Measuring Diversity: Choice in Local Housing Markets

In this paper a method of measuring object diversity, based on an application of a diversity index, is proposed. The problem of finding an appropriate measure of diversity is formulated as a projection from a finite‐dimensional space onto a one‐dimensional space. In such an approach, the measure of diversity is expressed in the form of a one‐dimensional descriptor (index). Properties of the index, such as exactness of measurement of diversity and examination of the behavior of the index as a function in three‐dimensional space, are described and illustrated. A procedure for normalizing the index and identifying characteristic points for the interpretation of the results is proposed. The utilization of characteristic points and a fuzzy set theory to distinguish the levels of diversity is also proposed. An application of the method to measure the diversity of the housing stock in local areas of some Australian cities is presented. A further application of the normalized diversity index, that is, to find a relationship between housing diversity and population characteristics in particular areas, is also developed.