Is Single Transferable Vote the best voting system ever?
an ideal voting system
In the past I have discussed First Past the Post (FPTP) and explained why it's a shitty crappy no-good voting system. I've also discussed an alternative system for electing one winner, Instant Runoff Voting (aka IRV, Alternative Vote (AV), or Ranked Choice Voting (RCV)).
IRV is also a form of Single Transferable Vote, in fact it's a special case of Single Transferable Vote (STV) that elects one winner.
So what is Single Transferable Vote? In short, it's a voting system for selecting multiple winners. (It is also known as STV, British Proportional Representation, PR-STV (Proportional Representation - Single Transferable Vote), P-RCV (for: Proportional Ranked Choice Voting)).
STV was created by Thomas Wright Hill, who was a schoolmaster. In 1821 he had his pupils elect a committee:
[Hill's] pupils were asked to elect a committee by standing beside the boy they liked best. This first produced a number of unequal groups, but soon the boys in the largest groups came to the conclusion that not all of them were actually necessary for the election of their favourite and some moved on to help another candidate, while on the other hand the few supporters of an unpopular boy gave him up as hopeless and transferred themselves to the candidate they considered the next best. The final result was that a number of candidates equal to the number required for the committee were each surrounded by the same number of supporters, with only two or three boys left over who were dissatisfied with all those elected.
This example demonstrates all the features of STV, i.e.:
(1) it's a method of electing a predetermined number of candidates (call this N)
(2) the N candidates with the most votes win
(3) each voter gets one vote
(4) voters can transfer their vote between candidates to get their most desired outcome from it
I'd like to be able to say that upon seeing this, Hill had a eureka moment and STV came to him in a flash. But that's apparently not how it happened; he had previously conducted an STV election 2 years earlier in 1819.
How do I vote in an STV election?
Here's an example of an STV ballot paper. In this election there are 6 candidates, 3 of whom will be elected:
To vote in an STV election, you mark "1" against the candidate you most prefer, "2" against your second-highest preference, 3 against your third etc until you have no more preferences among the remaining candidates.
The ballot paper has been filled in by a voter. The voter's favourite candidate is Charlie Carrot, so the voter has put "1" against him. The voter's second preference is Betty Banana so she gets a "2" against her, etc. The voter's next preferences are Eggplant and Fruit, but because the voter is indifferent between Apple and Date, they don't mark a 5th or 6th preference.
How are the votes counted?
In our example above, there were 1000 valid votes. Imagine a candidate has 251 votes. Then if two other candidates also have 251 votes, between them they have 753 votes and there are only another 247 votes. Thus if you have 251 votes, you are bound to be elected.
Thus, 251 votes is a magic number in that it is the minimum number of votes that if you get it you're certain to be elected. This number is usually called the quota. Formally, the quota is calculated as:
quota = int(nv/(ns+1)) + 1Where:
nv = number of votes
ns = number of seats (i.e. people to be elected)
int(x) = the highest integer that is <= x
In our example above, the quota is int(1000/(3+1))+1 which is 251.
On the first round, Charlie Carrot does really well. He gets 300 votes. This is more than he needs to get elected, so the surplus votes (300-251=49) are redistributed to their voter's lower preferences.
The way this is done is by fractional votes. For each vote, 251/300 of that vote goes to Carrot, and the rest of the vote (49/300) goes to the lower preference.
Taking our ballot paper above, Betty Banana gets an extra 49/300th of a vote from our sample voter. This is done for all the votes for whom Carrot was the 1st preference.
In the 2nd ballot, no candidate exceed the quota. So the candidate with the smallest number of votes is eliminated. In our example, this is Betty Banana. All her votes get redistributed to their voter's next preference.
So continuing with our sample ballot paper, the remaining 49/300th of a vote is now transferred from Betty Banana to the voter's 3rd choice which is Emily Eggplant.
This proceeds, with candidates being elected or eliminated on each round, until the number of candidates still in play is equal to the number of free seats -- these remaining candidates are all then elected.
STV in Scotland and around the world
STV has been used in Scottish local elections since 2007. The last Scottish local elections, for all 32 local authorities, were held on the 5th of May 2022. Every local authority divides its territory into a number of wards. Each ward then elects 3 or 4 councillors, with wards with higher populations electing more. There are a total of 1226 councillors so that means there are about 350 wards.
STV is mostly used in Britain and former British colonies. Notably, it is used to elect the parliaments of the Republic of Ireland and Malta, the Northern Irish Assembly, and the Australian Senate. In the USA it is used to elect Cambridge city council.
Why is STV good?
In an STV election, any quota's worth of voters will always be able to get their candidate elected.
More precisely, if there is any group of voters who want to elect a candidate with a particular characteristic (call it C), then they will always be able to do so, provided that there is at least one candidate with that characteristic, and that the group of voters is at least one quota large. (Generalising, if the group has multiple quotas, they can elect one candidate for each quota they have. This is known as Proportionality for solid coalitions, although I prefer the term proportionality for voter-defined coalitions, since the whole point of democracy is that the voters are supposed to be in charge).
The way they do this is for everyone in the group to give a higher preference for every candidate with C than for every candidate without C.
Note that it doesn't matter what C is -- it could be a policy preference, such as lower taxes or support for Scottish independence; or it could be something personal about a candidate, for example if a candidate is a woman or has blue eyes. The only thing that is necessary is that all the voters in the group know who all the C-candidates are (because otherwise the voters can't give a higher preference to all C-candidates over all non-C).
It doesn't matter if candidates with C are all in the same party -- they could be spread across multiple parties, but so long as the group of voters prefers all C-candidates over all non-C candidates, a C-candidate will get elected.
Nor does it matter if the voters in the group have different first preferences. There could be lots of C-candidates, but the pro-C vote will coalesce on one of them, because all the voters in the group prefer every C-candidate over every non-C candidate.
In this way the voters can decide for themselves how they group candidates. This is quite unlike party list systems, where you have to prefer one party or another. Under STV if I like candidate A1 from party A, and B3 from party B, but dislike A's other candidate A2 and B's other candidates B1 and B2, then I can vote according to my desire. But in a party list system I am forced to choose between pre-existing lists.
In fact I would argue that we should not be surprised if, when we contact intelligent aliens, they will also have STV. STV is like the programming language Lisp in that respect: while superficially complex it naturally emerges from a number of simple ideas. (In Lisp's case the simple idea is you have one data structure, the list, which is used for both programs and data).
Some problems with STV
So is STV perfect, or does it have problems? I see two potential problems: voting is cumbersome if there are lots of candidates, and an overall election result might not be very proportional if the election is split up into multiple districts.
I suggest solutions for these problems below.
Voting is cumbersome if there are lots of candidates
If there are a large number of seats to fill, STV is cumbersome. I once voted in an STV election where there were 50 candidates for 12 seats. In an election there will likely be some candidates you like, some you don't care about, and some you dislike. In an STV election, to signify that you dislike a candidate you have to rank other candidates above them. So in an election with 50 candidates, if I liked 10, disliked another 10 and was indifferent about 30, I would have to rank my top 40 candidates to vote against the 10 I disliked.
A fix for this would be to allow voters to score candidates, allowing equal scoring for multiple candidates. For example this ballot paper, where the voters have marked their preferences with X's:
Here the voter likes Carrot and Eggplant a lot, likes Banana and Hoffman somewhat less, really dislikes Fruit and is neutral on the other candidates.
If the candidates are members of parties, all the candidates for the same party could be listed together for the convenience of voters.
Lack of proportionality when there are multiple districts
Another problem is that if the election is split up into multiple districts, it might not be very proportional. Consider Glasgow City Council, which elects 85 councillors in 23 wards, each of 3 or 4 members. Imagine if a party stood a candidate in each ward, and each candidate got 2.4% of the vote. Proportionally, that party would deserve 2 seats because it got 2/85th of the total votes. But under STV, they probably wouldn't get any of their candidates elected.
One way round that would be to have extra top-up seats (similar to what happens with the Additional-member system used to elect the Scottish Parliament). There could be 0.5 of a top-up seat for each ward, rounded upwards (so 23/2 = 12 in Glasgow's case) with the seats allocated to parties based on the number of first preferences they received. The additional candidates elected would then be those parties' unelected candidates who did best, e.g. by getting the largest %age of first preferences.
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