A fair election for all: what’s voting got to do with it?
[Written by Haris Aziz and Barton Lee]
Imagine awaking to a disappointing election result and being told that your preferred candidate was not elected because he/she received too many votes — and your vote was part of the problem! This may sound like a dystopian world belonging to science fiction books but it is in fact a possibility for many elections around the world including those in Australia, India, Ireland, and Pakistan.
The type of elections we have in mind are ones whose common goal is proportional representation (PR). Proportional representation (PR) is a fundamental goal when voting to select members of a national parliament, a student union body, a scientific committee, or a company board. It captures the principle that the bigger a group of voters is, the more representation they should have — this ensures that the winning committee is representative of the diverse preferences of voters.
PR is the central concern of several electoral change movements around the globe. Most of these movements push for the change to a voting rule, or method, belonging to a family of rules referred to as STV (single transferable vote). STV has been in use in some form or the other for more than a century. It is used in several national elections including those of Australia. It is also used to select committees in the Oxford Union Society.
STV applies to scenarios where voters express their preference ranking over the candidates and a target number of candidates are selected based on these reported voter preferences. STV works in rounds whereby in each round, it either selects a candidate or eliminates some candidate until a target number of candidates are selected. A candidate who has the first position in the required number of voters’ vote is selected. The required number is typically the total number of voters divided by total number of candidates to be selected. Such a voter’s vote is either removed as well or her voting weight is reduced since she has already had a representative selected. If no such candidate exists, the candidate with the least number of first ranks is removed.
STV is indeed an excellent approach to achieving PR. British intellectual John Stuart Mill placed STV “among the greatest improvements yet made in the theory and practice of government.” The main mathematical justification for STV is that it satisfies PSC (proportionality of solid coalitions) the central PR axiom. PSC roughly captures the idea that as long as voters have the same top candidates (possibly in different order), those voters do not need to coordinate their preferences to get a justified number of such candidates selected. Well-known voting theorists have gone as far as to say that it is STV satisfying PSC that makes it so suitable for PR.
STV also has some drawbacks leading to counter-intuitive and widely agreed as `unfair’ election outcomes. For example, in some instances, a candidate may not be elected because they received too many high preference votes! Formally in the literature this phenomenon is known as a violation of monotonicity. This concept is far from hypothetical. In fact, in the 2010 Australian federal election, some political commentators anticipated a violation of monotonicity and encouraged voters to manipulate their vote — giving their most preferred candidate a lower preferential vote. Another drawback is that STV is not designed to cater for voters expressing ties among candidates.
Recently, we have come up with an alternate rule called EAR (Expanding Approvals Rule) that not only satisfies PSC but also has important advantages over STV. Firstly, EAR can handle cases where voters may rank two or more candidates equally. Secondly, EAR is considerably more monotonic than STV — this means that in many instances, the nightmarish scenario we began with can safely be confined back to the domain of science fiction.
EAR works by iteratively selecting candidates that have the required quota support from the voters and accordingly reducing the weight of voters who had some representatives selected. If no candidate has sufficient support, then lower preferred candidates from the voters’ lists are considered. Unlike STV, EAR does not involve elimination of candidates.
While we do not claim that EAR is the final answer to the discussion on which rule is best for PR, it is a compelling rule which deserves consideration in discussions concerning PR.
In general, taking proportional representation concerns seriously is important to avoid disenfranchisement and concentration of power. For any such well-informed discussion on this topic, an axiomatic approach to voting is helpful.
Written by Haris Aziz and Barton Lee
Haris Aziz is a senior research scientist and academic at Data61, CSIRO and UNSW.
Barton Lee is a Scientia PhD student at UNSW business school.
