Rethinking the D'Hondt method

ABSTRACT The D'Hondt method is the most popular proportional apportionment procedure, as well as one of the oldest. Despite this, the method is not fully understood, with serious normative and empirical implications for democratic representation. This paper provides insights into the D'Hondt method through a generalization that is based on a finite mixture model, extends to situations with missing data (e.g. imperfect records), and applies to allocation problems outside of elections. The generalization disproves several widely accepted beliefs, clarifying that the method maximizes the fraction of exactly proportionally represented votes, and providing intuitive measures of overall and party-level disproportionality. The crucial insights of this interpretation are easily communicated in natural language without any mathematical formalisms, which makes it particularly useful for lay audiences and civic education. I illustrate these features with the 1999–2014 British European Parliament elections