Phragm\'en's and Thiele's election methods

TL;DR

This paper provides a detailed analysis of Phragmén's and Thiele's election methods, exploring their properties, variations, and historical context, with comparisons to other voting systems like STV.

Contribution

It offers a comprehensive examination of the methods' definitions, properties, and historical development, including their relation to STV and property satisfaction.

Findings

Phragmén's and Thiele's methods satisfy certain proportionality criteria.

The methods exhibit specific monotonicity and consistency properties.

Historical insights on the development and variations of these election methods.

Abstract

The election methods introduced in 1894--1895 by Phragm\'en and Thiele, and their somewhat later versions for ordered (ranked) ballots, are discussed in detail. The paper includes definitions and examples and discussion of whether the methods satisfy some properties, including monotonicity, consistency and various proportionality criteria. The relation with STV is also discussed. The paper also contains historical information on the methods.