Tuesday, 02 June 2015 17:31

## Single transferable vote (STV) – an example

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Hello last week I was involved in a conference, where I had to vote via procedure called single transferable vote, for the first time in my life. Well the procedure is over a 100 years old and now days is broadly used in Australia, New Zeeland, Ireland and Malta, but being new for me I decided to learn something more about how it works. In Finland there is almost no literature about, so I developed the example bellow on the basis of what I’ve learned from the net. Verbally that’s an iterative voting process for multiple choices, where the excessive and the lacklustre votes are redistributed according to the ordered preferences of the voters. The qualifying quota is defined on the basis of the voters and the seats.

Let’s assume we have 4 applicants for 2 seats and 24 voters. Then the threshold (quota) , calculated by the formulae proposed by Newland and Britton in 1973 (there are also other options), would be V/(s+1)=24/(2+1) =8 votes, where “V” is the number of voters and “s” the number of seats. In a real vote you are not requested to arrange all candidates, but let’s see in how many ways we could arrange the 4 candidates assuming all possible ways, that’s 4!=4*3*2*1=24 or the number of permutations (arranged order) of the four options. Well for those of you who will perceive it better visually hear I made a table:

 ballot I II II IV 1 a b c d 2 a b d c 3 a c b d 4 a c d b 5 a d b c 6 a d c b 7 b a c d 8 b a d c 9 b c a d 10 b c d a 11 b d a c 12 b d c a 13 c a b d 14 c a d b 15 c b a d 16 c b d a 17 c d a b 18 c d b a 19 d c a b 20 d c b a 21 d a c b 22 d a b c 23 d b c a 24 d b a c

As I said that’s the full number of possible options, which in real elections will or may not be reached (some of the 24 options may not be chosen, some of the voters could put less than 4 options in the ballot paper, some of the ballots could be invalid or so). Well let’s assume that our 24 voters made the following 4 preferences:

 Raw/ballot I II II IV Voters 4 a c d b 5 10 b c d a 3 12 b d c a 4 16 c b d a 3 17 c d a b 3 22 d a b c 6 Sum 24

Then if we arrange the choices according to their first preference we get:

 Candidates Voters b 7 3 and 4 c 6 3 and 3 d 6 a 5