IN THIS
SECTION
Stay informed with ERS email updates.
Sign up...
Systems Guide
A model STV election
Our sample election uses a hypothetical 5-member constituency of 48 voters. In this case there are seven candidates from two political parties, A and B.
The Returning Officer sorts and counts the ballot papers according to the candidates marked as first preference. Here we are concerned with 48 electors, and 48 votes. First preferences for each candidate are represented by the number "1" on the ballot paper, and are indicated in the diagram below by appropriate letters. Imagine the voter lining up to stand beside their favourite candidate.
When the votes have been totalled, the Returning Officer calculates the quota needed for election, that is, the smallest number of votes a candidate needs in order to be elected.
Three candidates, Peter, Lance and Vann have already obtained the quota of votes, and are therefore declared elected at Stage I.
Peter has 16 votes, but only needs 8 to be elected. His surplus, the equivalent of 8 votes, must be transferred, i.e. he does not require eight-sixteenths of his votes. All sixteen of "Peter" first preference ballot papers are examined and transferred, each at a value of 8/16th, or 0.5 of a vote, to the next available preference. In the case of a second preference for Lance or Vann, (already elected) the paper is passed to the third preference (or fourth if second and third preferences are for both).
If we suppose that 10 of the 16 papers show a next available preference for Shaw, and 6 for Erin, then Shaw receives 5 (10 votes x 0.5) votes, and Erin receives 3 (6 votes x 0.5) votes from the surplus of 8. The transfer of this surplus constitutes Stage II of the Count. Shaw now has 8 votes, equal to the quota, and is elected.
As there are no further surpluses to be distributed, the candidate who now has fewest votes, Rodney, is excluded, and all his votes are transferred to the next available preferences of all those who voted for him. We may suppose that all four of Rodney's votes pass to Todd. Any with preferences for Lance or other elected candidates are passed to the next preference not already elected.
Exclusion of this candidate constitutes stage III of the count.
Lance and Todd, on attaining the quota, are declared elected.
As five candidates now have the quota, the count is complete. Erin is runner-up.
Apart from the 3 votes which Erin obtained in Stage I, 45 of the 48 electors have been effective in helping to elect a candidate. Party A with 30 votes has 3 seats, Party B with 18 votes has 2 seats, giving proportional representation to the main streams of opinion.
Stage I - Counting the Votes
The Returning Officer sorts and counts the ballot papers according to the candidates marked as first preference. Here we are concerned with 48 electors, and 48 votes. First preferences for each candidate are represented by the number "1" on the ballot paper, and are indicated in the diagram below by appropriate letters. Imagine the voter lining up to stand beside their favourite candidate.
When the votes have been totalled, the Returning Officer calculates the quota needed for election, that is, the smallest number of votes a candidate needs in order to be elected.
To calculate the quota, the Returning Officer divides the total number of valid votes (in this case 48) by one more than the number of members to be elected (in this case 5+1=6) to make a total (in this case 8.00). This total is exact to two places of decimals; otherwise it would then be rounded up to the next highest 0.01.In this case, the quota is 8 votes exactly.
| Candidates | Party | Votes | Totals | Results |
| Erin | A | EEE | 3 | -- |
| Lance | B | LLLL LLLL | 8 | Elected |
| Peter | A | PPPP PPPP PPPP PPPP | 16 | Elected |
| Rodney | B | RRRR | 4 | -- |
| Shaw | A | SSS | 3 | -- |
| Todd | B | TTTT TT | 6 | -- |
| Vann | A | VVVV VVVV | 8 | Elected |
| -- | -- | -- | 48 | -- |
Three candidates, Peter, Lance and Vann have already obtained the quota of votes, and are therefore declared elected at Stage I.
Stage II - Transfer of Peter's surplus votes
Peter has 16 votes, but only needs 8 to be elected. His surplus, the equivalent of 8 votes, must be transferred, i.e. he does not require eight-sixteenths of his votes. All sixteen of "Peter" first preference ballot papers are examined and transferred, each at a value of 8/16th, or 0.5 of a vote, to the next available preference. In the case of a second preference for Lance or Vann, (already elected) the paper is passed to the third preference (or fourth if second and third preferences are for both).
If we suppose that 10 of the 16 papers show a next available preference for Shaw, and 6 for Erin, then Shaw receives 5 (10 votes x 0.5) votes, and Erin receives 3 (6 votes x 0.5) votes from the surplus of 8. The transfer of this surplus constitutes Stage II of the Count. Shaw now has 8 votes, equal to the quota, and is elected.
| Candidates | Party | Votes | Totals | Results |
| Erin | A | EEE PPP | 6 | -- |
| Lance | B | LLLL LLLL | 8 | Elected |
| Peter | A | PPPP PPPP | 8 | Elected |
| Rodney | B | RRRR | 4 | -- |
| Shaw | A | SSS PPPP P | 8 | Elected |
| Todd | B | TTTT TT | 6 | -- |
| Vann | A | VVVV VVVV | 8 | Elected |
| -- | -- | -- | 48 | -- |
Stage III - Exclusion of Rodney
As there are no further surpluses to be distributed, the candidate who now has fewest votes, Rodney, is excluded, and all his votes are transferred to the next available preferences of all those who voted for him. We may suppose that all four of Rodney's votes pass to Todd. Any with preferences for Lance or other elected candidates are passed to the next preference not already elected.
Exclusion of this candidate constitutes stage III of the count.
| Candidates | Party | Votes | Totals | Results |
| Erin | A | EEE PPP | 6 | Runner-up |
| Lance | B | LLLL LLLL | 8 | Elected |
| Peter | A | PPPP PPPP | 8 | Elected |
| Rodney | B | -- | -- | -- |
| Shaw | A | SSS PPPP P | 8 | Elected |
| Todd | B | TTTT TT RRRR | 10 | Elected |
| Vann | A | VVVV VVVV | 8 | Elected |
| -- | -- | -- | 48 | -- |
Lance and Todd, on attaining the quota, are declared elected.
As five candidates now have the quota, the count is complete. Erin is runner-up.
Apart from the 3 votes which Erin obtained in Stage I, 45 of the 48 electors have been effective in helping to elect a candidate. Party A with 30 votes has 3 seats, Party B with 18 votes has 2 seats, giving proportional representation to the main streams of opinion.
Summary
The successive stages of the model election just discussed are exhibited by the Returning Officer on a Result Sheet.
| Candidates | Party | Stage I | Stage II | Stage III | |||
| Erin | A | 3 | +3 | 6 | 6 | Runner-up | |
| Lance | B | 8 | 8 | 8 | Elected | ||
| Peter | A | 16 | -8 | 8 | 8 | Elected | |
| Rodney | B | 4 | 4 | -4 | -- | ||
| Shaw | A | 3 | +5 | 8 | 8 | Elected | |
| Todd | B | 6 | 6 | +4 | 10 | Elected | |
| Vann | A | 8 | 8 | 8 | Elected | ||
| Total | 48 | 48 | 48 | ||||
Latest News
Electoral Reform Society announces new Chief Executive
Published: Thursday, August 26th 2010
Katie Ghose has been appointed the new Chief Executive of the Electoral Reform Society. Katie Ghose has been director of the British Institute of Human Rights for 5 years. An experienced campaigner and barrister, she has previously held positions at Age Concern England (now Age UK) and Citizens Advice. More...
AV in practice: ERS response to Australian Election
Published: Sunday, August 22nd 2010
The Electoral Reform Society has released its initial findings on the latest Australian Federal Election. Australia’s House of Representatives is elected by the Alternative Vote (AV) system, which will be offered to the British public in a referendum next May. More...
AV EDM: Mischief Makers out in force
Published: Tuesday, July 27th 2010
The Electoral Reform Society has criticised 40 Conservative MPs who have signed up to an Early Day Motion (EDM) proposing changing the date of the forthcoming referendum on the Alternative Vote. More...