Apportionment methods

TL;DR

This paper evaluates various apportionment methods used in democratic elections by measuring their error and discusses paradoxes associated with these methods, including the Alabama Paradox.

Contribution

It introduces a framework to identify the most suitable apportionment method for a given error function and analyzes paradoxes in popular methods.

Findings

The Alabama Paradox occurs in the Hare/Hamilton method.

Different apportionment methods have unique paradoxes.

A method to find the best apportionment approach based on error measurement.

Abstract

Most democratic countries use election methods to transform election results into whole numbers which usually give the number of seats in a legislative body the parties obtained. Which election method does this best can be specified by measuring the error between the allocated result and the ideal proportion. We show how to find an election method which is best suited to a given error function. We also discuss several properties of election methods that have been labelled paradoxa. In particular we explain the highly publicised ``Alabama'' Paradox for the Hare/Hamilton method and show that other popular election methods come with their very own paradoxa.