Measuring the Unmeasurable

32 Pages Posted: 26 Feb 2012

See all articles by Kim R. Sawyer

Kim R. Sawyer

University of Melbourne - School of Historical and Philosophical Studies

Howard Sankey

University of Melbourne - School of Historical and Philosophical Studies

Ric Lombardo

RMIT University

Date Written: February 25, 2012

Abstract

Galileo suggested that what is not measurable be made measurable. It is this principle which underscores an unwritten law of both the sciences and the social sciences that it is better to measure than not to measure. But, the assumption of measurability is rarely considered. In this paper, we consider a set of invariance and continuity conditions which a measure should satisfy. These conditions provide a test of whether a given mapping onto the real line constitutes a measure, and not simply an arbitrary mapping. They represent a test for measurability. In the social sciences, it is common to construct measures based on multi-dimensional attributes. In the paper, we characterise this multi-dimensional measurement as portfolios, with weights determined a priori. Measurement becomes a process of convergence towards a preferred measure which anchors the measurement. Measurement is valid if there is convergence to a measure satisfying the invariance and continuity conditions.

Keywords: Measurability, invariance, continuity, anchoring, convergence

JEL Classification: C60, C80

Suggested Citation

Sawyer, Kim Russell and Sankey, Howard and Lombardo, Ric, Measuring the Unmeasurable (February 25, 2012). Available at SSRN: https://ssrn.com/abstract=2011239 or http://dx.doi.org/10.2139/ssrn.2011239

Kim Russell Sawyer (Contact Author)

University of Melbourne - School of Historical and Philosophical Studies ( email )

Melbourne
Australia

Howard Sankey

University of Melbourne - School of Historical and Philosophical Studies ( email )

Australia

Ric Lombardo

RMIT University ( email )

124 La Trobe Street
Melbourne, 3000
Australia

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