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How does the STV voting system work?

STV (the single transferable vote) works as follows:-

1. During the election, the voters rank the candidates in order of preference, 1, 2, 3, etc.

2. Counting begins with a quota being calculated. The quota is the amount of votes a candidate needs to guarantee election. The quota is calculated as
No. of votes / (No. of seats + 1) + 1

3. The first preference votes of each candidate are counted. If any candidate has reached the quota, they are deemed elected.

4. If there are seats remaining to be filled, then the next stage is either the distribution of the surpluses of elected candidates or the elimination of the lowest candidates and the distribution of their votes.
The surplus of an elected candidate is the number of votes by which they exceed the quota. These votes are distributed proportionally among the remaining candidates according to the preferences expressed on the ballot papers.
If there is no surplus to distribute, or if the undistributed surpluses are too small to make a difference, then the lowest-placed candidate is eliminated and their votes are assigned to next preference.
This step is repeated until all seats are filled.

The following example shows an election process in a 2-seat constituency with 4 candidates. The total no. of votes cast is 600, so the quota is calculated as 201. (The quota is represented by the red line in the example).

The following shows the first count result:-
     
A 250 votes
     
B 150 votes
     
C 120 votes
     
D 80 votes
Candidate A is elected after reaching the quota. Now his surplus of 49 votes is distributed. B gets 10 votes, C gets 5 votes and D gets 30 votes. The remaining 4 are non-transferable.
     
A (elected)
       
B 160 votes
       
C 125 votes
       
D 110 votes
No candidate has reached the quota. There are no surpluses to distribute so the lowest-placed candidate, D, is eliminated. Of his 110 votes, 30 go to B, 70 go to C and 10 are non-transferable (the voters have not expressed any further preference).
     
A (elected)
         
B 190 votes
         
C 195 votes
     
D (eliminated)
There are now only 2 candidates left, B and C. C has the higher vote and is elected without reaching the quota.
© Ciaran Quinn, Dublin - last updated on 24th June 2000