Meaningful, useful and legitimate information in the use of index numbers for decision making

Often information relevant to a decision is summarized in an index number. This paper explores conditions under which conclusions using index numbers are relevant to the decision that needs to be made. Specifically, it explores the idea that a statement using scales of measurement is meaningful in the sense that its truth or falsity does not depend on an arbitrary choice of parameters; the concept that a conclusion using index numbers is useful for the specific decision that needs to be made; and the notion that such a conclusion is legitimate in the sense that it is collected and used in a way that satisfies cultural, historical, organizational, and legal constraints. While meaningfulness is a precisely defined concept, usefulness and legitimacy are not, and the paper explores properties of these concepts that lay the groundwork for making them more precise. Many examples involving two well-known and widely-used index numbers, body mass indices and air pollution indices, are used to explore the properties of and interrelationships among meaningfulness, usefulness, and legitimacy.