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The math behind STV

For the past few weeks, I have been explaining different types of electoral systems. I began by looking at single-member plurality and majority systems and last week I started to look at systems of proportional representation.
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For the past few weeks, I have been explaining different types of electoral systems. I began by looking at single-member plurality and majority systems and last week I started to look at systems of proportional representation. The first system I covered was the list system. This week I will look at the single-transferable vote system. I reference An Introduction to Government and Politics by Mark O. Dickerson, Thomas Flanagan and Brenda O'Neill and the excellent resources at Fair Vote Canada and Elections B.C.

Just as a reminder that I said last week that pure proportionality would equate seat distribution with the popular vote by treating the country like one big constituency. In other words, if a political party receives 40 per cent of the votes then they should receive 40 per cent of the seats. However, I also said that in a large country, like Canada, a single constituency is not desirable because voters like to have some relationship with their local representative.

The single-transferable voting system is probably familiar to British Columbians because it was the system that we voted on in both 2005 and 2009. I will focus specifically on the B.C.STV proposal as it probably still resonates as a system that voters have heard about before.

So the first thing to know about STV is that there are large multi-member constituencies. The aim is not to change the number of representatives in Parliament but to have a broader range of representation in each constituency. So you may still have 338 MPs but not 338 constituencies. The number of representatives per constituency would vary based on the size of the electoral district. So, urban electoral districts would be smaller than rural electoral districts.

STV normally produces an outcome that replicates closely the popular vote thus it has a high degree of proportionality.

The ballot for an STV vote would have a list of candidates at least as large as the number of seats available in the electoral district. The voter is asked to rank the candidates in order of preference. Now, in some ways, this system focuses more on the candidate and less on the party although the ballot still shows to which party the candidate is affiliated. Parties may run more than one candidate. Fair Vote Canada (www.fairvote.ca/wp-content/uploads/2015/07/FVC-Tabloid.pdf ) explains that:

"STV can be used for traditional party-based national and provincial elections, as it is in Ireland, Malta, and for the Australian Senate. Because STV is not dependent on party proportionality, it is well suited for use in civil society elections - for example, electing the boards of community groups, unions, co-ops, NGOs and businesses. It is also suitable for municipal elections where candidates have no party affiliation. It was used in many western Canadian municipalities in the early 20th century....With STV, you rank as many candidates on the ballot as you wish in order of preference, 1, 2,3, etc. If candidates are affiliated with parties, you can vote across party lines, or in any manner you wish. You can vote by party, by gender, by ethnic group, by geographic location or whatever criteria you wish."

It seems that most of the issues that arise around the adoption of STV occur when proponents try to explain how the votes are counted. The system is somewhat complex. First, a quota is determined for the number of votes needed to win a seat in the riding. The equation, as outlined in the Dickerson, Flanagan and O'Neill book, is: "[Total number of valid ballots/(Number of seats +1) +1 = Quota)."

Drawing on the example in the wonderful animation that is available on YouTube at www.youtube.com/watch?v=y-4_yuK-K-k, I will use the number 10,000 valid votes and assume that there are three seats in the riding. So the quota is (10,000/3+1)+1= 2,001. Once the quota is determined, the votes are counted. In this case, if a candidate gets more than 2,001 votes they are elected and if they received more than 2,001 their "surplus" votes are redistributed based on the second choices of those voters. The votes are transferred using what is called a "transfer value."

Candidates are elected as votes are moved around so votes are not "wasted." STV aims to achieve greater diversity of representation and a more proportional outcome.

Next week I will look at a few electoral systems that are in the category of "mixed systems." In the meantime, I wish you a joyous, safe and happy New Year.