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Single Transferable Vote System (The Hare System)

This is a voting system which is designed to achieve proportional representation thorough preferential voting. Under STV, an elector’s vote is initially allocated to his/her most preferred candidate, and then after the candidate is either elected or eliminated, any surplus or unused vote are transferred to according to voter’s stated preference. The system minimizes “wasted” votes, provides approximately proportional representation, and enables votes to be explicitly cast for individual candidates rather than for closed party lists. It achieves this by using multi-seat constituencies (voting district) and by transferring votes to other eligible candidates that would otherwise wasted on sure losers and sure winners.

Voting:
In STV each voter ranks the list of candidates in order of preference. In other words, the voter places a “1” beside their most preferred candidate, a “2” beside their second preferred candidate, and so on. The ballot paper submitted by the voters therefore contains an ordinal list of candidates.
Counting of Votes:

Setting the Quota
In an STV election, a candidate requires a certain minimum number of votes – the Quota (or threshold) – to be elected. A number of different quotas can be used; the most common is the Droop quota, given by the formula:


Where the quota is an integer. When the quota is not an integer, the fractional part is rounded off. The Droop quota is an extension of requiring 50% + 1 majority in single winner election. This 50% + 1 quota is used in the election of Presidential election in India.
As per Droop quota, at most 3 people can have 25% + 1 in a 3 winner elections, 9 can have 10% + 1 in 9 winner elections, and so on.

Finding the Winner:
An STV election proceeds according to the following steps:
  1. Any candidate who has reached or exceeded the quota is declared elected.
  2. If a candidate has more votes than the quota, that candidate’s surplus votes are transferred to other candidates.  Votes that would have gone to the winner go instead to the next preferred candidates.
  3. If no one new meets the quota, the candidate with the fewest votes is eliminated and that candidate votes are transferred. This process repeats until a winner is found for every seat or there are as many seats as remaining candidates.

Example:
Suppose in a fictitious election, there are six candidates A, B, C, D, E and F. Total valid votes cast are 100. Total seats are 3.
Total number of candidates = 6
Total number of valid votes = 100
Total Seats = 3
Quota (Threshold) = (100 / (3 + 1)) + 1 = 26


Following is the list of votes gained by candidate and preference.
No of Votes / Preference
10
10
10
10
10
10
10
10
10
10
1st
A
A
B
A
C
E
B
F
A
F
2nd
B
C
D
B
D
F
D
C
F

3rd


A
C


C
B


4th



D


A




As First Preference,
A’s Votes = 40
B’s Votes = 20
C’s Votes = 10
D’s Votes = 0
E’s Votes = 10
F’s Votes = 20

So A exceeds the quota. Hence he is elected.
Except A no one could reach the quota.
Surplus votes of A = 40 – 26 = 14
Second preference of A with their ratio are B : C : F ≡ 20 : 10 : 10
Hence, votes to be divided are
B’s share = 14/2 = 7
C’s share = 14/4 = 3 (.5 rounded off)
F’s share = 14/4 = 3 (.5 rounded off)

Now votes by candidate are
B’s Votes = 20 + 7 = 27
C’s Votes = 10 + 3 = 13
D’s Votes = 0
E’s Votes = 10
F’s Votes = 20 + 3 = 23

So B reaches the Threshold, so elected.
B’s excess vote = 27 – 26 = 1
B’s next preferences are C and D.
C : D ≡ 10 : 20
So votes division is 1/3 for C and 2/3 for D.
That is C’s share = 0 (After rounding off .33 votes)
And D’s share = 1 (After rounding .66 votes)

Now votes by candidate are
C’s Votes = 13 + 0 = 13
D’s Votes = 0 + 1 = 1
E’s Votes = 10
F’s Votes = 23

Now no one reaches the threshold. So the candidate with the least votes shall be eliminated.
Candidate with least votes is D.
Next preference of D are A and C. A has already been elected, so D’s vote shall go to C.

Now votes by candidate are
C’s Votes = 13 + 1 = 14
E’s Votes = 10
F’s Votes = 23

Now again, no one qualifies. So candidate with least votes shall be eliminated. Hence E is eliminated. E’s second preference is F. so his votes shall go to F.

Now votes by candidate are
C’s Votes = 13 + 1 = 14
F’s Votes = 23 + 10 = 33

Now F qualifies by exceeding the quota. Hence he is elected.


So the elected candidates are A, B and F.

Courtesy: wikipedia
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