Cumulative distributions calibrate fuzzy-set codings but must not be applied automatically

Evidence

One of the things that one can do in making these transformations, as a guide, is to look at the actual distribution of the cases; see figure 5.1. In fact, in the fuzzy-logic literature on poverty (e.g., Cerioli and Zani 1990; see Alkire et al. 2015 for a critical overview) this is the main approach: one uses the cumulative distribution function as a way to calibrate and transform the underlying data into the [0, 1] interval. While this should not be done in an automatic fashion, it does provide a way to think about the levels. One of the things that comes out when looking at the histogram of the PTS data, as with much social science data, is that they are skewed: there are relatively few cases at the highest level of human-rights violations, less than half those with the best scores. — Gary Goertz, Social Science Concepts and Measurement, 790

Categorization

• XREF: Connects to the earlier poverty/wealth measurement chapter’s use of distributional calibration for fuzzy concepts.