Composite Index Ranking of Economic Well-Being in U.S. Metropolitan Areas: How Prevalent are Rank Anomalies?

Abstract

Composite indicators have the advantage of summarizing complex multi-dimensional concepts in a single measurement. They also suffer from disadvantages such as subjectivity in choice of indicators, weighting, and aggregation methods. In this paper, we update Medcalfe’s (Social Indicators Research 139(3), 1147–1167. https://doi.org/10.1007/s11205-017-1755-5 . 2018) Economic Well-Being (EWB) index of US Metropolitan Statistical Areas with the latest (2017) available data. Using this index of EWB, we investigate two social choice violations that have been understudied in the composite indicators literature. We provide theoretical and empirical evidence of cycles and violations of independence of irrelevant alternatives. Depending on the number of cities and ranking components, incidence of these social choice violations can be large, creating ambiguity in a set of rankings. In general, having more ranking components reduces the expected and, for the most part, realized, incidence of social choice violations. Further, the results suggest that the EWB index rankings should potentially be interpreted in terms of rank tiers rather than in terms of individual rankings.