1. Single Transferable Vote (STV) System -an explanation of how to allocate seats using STVBy
CA VISHAL LANGALIA

2. STV System CA Vishal Langalia vishal@langalia.com
The Single Transferable Vote seat allocation system is a “Preferential voting system” where vote for candidates in the sequence they would like to see them elected.
It provides a method of Proportional Representation for multi- seat constituencies using the sequential preference of voters.
CA Vishal Langalia

3. Make the following candidates in your order of preference:
Sample ballot for STV
Ballot design for STV
The ballot for the Single Transferable Vote system requires the voter to mark their order of preference eg “1” for their first choice, “2” for their second, etc.
Make the following candidates in your order of preference:
Example STV Ballot
Voters will normally supply as many candidates as they are available seats.
It is possible due to the quota system that someone wins by accumulating more purely second and third preference votes than another candidate with purely first preference seats
Mitul Ghelani (MG)
Sandip Sagathia (SS)
Ketan Rana (KR)
Saurabh Dave (SD)
Jyotasana Shah (JS)
CA Vishal Langalia

4. Make the following candidates in your order of preference:
Sample ballot for STV
Ballot design for STV
The ballot for the Single Transferable Vote system requires the voter to mark their order of preference eg “1” for their first choice, “2” for their second, etc.
Make the following candidates in your order of preference:
Example STV Ballot
Voters will normally supply as many candidates as they are available seats.
It is possible due to the quota system that someone wins by accumulating more purely second and third preference votes than another candidate with purely first preference seats 2
Mitul Ghelani (MG) 1
Sandip Sagathia (SS) 5
Ketan Rana (KR) 3
Saurabh Dave (SD) 4
Jyotasana Shah (JS)
CA Vishal Langalia

5. Caculating a Quota value for deciding if a candidate has won a seat under STV
Quota Calculation
To decide when a particular candidate is elected they need to accumulate enough votes to meet a certain criteria. This “quota” value needs to be calculated .
Quota =
The use of this quota will be demonstrated in the following example. ( )
Total Valid Votes
Seats + 1
CA Vishal Langalia

6. Sequences of candidates on each ballot
Example of using STV
Sequences of candidates on each ballot
Number of Ballots
VOTES AND CANDIDATES 1 2 3 4 5 SS MG
53 Ballots
Mitul Ghelani (MG) SD KR JS
27 Ballots
Sandip Sagathia (SS)
5 Ballots
Ketan Rana (KR)
26 Ballots
Saurabh Dave (SD)
25 Ballots
Jyotasana Shah (JS)
1 Ballot
CA Vishal Langalia

7. Sequences of candidates on each ballot
Example of using STV
Sequences of candidates on each ballot
Number of Ballots
VOTES AND CANDIDATES 1 2 3 4 5 SS MG
53 Ballots
Mitul Ghelani (MG) SD KR JS
27 Ballots
Sandip Sagathia (SS)
5 Ballots
Ketan Rana (KR)
26 Ballots
Saurabh Dave (SD)
25 Ballots
Jyotasana Shah (JS)
1 Ballot
This is a simple example of how the STV system works.
The example is for 5 candidates seeking to be elected, shown in the top right box. There are only 4 seats available and STV will be used to allocate the seats according to their preferential votes.
The box in the top left shows how many of the 137 ballots were marked with each of the sequences shown. Eg. on the first line: there were 53 ballots which all have SS marked as 1 and MG as 2 with no other people marked. The second line shows 27 ballots marked as SD, SS, KR, MG, JS.
CA Vishal Langalia

8. Sequences of candidates on each ballot
Example of using STV
Sequences of candidates on each ballot
Number of Ballots
VOTES AND CANDIDATES 1 2 3 4 5 SS MG
53 Ballots
Mitul Ghelani (MG) SD KR JS
27 Ballots
Sandip Sagathia (SS)
5 Ballots
Ketan Rana (KR)
26 Ballots
Saurabh Dave (SD)
25 Ballots
Jyotasana Shah (JS)
1 Ballot
Seats to be won : 4
Quota = (Total Valid Votes / (Seats +1) ) + 1
= (137 / (4 + 1) ) +1
= 28.4
CA Vishal Langalia

9. Sequences of candidates on each ballot
Example of using STV
Sequences of candidates on each ballot
Number of Ballots
VOTES AND CANDIDATES 1 2 3 4 5 SS MG
53 Ballots 5 
Mitul Ghelani (MG) SD KR JS
27 Ballots
 53
Sandip Sagathia (SS)
5 Ballots 26
Ketan Rana (KR)
26 Ballots
 27
Saurabh Dave (SD)
25 Ballots
Jyotasana Shah (JS)
1 Ballot
Seats to be won: 4
Quota = 28.4
Round 1
Count up the total of first preference votes for each candidate.
If the total number of votes is more than the quota then they are immediately elected.
In the example above, only Sandip Sagathia (SS) has more first preference votes (53) than the quota (28.4) so is elected immediately.
CA Vishal Langalia

10. Sequences of candidates on each ballot
Example of using STV
Sequences of candidates on each ballot
Number of Ballots
VOTES AND CANDIDATES 1 2 3 4 5 SS MG
53 Ballots 5 
Mitul Ghelani (MG) SD KR JS
27 Ballots
Sandip Sagathia (SS)
5 Ballots 26
Ketan Rana (KR)
26 Ballots
 27
Saurabh Dave (SD)
25 Ballots
Jyotasana Shah (JS)
1 Ballot √
Seats to be won: 4
Quota = 28.4
Round 1
Count up the total of first preference votes for each candidate.
If the total number of votes is more than the quota then they are immediately elected.
In the example above, only Sandip Sagathia (SS) has more first preference votes (53) than the quota (28.4) so is elected immediately.
CA Vishal Langalia

11. Sequences of candidates on each ballot
Example of using STV
Sequences of candidates on each ballot
Number of Ballots
VOTES AND CANDIDATES 1 2 3 4 5 SS MG
53 Ballots 5 
Mitul Ghelani (MG) SD KR JS
27 Ballots
Sandip Sagathia (SS)
5 Ballots 26
Ketan Rana (KR)
26 Ballots
 27
Saurabh Dave (SD)
25 Ballots
Jyotasana Shah (JS)
1 Ballot √
Seats to be won: 4
Quota = 28.4
Round 1
The surplus votes over the threshold value for Sandip Sagathia (SS) are allocated to the second preference for those ballots. The 53 ballots for SS give a surplus of (53 – 28.4) = 24.6 votes. You can see from the ballot sequence on line one that MG is the next in the sequence so those ballots are transferred to their total: ( ) = 29.6.
CA Vishal Langalia

12. Sequences of candidates on each ballot
Example of using STV
Sequences of candidates on each ballot
Number of Ballots
VOTES AND CANDIDATES 1 2 3 4 5 SS MG
53 Ballots
29.6
Mitul Ghelani (MG) SD KR JS
27 Ballots
Sandip Sagathia (SS)
5 Ballots 26
Ketan Rana (KR)
26 Ballots
 27
Saurabh Dave (SD)
25 Ballots
Jyotasana Shah (JS)
1 Ballot √
Seats to be won: 4
Quota = 28.4
Round 1
The surplus votes over the threshold value for Sandip Sagathia (SS) are allocated to the second preference for those ballots. The 53 ballots for SS give a surplus of (53 – 28.4) = 24.6 votes. You can see from the ballot sequence on line one that MG is the next in the sequence so those ballots are transferred to their total: ( ) = 29.6.
CA Vishal Langalia

13. Sequences of candidates on each ballot
Example of using STV
Sequences of candidates on each ballot
Number of Ballots
VOTES AND CANDIDATES 1 2 3 4 5 SS MG
53 Ballots
29.6
Mitul Ghelani (MG) SD KR JS
27 Ballots
Sandip Sagathia (SS)
5 Ballots 26
Ketan Rana (KR)
26 Ballots
 27
Saurabh Dave (SD)
25 Ballots
Jyotasana Shah (JS)
1 Ballot √
Seats to be won: 4
Quota = 28.4
Round 2
The additional votes from SS have now increased MG’s vote count above the Quota value so they are now elected in second reound. There own surplus votes, ( ) = 1.2 votes, now transferred to the next un-elected candidate by preference, in this case KR because SS has already been elected. KR’s total now changes from 26 by adding 1.2 to become 27.2.
CA Vishal Langalia

14. Sequences of candidates on each ballot
Example of using STV
Sequences of candidates on each ballot
Number of Ballots
VOTES AND CANDIDATES 1 2 3 4 5 SS MG
53 Ballots
Mitul Ghelani (MG) SD KR JS
27 Ballots
Sandip Sagathia (SS)
5 Ballots
27.2
Ketan Rana (KR)
26 Ballots
 27
Saurabh Dave (SD)
25 Ballots 26
Jyotasana Shah (JS)
1 Ballot √ √
Seats to be won: 4
Quota = 28.4
Round 2
The additional votes from SS have now increased MG’s vote count above the Quota value so they are now elected in second reound. There own surplus votes, ( ) = 1.2 votes, now transferred to the next un-elected candidate by preference, in this case KR because SS has already been elected. KR’s total now changes from 26 by adding 1.2 to become 27.2.
CA Vishal Langalia

15. Sequences of candidates on each ballot
Example of using STV
Sequences of candidates on each ballot
Number of Ballots
VOTES AND CANDIDATES 1 2 3 4 5 SS MG
53 Ballots
Mitul Ghelani (MG) SD KR JS
27 Ballots
Sandip Sagathia (SS)
5 Ballots
28.2
Ketan Rana (KR)
26 Ballots 52
Saurabh Dave (SD)
25 Ballots
Jyotasana Shah (JS)
1 Ballot √ √ Х
Seats to be won: 4
Quota = 28.4
Round 3
There are now no more candidates with an accumulated number of votes above the quota.
This time we eliminate the candidate with the lease accumulated votes (i.e. JS) and share their votes out according to their second preference – 25 votes to SD and 1 vote to KR. We add those votes to the accumulated votes of those candidates: KR =28.2, SD 27+25=52.
CA Vishal Langalia

16. Sequences of candidates on each ballot
Example of using STV
Sequences of candidates on each ballot
Number of Ballots
VOTES AND CANDIDATES 1 2 3 4 5 SS MG
53 Ballots
Mitul Ghelani (MG) SD KR JS
27 Ballots
Sandip Sagathia (SS)
5 Ballots
28.2
Ketan Rana (KR)
26 Ballots
Saurabh Dave (SD)
25 Ballots
Jyotasana Shah (JS)
1 Ballot √ √ √ Х
Seats to be won: 4
Quota = 28.4
Round 4
The additional votes from JS have now increased SD’s vote count above the Quota value so they are now elected in the fourth round. Their own surplus votes, ( ) = 23.6 votes, are now transferred to the next un-elected candidate by preference, in this case KR ( =51.8) as everyone else has been elected or eliminated.
CA Vishal Langalia

17. Sequences of candidates on each ballot
Example of using STV
Sequences of candidates on each ballot
Number of Ballots
VOTES AND CANDIDATES 1 2 3 4 5 SS MG
53 Ballots
Mitul Ghelani (MG) SD KR JS
27 Ballots
Sandip Sagathia (SS)
5 Ballots
51.8
Ketan Rana (KR)
26 Ballots
Saurabh Dave (SD)
25 Ballots
Jyotasana Shah (JS)
1 Ballot √ √ √ Х
Seats to be won: 4
Quota = 28.4
Round 4
The additional votes from JS have now increased SD’s vote count above the Quota value so they are now elected in the fourth round. Their own surplus votes, ( ) = 23.6 votes, are now transferred to the next un-elected candidate by preference, in this case KR ( =51.8) as everyone else has been elected or eliminated.
CA Vishal Langalia

18. Sequences of candidates on each ballot
Example of using STV
Sequences of candidates on each ballot
Number of Ballots
VOTES AND CANDIDATES 1 2 3 4 5 SS MG
53 Ballots
Mitul Ghelani (MG) SD KR JS
27 Ballots
Sandip Sagathia (SS)
5 Ballots
Ketan Rana (KR)
26 Ballots
Saurabh Dave (SD)
25 Ballots
Jyotasana Shah (JS)
1 Ballot √ √ √ √ Х
Seats to be won: 4
Quota = 28.4
Round 5
There is now only candidate left (KR) so they win the last seat.
CA Vishal Langalia

19. Sequences of candidates on each ballot
Example of using STV
Sequences of candidates on each ballot
Number of Ballots
VOTES AND CANDIDATES 1 2 3 4 5 SS MG
53 Ballots
Mitul Ghelani (MG) SD KR JS
27 Ballots
Sandip Sagathia (SS)
5 Ballots
Ketan Rana (KR)
26 Ballots
Saurabh Dave (SD)
25 Ballots
Jyotasana Shah (JS)
1 Ballot √ √ √ √ Х
This is a simple example of how the STV system is used to allocated votes based on preferential voting, by re-allocating votes from elected and eliminated candidates until the accumulated votes meet the quota and that candidate is elected.
The above example is quite simple in that it does not show the complete range of combinations of selection sequences but it does explain the process – normally the vote re-allocation is done in all cases by sharing out the surplus ballots proportionally to the next choice candidate.
The process for doing this with real ballots can take a lot of time but works in similar way.
CA Vishal Langalia

20. Sequences of candidates on each ballot FIRST PREFERENCE VOTE COUNT
Make my vote count
Sequences of candidates on each ballot
Number of Ballots
FIRST PREFERENCE VOTE COUNT 1 2 3 4 5 SS MG
53 Ballots 5 
Mitul Ghelani (MG) SD KR JS
27 Ballots
 53
Sandip Sagathia (SS)
5 Ballots 26
Ketan Rana (KR)
26 Ballots
 27
Saurabh Dave (SD)
25 Ballots
Jyotasana Shah (JS)
1 Ballot
If we take analysis on first preference vote count and elected candidate, Please note that MG with least first preference vote count (5) is elected against JS with 26 first preference vote count. Х Х
CA Vishal Langalia