What is “Single Transferable Vote”?

I’ll let you all into a secret. I hate Single Transferable Vote. It is too complex, and the outcomes can be too freakish. Furthermore, contrary to widespread belief, it is not proportional. But it’s what we have – so how does it actually work?

The basic principle is this: votes are transferable among candidates, and they continue to be transferred among candidates until the required number of candidates have the number of votes they require (known as the “quota”) to be sure they cannot be overtaken.

Let us start with the most straightforward version: if we are electing one candidate, that candidate needs a 50% vote share plus one vote. Thus the “quota” that candidate needs is half of all the votes cast, plus one (actually, to be specific, rounded up to the nearest integer) – or, mathematically V/(C+1)+1 where V is the number of valid votes cast and C is the number of candidates to be elected. Thus, if 1000 votes are cast, the “quota” required to be elected is 501 – that is, 1000/(1+1)+1.

If there are three candidates, let us say that Candidate A scores 200, Candidate B scores 250, and Candidate C scores 550. Candidate C is over the quota and is elected. Easy!

Let us say, however, that Candidate A scores 200, Candidate B scores 350, and Candidate C scores 450. Here, no candidate has reached 501. The lowest candidate (Candidate A) is eliminated, and their votes transferred to the next preference still left in the race. Let us say that the 200 votes are split evenly; Candidate B would now have 450, and Candidate C 550, thus Candidate C is elected.

Let us say, then, that Candidate A scores 200, Candidate B 350 and Candidate C 450. However, only 125 of Candidate A’s votes were marked with a further preference, all for Candidate B. Thus Candidate B has 475 and Candidate C 450. No candidate has reached the quota. In this case, there being no remaining eliminations, the lead candidate (Candidate B) is deemed elected.

Now then, let us move on to a slightly more complex version: if we are to elect three candidates from the same votes, the formula remains V/(C+1)+1 but now that means 1000/(3+1)+1=251. This is a bit more complex. Let us say there are seven candidates with first preference votes cast as follows: Candidate A 251, Candidate B 249, Candidate C 120, Candidate D 110, Candidate E 100, Candidate F 90 and Candidate G 80.

Candidate A is elected having reached the quota precisely. However all others, including Candidate B, are in fact short of the quota. Candidate G would be eliminated, and those votes transferred, and so on, until three candidates had reached 251 (or there was only one remaining).

However, let’s say – and this is where it gets tricky – the outcome is this: Candidate A 360, Candidate B 140, and the rest as above.

Here, Candidate A has not only reached quota but in fact has done so with 109 votes to spare. It would be most unfair to penalise Candidate A for having done so well by leaving those 109 votes wasted, particularly if one or some of the remaining candidates were from the same party. So what happens, before any eliminations (unless it can make no difference) is that Candidate A’s “surplus” is transferred. How this is done varies – in some locations, the authorities would simply lift 100 votes from the candidate’s pile and transfer them according to their next preference; in Northern Ireland, however, all the original 360 votes would be reanalysed, and transferred at a fraction of a vote to make the overall total transferred 109. So, for example, if 36 of the 360 (i.e. 10%) had Candidate B as the next preference, Candidate B would receive 10% of 109 votes – i.e. 10.90 votes (it is done to two decimal points).

This process then continues – surpluses first if they can make a difference, and then eliminations – until three candidates have reached the quota or only three are left standing, whichever comes first.

Clear? Hmmm…

Clearer, I hope!


14 thoughts on “What is “Single Transferable Vote”?

  1. martyntodd says:

    A few years ago in The New Scientist there was a lengthy analysis of all voting systems currently used around the world. The article showed that every one of them had flaws and could be tricked by special circumstances into producing a result that was not “fair” in those circumstances.

    STV is like democracy itself, very questionable in itself but better than the alternatives.

  2. Mustard says:

    What system would mr parsley prefer for council and stormont ?

  3. efgd says:

    No wonder the first past the post voting is so popular. Unfair as it is. It is understandable.

  4. other paul says:

    Hi Ian,
    This seems straightforward and fair to me so I’ve clearly missed the bit in your post where you described how it wasn’t proportional. in fact the part you seem to take particular umbrage with (second last paragraph) seems suspiciously like proportional representation to me.

    • It isn’t proportional for two reasons (although its outworkings are *more* proportional than other systems).

      Firstly, technically, it isn’t designed to be in any way proportional, but rather *preferential*. In other words, it sets out to give the voter options, but not to make the outcome proportional.

      Secondly, practically, it isn’t proportional for a number of reasons, most notably the final seat.

      By way of example (also an example of how not every vote counts): in North Down at the last Assembly Election the Alliance Party received 19% in North Down, Independent Unionists 14%, UUP 10%, Green 9%. The seats allocation was Alliance 1, UUP 1, Green 1. Now, in no way was that proportional. Also, in fact, the Alliance candidates did *better* out of transfers and yet *still* only ended up with the same number of seats as two other parties which received half their vote. My own vote, by the way, didn’t count at all – I voted Wilson (Alliance) first preference and she was left runner-up (i.e. the seventh candidate left standing with six to be elected).

      Of course, it is *more* proportional and *more* likely to see votes counted than First Past the Post.

  5. other paul says:

    Hi Ian,
    Thanks for replying but I’m afraid I would still disagree with you. I think perhaps there’s a flaw in your logic in that you’re taking a system designed to elect individuals and applying it to parties and thinking it would still behave the same.

    • Actually I don’t see where we disagree! I’m not expecting it to behave a particular way; people who describe it as “proportional” are!

      My point is the system *is* designed around individuals and is thus not proportional. It doesn’t even attempt to be. In election system guides it does not appear under “proportional” because it ain’t!

      Overall (i.e. for an entire Assembly) the result usually *looks* proportional, but then it would under almost any multi-member system. (Even then, there was a notable exception in 1982 when some freakish last seats gave Alliance far more seats and Sinn Féin far fewer than any really proportional system would have done.)

      • other paul says:

        Hmm…, perhaps this hinges on your definition of proportional I guess. Thanks for the discussion though!

  6. Glenn S says:

    The system I like the least is the party list system as we have in Euro elections in GB, be glad you can vote for a person!

  7. […] wrote a fortnight ago about how Single Transferable Vote works. I was asked then why I don’t like it. To be clear, I can see its merits, particularly […]

  8. […] electoral system is a preference system – you don’t have to agree with any given candidate absolutely (in […]

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