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.
Calculate how many candidates have quota.
Declare elected all those who have at least quota.
If their election fills the seats, the process ends.
If some are declared elected but there are still seats to fill, go to Step A.
If none are declared elected, go directly to Step B.
Step A.
Calculate and transfer out any surplus votes of any elected candidates, if possible.
All the votes above the quota are stripped from the successful candidates and transferred to other candidates, or as many of them as bear one or more usable backed-up preferences.
The surplus votes are only transferred if the transfers can make a difference in the order of popularity of the remaining candidates.
(The transfer of surplus votes is explained below.)
If there are still seats remaining to be filled, 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 (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. -----------------------------------------------
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 successful candidate retains all votes that do not bear any usable back-up preferences.
If these "exhausted" ballots surpass the quota, the transfers of the transferable ballots are very simple - simply refer to the marked back-up preference on the transferable ballots and move the ballot to that candidate's pile.
If the "exhausted" ballots do not surpass the quota, that is, if there are more transferable ballots than the surplus to be transferred, the make-up of the transfers and the make-up of transferable ballots left with the successful candidate are derived proportionally through math as outlined next.
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 set aside. They will stay with the winning candidate.
If the number equals or exceeds quota, the transfer of the remaining votes is done by simple reference to the next usable marked back-up preference marked on each ballot.
If the exhausted ballots are fewer than quota, calculate how many transferable votes must remain behind as well, to bring the number of votes left with the successful candidate up to quota.
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 (to bring the number of votes up to 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 were marked: (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 left with A. This leaves 45 to be sorted for proportional fulfillment of the remaining quota (20 (30 minus 10)) 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.
With 25 to be transferred, that leaves two. 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. Due to these transfers, the quota that remains with A is made up of 10 ballots 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 single-winner 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 29 percent are sometimes effectively used to elect someone.)
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