009; Borsboom and Mellenbergh, 2004; Barrett, 2008; Borsboom and Scholten, 2008; Kyngdon, 2008a; Trendler, 2009). What started as a promising foundation to solve the everlasting debate about the quantitative nature of psychological attributes (Ferguson et al., 1939) ended in perseverative debates with very little transfer to mainstream psychological science still being dominated by structural equation modeling (SEM) and item response theory (IRT). After reading the aforementioned articles, and comparing their implications with the day-to-day business of mainstream psychological science, even an unbiased reader would certainly agree with Cliff (1992) that ACM was a “… revolution that never happened” (p. 186). It is not the aim of this article, to discredit the efforts of mathematical psychology and proponents of ACM in particular. I just want to address the naive but relevant question why ACM as a stringent way to formalize and to test the requirements of quantitative measurement in psychology has not been embraced by mainstream psychology as a means to an end to test what they always claim: that most of the attributes (e.g., intelligence and personality factors) are quantitative. An attribute possessing a quantitative structure is required to satisfy the three conditions of ordinality (transitivity, antisymmetry, and strong connexity) and the six conditions of additivity (associativity, commutativity, monotonicity, solvability, positivity, and the Archimedean condition; cf. Michell, 1990, p. 52f.). Most of these conditions are testable hypotheses but I have never seen any empirical test in psychological articles before data were analyzed with SEM or IRT models, which already assume the quantitative structure of the attributes under consideration as argued below. Somewhere during my psychology studies at the university I learned that psychology is an empirical science and that there is therefore no room for claims that should just be believed. However, given the assumed but almost never tested quantitative nature of most of the psychological attributes as reflected in factor analysis, SEM and IRT models, I must have missed or misunderstood something.