Measuring democracy: axiomatic foundations for aggregating characteristics

Abstract

The determination of appropriate criteria for the selection of an aggregation rule for composite indices represents a nuanced area of inquiry. This study embarks on an axiomatic exploration of the aggregation methodology employed by the Economist Intelligence Unit (EIU) in the formulation of its Democracy Index. We introduce two axiomatic precepts and demonstrate that while the EIU's additive aggregation rule satisfies one axiom, it does not uphold the other. In contrast, we suggest the implementation of the Borda count for the aggregation of identical indicator categories and reveal that this method adheres to the axiom contravened by the additive rule but does not fulfill the axiom that the additive rule meets. Moreover, we scrutinize the empirical ramifications of applying diverse aggregation rules across the span from 2006 to 2020. It is observed that the two aggregation approaches yield markedly divergent outcomes, particularly among nations with lower democratic rankings. The insights garnered from this investigation underscore the pivotal role of the selection of aggregation rules in the constitution of indices and advocate for a more profound examination of the axiomatic principles that undergird such choices.