STV in three easy steps!
Single Transferable Voting, a form of district-level PR, is produced simply through three actions:
1. forming multi-member districts, usually by grouping several single-member districts. Say 7 seats in a large city would be combined to make one “grouped district” covering the whole city and electing its seven councillors or MLAs. If the existing system already uses one or more multiple-member districts, such as city elections in almost all the cities in Alberta, then this step has already been done. 2. each voter can cast only one vote. The voter has opportunity to mark his first preference and as well to mark back-up preferences, which requires the next step. (The existing system used in provincial and federal elections already gives each voter just one vote so no change is required in those cases. The only change required is regarding the type of single vote cast, as listed next.) 3. voters are instructed in how to mark ranked ballots.
(And of course election officials would have to learn how to deal with any vote transfers that might be necessary).
The transfers eliminate the waste of votes of scattered less-popular candidates and also eliminate what amounts to a similar waste in overwhelming majorities.
Surplus votes are calculated by subtracting quota from a successful candidate’s vote tally. (Transfers are explained below.)
Simple as one - two - three!
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How Does STV Work?
The vote-counting process under STV is straightforward - if a bit time-consuming.
Count all the votes and establish the tallies for each candidate.
This is the First Count.
Calculate quota. This is the minimum votes needed to win (although it is possible to be elected without it.)
Usually quota is calculated by dividing the total number of valid votes by one more than the number of seats to be filled, rounded up.
Than apply Step A or B.
Step A. Declare elected all those who have at least quota. Calculate and transfer out any surplus votes of the elected candidates.
All the votes above the quota are stripped from the successful candidates and transferred to other candidates, if the voter has marked backed-up preferences, or to a pile marked "exhausted ballots" if the voter did not mark usable back-up preferences.(The transfer of surplus votes is explained below.)
Then repeat Step A or apply Step B.
Step B. Eliminate the least-popular candidate and transfer each vote to the next marked back-up preference who has not been elected or eliminated, if any. Ballots not bearing usable back-up preferences go to the "Exhausted" pile (see below). Apply Steps A and/or B until all the seats are filled by quota or until there are only as many remaining candidates (not yet elected, not yet eliminated) as there are remaining open seats. In the latter case, the remaining candidates are declared elected even if they do not have quota.
The process ends as soon as all seats are filled. Note: Once a candidate is elected or eliminated, he or she receives no vote transfers.
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Transfers of Surplus Votes When a candidate is elected, any surplus must be transferred if possible to ensure fair representation.
But which votes are transferred and which stay behind with the elected candidate?
The transfers are arranged in such a way that the quota and the transfers are each assembled so as to replicate in miniature the votes cast for the candidate, at least as far as the next choice goes.
First, any exhausted ballots are removed. They will stay with the winning candidate.
The winning candidate's remaining ballots are then sorted by the next marked back-up preference directed to a candidate not yet elected nor eliminated. The transfer of surplus votes is done proportionally. The votes left behind with a successful candidate (the quota) bear the names of the next back-up preference in the same proportion as the whole votes garnered by the candidate. And votes are transferred in the same proportion.
Mathematically, the transfer of surplus votes from successful candidate A to candidate B can be expressed thus: [the number of second choices marked on A's ballots for Candidate B]
divided by
[the total number of A's ballots minus any exhausted ballots]
multiplied by
[the number of surplus votes].
In the Alberta system, whole votes, not fractions, were transferred. The math set forth often produced results that included candidates claiming fractional votes and surplus votes not allocated. These fractions of votes were dealt with, in the Alberta system, by allocating whatever votes of the surplus were not yet allocated to the candidates with the largest fractions claimed.
This was the system formulated by John D. Hunt and described in his 1924 pamphlet Key to P.R. (1924), reprinted in many sources on Alberta elections.
Here is an example in practice:
Quota is 30. A received 55 votes in the first count and is declared elected.
A's votes (just considering 1st and 2nd preferences): 24 A-B 12 A-C 7 A-D 2 A-E 10 A with no back-up preference marked
Surplus is 25.
The 10 exhausted votes are put aside.
This leaves 45 to be sorted for proportional quota and proportional transfers.
Composition of transfers 25 votes are to be transferred: votes marked for B 24/45 X 25 = 13.333 votes marked for C 12/45 X 25 = 6.67 votes marked for D 7/45 X 25 = 3.89 votes marked for E 2/45 X 25 = 1.11.
The whole numbers above (B 13, C 6, D 3, E 1) add up to 23. The two votes remaining to be transferred are allocated to the candidates with the largest un-used fractions. Thus, C and D get one more each.
A's final vote transfers are: 13 votes transferred to B 7 transferred to C 4 transferred to D 1 transferred to E.
These transfers are added to the votes those candidates already have to create new running totals.
The quota that remains is made up of
10 marked only A 11 ballots marked A-B 5 marked A-C 3 marked A-D 1 marked A-E.
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Exhausted ballots
When a candidate is eliminated, some of the votes have no un-used marked back-up preferences or the only back-up preferences that are marked there are for candidates who have already been elected or eliminated.
In those cases, the ballot is put on the pile of exhausted ballots. A tally is kept of the votes in that pile but otherwise they are ignored from here on. They make up most of the small proportion of votes that are wasted under STV.
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STV proves itself effective at electing mixed proportionate representation in each district where it is used.
That was its record during its use in Canada from 1917 to 1971 -- in eight Alberta provincial elections, nine Manitoba provincial elections and in 150 city elections.
STV's use of multi-member districts and each voter casting only a single vote means:
- no one group can take all the district's seats
- groups that take more quotas (units of votes) take more seats than groups that take fewer votes
- transferable votes means that votes cast for candidates who have little specific support can be shifted elsewhere to hap elect another candidate also appealing to voter. (The voter does not need to scope out who will likely be elected before casting the vote. He or she can cast their vote based on their actual sentiment. There is need to prejudge and to mis-represent their view in order not to see their vote ignored, as under First-past-the post winner-take-all system.)
The STV system's goal of achieving representation of all (excepting about a quota's worth of the votes), and the combination of multiple members and the transferable vote, means that 80 to 90 percent of the voters elect someone.
(This percentage of representation is far better than FPTP winner-take-all system where as little as 34 percent are sometimes effectively used to elect someone.)
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