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.

A Spatial Typography of Environmentally Friendly Common Agricultural Policy Support Relevant to European Green Deal Objectives

“…The second method was the D'Hondt method [29], which allows any structure to be objectively examined [30,31]. The method is practically applied, among others, to distributing seats in the electoral systems of many countries [32]. In this case, it consists, in essence, of dividing each absolute value or percentage assigned to O, E and H by the integers 1 to 6, producing a set of 18 quotients.…”

The Theory of Democratic Voice Expression

“…Traditionally, seats remaining after allocation of full quotients are filled based by residual quotients. It is known that the D'Hondt method of deciding residuals results in the greatest number of essential ballots and lowest number of losing ballots and is therefore most compatible with voice expression [37].…”

Measuring Democratic Voice

“…Allocation of seats within an allocation division is by proportional representation, using D'Hondt to maximize essential ballot count [12] in accord with Canadian jurisprudence [13,14,15,10,16,9]. Matching of candidates to allocated seats is by rank based on local performance, i.e., ballots polled divided by riding electors.…”