STV

Rev. 22 Dec 25

Initial draft. Please comment.

What. The Single Transferable Vote (STV)[1] system is an established, known mechanism for determining the result of preferential voting in a multi‑seat constituency.
STV is vigorously supported by vociferous supporters of electoral reform (including ERS) and therefore more readily saleable than potentially better alternatives. And it is perhaps at the limit of what can be achieved with a manually operated vote counting system.

The count. STV would use the same sort of voting form as that used for PV: a list of candidates marked with optional rankings (1,2,3, etc.).
The count (the evaluation procedure/mechanism/algorithm) is based on that used for PV. STV inevitably entails an extra level of complication in the evaluation process, because the election of a candidate is not the end of the process while there are more seats to be filled. But it remains within the capability of a largely manual count.
In essence the procedure is an alternation between
(a) identifying candidates who have enough votes to guarantee their election, and transferring any surplus to the next choice of their voters
(b) when there are no more of these, eliminating the least favoured candidates, and transferring their votes to their voters’ next choices, until winners again emerge.
More formally, the procedure is to fill seats one at a time by repeating the following steps until all seats are filled.
(1) First calculate the minimum number of votes required to win a seat, called the “quota”. When there is a total of V active voters in the election for S unfilled seats then the quota is int(V/(S+1))+1.[2]
(2) If any candidates attain that quota of top choices the highest is elected.[3]
(3) When a candidate is elected any “surplus” votes above the quota are distributed pro rata, i.e. each multiplied by (total surplus)÷(total votes for candidate), to the highest remaining choice of the voters concerned[4][5]. The candidate is then deactivated and all votes for them are ignored. The nett effect is generally that the total of effective votes is reduced by the quota.
(4) Alternatively, if no candidate attains the quota of first choices, then the candidate with the lowest number of top choices is eliminated. Votes for them are thus automatically transferred to the highest remaining choice of the pertinent voters.[6]

Proportionality. STV is described as [Wiki]“proportional representation by means of the single transferable vote”. Rather more accurately, “STV aims to approach proportional representation based on votes cast in the district where it is used, so that each vote is worth about the same as another”. And it is certainly true that STV can be expected to be far less disproportional than FPTP. In a 5-member constituency and the traditional 2½-party system, STV would tend to elect MPs in approximate proportion to voters’ wishes, whereas under FPTP any party could win all 5 seats, perhaps on only 40% of the vote. But if there were 6 significant parties, a rather lower degree of proportionality is it clearly inevitable. Perhaps best not to describe STV as actually being PR: it’s a perfectly tolerable electoral system and does not need that claim.[7]

Constituency link. Like any multi-seat system, STV weakens the link between MPs and constituencies. Constituency MP surgeries are a valued part of current practice.
Which is why some favour a system where half the MPs are for single-member constituencies[8], and half are elected by a more “proportional” multi‑seat system. Which sounds reasonable. But the parties generally insist (a) that the proportional system should be strictly party‑proportional, and (b) that the proportionality should be imposed on the whole system and not just the multi‑seat component of it. However, this form of proportionality does retain a constituency link, and for that reason is more palatable than pure D’Hondt.

Elimination rule. The STV evaluation procedure/mechanism/algorithm, being based on that used for PV, has the same weaknesses. In addition, the STV version of that employs an arguably even more defective elimination rule, basing it only on top choices even though there are multiple seats available. For example, to eliminate on the basis of first choices when there are five seats available has to be questionable. However, to look instead at the first five choices is bound to make the difficult manual count effectively impossible. So any improvement to the elimination rule must wait until we are no longer reliant of having a largely manual evaluation process.

Constituency size. STV too often comes with a doctrinaire assumption that constituencies should be of uniform size (e.g. 5 seats), regardless of local circumstances. But why? It is not obvious that this is the fairest or most practical policy. If a town is currently divided into 4 single-seat constituencies, it clearly makes sense to combine them. To have to add in a rural constituency on principle risks disenfrachising its voters and is bound to diminish the coherence of the result. And there are already a few sparsely populated constituencies so vast as to be difficult to manage in an election. Why be forced to make things even more difficult? In all cases, so much better to let local circumstances dictate local groupings.

Long list. A major practical problem could be the length of the ballot list.
Consider a 5-seat constituency in today’s UK political climate. Assume that Lab, Con, LibDem, Reform, Green, and NuParty, each wish to field 5 candidates. Throw in one independent and a couple of humorists and you have a bedazzling list of 33 candidates, possibly in alphabetical order, for voters to rank in their sequence of preference. Possibly after reading their 33 half-page profiles? It’s not going to happen, is it?

Party lists. We might address the problem by making the list longer! 🙂 To make life easier, add 6 party lists, and allow voters to declare preferences for parties or individuals as they choose. You thus offer party-PR as an option to those voters who want it.
Evaluation of voting continues to be based on preferences for individual candidates, and where preference is expressed for a party that is deemed to a preference for all the individuals in that party list, except any already voted for individually, in the party’s declared sequence.[9]
Or, much simpler to explain to voters and much simpler to operate at the count, just have any votes for parties be effective only after all preferences for individuals have been taken into consideration.

What to do. If STV is what we want, the best plan would thus arguably be:

  • Introduce PV without delay, possibly before the next general election.
    • It is much better than FPTP.
    • It entails no boundary changes.
    • It introduces preferential voting.
    • It entails the least possible change to the vote counting system.
  • Implement STV as quickly as you can thereafter.
    • Change boundaries progressively, to fit in with local circumstances.
    • Make sure you have a workable vote counting system
    • Give serious consideration to allowing party lists
  • Initiate urgent research and debate on a better system for evaluating preferential votes.
  1. [1] STV is “proportional-ranked choice voting (P-RCV), also known as PR-STV”[Wiki]. It has numerous variants. We discuss here only the simplest and most widely used. ↩︎
  2. [2a] This is mathematcially guaranteed to be a threshold that can be attained by no more then S candidates. It needs to be calculated afresh for each round because (a) rounding errors may cause very small variations but, more significantly, (b) when voters for candidates who are victorious or are eliminated have made no further choices the number of active voters decreases.
    At first sight, this quota appears to overvalue votes for leading candidates. For example, if there are 4 seats then >20% guarantees a seat, and a combined vote over 40% guarantees 2 seats, leaving the remaining 60% to fight it out for the 3rd and 4th seats. However, the apparent bias can have no clearly wrong effect. In general, if there is a total of V voters in an election for S seats the first S-1 seats will consume more than (S-1)*V/(S+1) votes, leaving less than 2/(S+1) (i.e. 2 quotas) available for the final seat. Thus no injustice is possibly caused. ↩︎
  3. [2b] Note that, because of the transfer of the surplus, the second highest may sometimes not become the highest after the first has been elected. But if they have the quota they are bound to be elected eventually! ↩︎
  4. [2c] This prevents a party from losing a candidate in the early stage who might be elected later through transfers.[Wiki] ↩︎
  5. [2d] That is how it is usually described, but it is MISLEADING. When a candidate … ?? ↩︎
  6. [2e] The eliminated candidate’s votes are transferred to the next-preferred candidate rather than being discarded.[Wiki] ↩︎
  7. [3] ERS foolishly insist on calling it PR, which it is not, on the grounds that (a) that’s what they’ve always called it, and (b) STV is less disproportional than FPTP. ↩︎
  8. Traditionally elected by FPTP, but much better by PV. ↩︎
  9. Given which we can allow independents to register preference lists, if they wish. Even allow party to have multiple lists! ↩︎