James Gilmour of Scotland has shared a research piece on the variations of STV.
Here's some of what I see are the most important points of what James says, with emphasis on what may be new or surprising to many of us (me anyway).
James is looking at the types of STV systems used today.
The systems discussed below are those currently used in the world today but one simple system not used today is worth mentioning. In the first part of the 20th Century New York City was plagued by schemers and shenanigans of the Tammany Hall clique. Finally by 1937 reformers were able to change the playing field by managing to get the city to adopt PR-STV (or STV-PR if you prefer).
The STV system that the City of New York adopted was a simple one where anyone who got 75,000 votes or more was elected. This meant that the number of members fluctuated depending on voter turn-out.
It seems that the members were elected as members of the different boroughs of the city. This means districts were used. As in all STV, the districts used must have elected multiple members. (If ranked voting is used but a district elects a single member, not multiple members, the system is Instant-Runoff Voting AKA Preferential Voting.)
It is said that each borough had a number of members commensurate with the number of votes cast in the borough. The system might have worked this way:
any borough with less than 200,000 votes might have two seats.
any borough with 200,001 to 250,000 votes might have three seats.
any borough with 250,001 to 300,000 might have four seats.
Under such a ratio, each borough would have been given the number of seats commensurate with the number of votes cast, and no more members could have won than the number of seats in the borough.
(What they did if not enough members passed quota to fill a borough's seats - I don't know. Maybe there was never an issue as votes were required or voluntarily marked enough preferences that always enough passed quota.)
At any rate, the system was simple and effective at quelling the power of the Democratic Party, who controlled Tammany Hall.
The relationship between member and voters was direct - the parties were sidelined;
candidates ran under their own name (and party label secondarily) so the party was sidelined;
Any candidate - and therefore any party - with 75,000 votes was given a seat; so that addressed the historic problem of under-representation of minority parties;
votes meant seats so there was no seat imbalance from borough to borough -- all votes had same value.
(Some say that the brutal honesty of New York's STV system made enemies out of the schemers and wire-pullers in a way that a less-comprehensive reform might not have.)
The quota, used to establish the number of surplus votes that need to be transferred from those elected, appears to be 75,000.
In other STV systems, quota is set as a percentage of votes cast. It must be high enough that no more can pass quota than there are seats to fill. But in early days STV systems used the Hare Quota (the total number of votes cast divided by the number of seats).
But then most STV systems began to use the more-fair Droop quota, which is still used today in most STV systems. Droop quota is the total number of votes cast divided by one more than the number of seats, plus 1.
And sometimes surplus votes are not transferred at all so no quota is necessary.
Thus, we see some basic variations in STV already:
whether or not surplus votes are transferred?
Some might say that if surpluses are not transferred, it should not be called STV and they might be right. But such systems do exist.
If surpluses are not transferred, votes are only transferred when candidates are eliminated - the so-called bottom-up STV.
Or under some systems, votes are not transferred at all, neither for surplus votes nor after the elimination of candidates. This is of course is not STV but Single Non-Transferable Voting. This seems crude and impractical, but it can be seen that in all STV elections the front-runners in the 1st Count make up most -- and sometimes all -- of the winners in the end after transfers. Thus the SNTV system produces much of the same winners as STV does.
But most STV systems transfer surplus votes of elected members as well as votes of eliminated candidates.
Transfers of surplus votes and votes belonging to eliminated candidates may not make any difference - the front-runners in the 1st Count may be elected in the end anyway. So transfers and ranked voting should not be thought of as all-important in STV or at least should be considered as being merely verification of the 1st Count results and perhaps as polishing of the 1st Count front-runners if needed.
And even if transfers make no difference, the result is still balanced and mixed. In STV's first count (as in SNTV), no one party can take all the seats -- or all the front positions -- in the 1st Count -- unless a vast majority of voters vote for that party - which is seldom the case.
STV systems are differentiated by the quota
As well as the question of what transfers are done, we also have seen that systems are also differentiated by the quota used, if any: Hare or Droop.
These distinctions are moot for STV systems used today, as all of them transfer surplus votes as well as votes from eliminated candidates and all use the Droop quota.
Other ways that STV systems used today vary
But there are other ways that the STV systems used today do vary.
One that is often overlooked is the question of at-large contests versus district contests. Districts ensures local representation in way that at-large contests do not. At-large contests allows a party that has support thinly spread across the whole electorate to gather its support behind one candidate and secure one seat. while if its support was divided into separate districts, its support would be seen as marginal and not worthy of any representation at all. This marginalization of the thinly-spread party (say nannies or car mechanics) is most strong when there are many districts and not so biting when the electorate is split into only two or three large districts.
We see Thomas Hare's name again in a discussion of this question of district-ing.
When Hare "invented" Single Transferable Voting in the 1850s (his work was based on work done by others earlier), he pictured an election contest covering the whole country of Britain as one at-large district.
That kind of basic system is used today in New South Wales for state (provincial) elections. The state is not divided into separate districts but 21 seats (half of the assembly) are filled at one time in one big contest. Local representation is able to be produced by fact that any locality that has quota (only 5 percent of the votes) will elect someone if the voters there give their first preferences and back-up preferences to candidates of their locality - and there is nothing anyone elsewhere can do about it.
(Arbitrary geographic local districts are funny anyway - members vote on matters concerning anything anywhere and not just things concerning their own district - and the idea of one member representing all the people in a district (as expected under FPTP) is impossible anyway.)
Catherine Helen Spence (and fellow Australian Inglis Clark) is credited with the idea of the electorate being divided into separate multi-member districts so that STV could provide both guaranteed local representation and proportionality. Such district-ing also makes for more manageable ballot sizes - voters find they can better manage a ballot that has less than say 30 names used to fill five seats than one containing more than 200 names used to fill 21 seats.
And now most STV systems do use districts and not at-large elections.
But at-large contests does have use even today -- in city elections where at most 10-15 councillors are usually elected. (Although we see that Portland, Oregon, which has just now adopted STV, will be using four multi-member wards and will not be electing its 12 councillors at-large.
But we can look at history and see that Winnipeg was successfully electing its 10 MLAs in one city-wide district back in 1920, so we know at-large election of ten members worked even before computers. And today's NSW elections show that as many as 21 elected at once can work too (using computers).
What differentiates the STV systems used today?
I think I saw somewhere that there are 14 characteristics that can distinguish different STV systems.
But the five main differences are:
District Magnitude - the number of members elected in an election contest. included in this is the question of districts/at-large - are members elected at-large or in separate districts?
Method of transferring surplus votes (as described below)
How many preferences a voter has to mark. Some systems do not require the marking of any back-up preferences at all; others require a certain number of back-up preferences. (in Canadian uses of STV, voters had right to mark as few or as many back-up preferences as they wanted.)
Ballot format
How to deal with seats coming empty between general elections
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District Magnitude is important but STV has used anywhere from two to 21 seats in a district. So the number used basically comes down to a function of the total number of members being elected and geography.
Over the whole world the DM used in STV ranges from two to 21.
The smallest STV district elects just two members. We see this in Scottish local authorities. Any fewer would not be STV at all.
The highest DM used so far in a government election is 21.
Most assemblies elected by STV contain more than 21 members so choice that must be made is
to elect more than 21 at once (likely not with STV)
or use districts to divide the electorate and the seat-filling process.
or to use temporal variation to to divide the electorate and the seat-filling process - that is, to elect the members in different batches serving staggered terms.
New South Wales elects its lower house members in two batches so that despite having 42 members, elections are held at-large but no more than 21 are elected at one time.
Under STV as used in western Canadian cities pre-1972, city councillors were elected at-large. Cities were taken as whole entities and wards were not used. But sometimes wards were used. Generally city STV elections did not fill more than 8 seats in a contest, if more seat than that were up for eleciton, the number was brought down either through use of districts - Winnipeg elected its councillors in three 4-seat wards - or if filled at-large through using staggered terms - Edmonton elected 5 to 8 in each of its STV contests (numbers varied due to seats coming empty between elections).
Sometimes staggered terms and districts are both used. Together they might drive the DM down to just one. as we see in most of the Calgary city election contests in the 1960s. (STV was not used - but instead Instant-Runoff Voting.)
So DM is function of total members in the assembly, the total number of seats to be filled and the number of districts used to fill those seats.
Also we often see use of single-member districts and multi-member districts in same country or province.
Say with 20 members being elected, we might see a district elect ten while ten other members are elected in single-member districts.
Or we might see ten districts elect two each.
Or four districts elect five each.
Or 20 elected in one at-large contest. (STV could not be used in that case.)
Each has certain advantages and disadvantages for different-sized parties and for parties whose supporters have different geographic distribution.
The district-ing is chosen through politics or through a non-partisan process - with the interests of the different parties and the electorate in different localities valued or ignored as the political culture allows.
The choice is up to those who make the system -- and perhaps the voters who have to vote under it.
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How are surplus votes transferred?
The main variation between STV systems (in my mind) is the way that surplus votes are transferred.
Demonstrating the wide variance of STV,
James lists five types of transfers of "relevant surplus votes" that are used in STV systems in the world today - and a couple sub-types. (See page 4 of his brief)
Type 1. Whole Vote method type
includes two different methods:
1A. random whole vote method - Cambridge (Massachusetts) city elections.
This is the "truly random" system (which Ed and i discussed in recent email) where votes are just drawn randomly or any additions - whatever they are - are moved on to others when candidate accumulates quota.
1B. whole vote method with less random-ness but still some (at least potentially) - Republic of Ireland (Dale Eiran) and Malta.
This was type used in most STV elections in Canada historically. and also is type used in the Republic of Ireland and Malta. As well, I think, it is used in New South Wales lower house elections (where 21 are elected at one time).
James is careful to say that in cases where the number of exhausted votes exceeds the quota [I have reworded what he said]., "ballot papers and votes [that bear a next usable preference] are transferred to continuing candidates" - thus you do not need any math at all, just simple reference to next usable marked preference on each non-exhausted vote.
(him mentioning this in the whole vote system leads me to think that this is not a possibility in the fractional vote systems, but perhaps that is wrong assumption.)
James lumps 1B and 1A together under one type.
I would posit that the two systems should be analyzed differently. as 1B is math based, at least as to next usable preference (which may be all that will be considered thereafter), while 1A is random (but Cambridge would I expect say it is balanced in that it is random).
I see that James has a scientific perspective and lumps both together as being primitive or close to primitive, while the other four fractional vote systems are regarded as much superior due to their exactness, even transferring votes at two or more decimal points value.
Hoag and Hallett's 1924 book Proportional Representation calls the whol vote method where next usable preferences are used to set transfers (1B) as the Exact Method.
The next four types transfer surplus votes at fractional values.
They also use more than just next usable preference to set transfers.
Type 2. Gregory method -- Republic of Ireland Seanad, Northern Ireland
two sub-types
2A. Senatorial Seanad
2B. Northern Ireland
two methods of surplus transfers - consideration of all of candidate's votes
- consideration of just last parcel of incoming transfer
(James here throws in wrinkle mentioning that in some systems votes are transferred to already elected candidates (I don't know what happens to them later). So that is another difference between STV systems.
Meek system below transfers votes to those already elected for example.)
Type 3. Inclusive Gregory method
although it is used in Australian federal elections and in three Australian states (I think that Western Australia may have dropped it fairly recently). James says IG is fundamentally flawed. He notes that repeated calls for reform have been ignored. (I'll let you draw your own lessons on human nature!)
Type 4. Weighted Inclusive Gregory Method
used in Western Australia Legislative Council (at least in 2009), Minneapolis (2008) and Iceland (2010). (so this adds Iceland to the list of those in the world who use STV)
Scottish Local Elections in 2007, the first use of WIGM anywhere in the world [so it seems actual application of STV is changing even at this late date.]
very exact -- vote values go to as much as 8 decimal places.
[I understand to accommodate the splitting through fractions under some STV, in some systems votes are valued at 100 in the initial count.]
Type 5. Meek
WIGM (same as type 4), with innovation that votes may be transferred to already elected candidates.
used in New Zealand Health Boards.
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Types 1 to 4 have been conducted using manual counting (no computer)
Type 5 its only use used computer
Northern Ireland uses Gregory method (type 2) and the election officials there have it down to a science where results are released in one day.
[same one-day turn-around is achieved for Scottish local elections in 2022 also using STV]
James says WIGM is used in Scottish Local Authority elections provided the counts are computerized. Thus apparently some Scottish Local Authorities use manual counting (and Gregory method?), and some use WIGM and computers.
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Computer programs have been invented for all five types.
James says he recommends that if computers are used, that a paper version be marked by votes and retained for manual verification if needed.
[I understand currently in Edmonton city elections (FPTP/computer] there is no paper copy retained for human verification - gasp]
James is opposed to both types of the whole-vote surplus transfer method (type 1) due to their random-ness.
DISTRICT MAGNITUDE
On ward size of the MMDs, James (page 13) says DM has three effects:
1. determines how many members can directly represent the district's voters, thus setting maximum on the number of parties that can have representation in the district.
2. DM sets proportionality. Each (roughly) quarter+ of voters represented in 3-member district; each roughly 11-percent gets a seat in nine-seat district.
3. regarding gender rep (women are historically under-represented) and rep of various ethnic and racial groups -- large districts encourage diverse representation; small wards limit that - single-member district often sees male white take the one seat.
Wales Local Government Act (2021) stipulates that MMDs may not have less than three and no more than six members.
James says he finds this arbitrary ceiling "in the cities and more densely populated urban areas" to be un-necessary, "imposes limit on direct representation and on the degree of proportionality of that representation"
In short, "the greater the number of members a district elected together, the more representative the council will be of the community it serves."
[But he does not state - as far as I saw - the upper limit of good DM or what should be used in Wales if it adopts STV.
21 are being elected in NSW Australia through STV.]
Filling seats vacated between elections - varies from system to system
in Canada (FPTP) they are filled through by-elections or simply left empty pending general election perhaps a year away. (This meant that by-eletions were held to fill one seat but votes were collected from all across the city, just to fill that one seat.)
But James endorses a STV system that fills the empty seats immediately through
count-back, looking at vote count in previous election.
This has side benefit of pushing parties to run more than full slates to have back-up candidate to fill vacated seats. James notes that the larger a slate, the more diverse the party's offering to voters.
[due to STV's back-up preferences, parties do not need to worry that large slates will cause dangerous vote splitting --
even if spread over many party candidates in 1st Count, transfers will concentrate a party's votes on the party candidates who can win -- if voters vote that way. And then the party will get its full share of seats no matter how large the initial party slate of candidates was.
A party with quota will eventually take a seat - if its voters mark back-up preferences for party candidates -- and there is nothing (no electoral gamemanship or trickery) the other groups can do about it.
Malta uses STV and it has a two-party system (created by voters themselves). The 1st count in each district shows almost always and almost exactly how many seats each of the parties will win. The two main parties' totals divided by quota tell us how many seats each party will take; later transfers merely concentrate the party votes into the 1-4 candidates who will take the party's allotment of seats in the district.
each party is so confident of the disciplined support of its supporters than it runs sometimes more than 10 candidates in a 5-seat district. (this also lines up candidates to fill any seat that may come vacant.)
As many counts as it takes to concentrate the party vote, that is how long it takes - very few votes trickle across party lines, until a party's slate has filled all the party's seats with all the party's candidates either eliminated or elected.
voters in such a Multi-Member District have wide choice of candidates.
Parties have leeway to run niche or improbable candidates, leaving it up to voters to align their votes on those who are most generally acceptable among party voters. and the concentration through transfers continues until a party's votes are more than quota and a seat is still empty.
some candidates are personally popular and win in the 1st Round. Others are elected only after votes are accumulated even though initially placed on perhaps wide assortment of other candidates.
Ballot Paper Design
Ballot paper design also varies from system to system. But I did not get into that here. One style for example is "down = candidate names (alphabetical); includes party labels". Dividing STV systems by ballot design is obviously arcane/super-technical.
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A table showing variety of STV systems in use based on four criterion
might look something like this:
(from Farrell and McAllister, The Australian Electoral System, p. 60-61)
(LH = lower house) (UH = Upper House)
District surplus preferences casual
size transfer required vacancies
Ireland LH 3-5 whole vote (1B) at least one filled through by-election
Malta LH 5 whole vote (1B) at least one filled through count back
Australia 2 or 6* all ballots at fractional value State parliament selects
Inclusive Gregory (Type 3) someone to fill seat
12 candidates must be marked
or if group ticket marked, at least one
(six are recommended)
*12 represent each state but only six are up for election each 3 years. (some exceptions apply)
Australian states
NSW 21 whole vote (1B) at least 15 candidates, joint sitting selects
if group tickets used, minimum 1. someone from
same party.
other states also use STV if not for Legislative Assembly then for Legislative Council
I have not added them to this table)
As we have seen, there are a variety of STV systems.
But all STV systems share these elements:
- each voter has just one vote.
- back-up preferences are contingency votes -- only used if first preference candidate is eliminated or elected.
- vote when used will be used to elect someone preferred by voter over others, but this may not be the voter's first choice.
- MMDs multiple members elected in a contest.
- each voter can help elect just one member in the end. (no multiple voting).
- votes are cast as whole vote. (no Cumulative Voting)
- not all votes are used to elect someone (the votes of the last candidate to be eliminated are not necessarily transferred, for example)
- until last seat is filled, each count (stage as James terms it) either eliminates the least-popular candidate* or transfers surplus votes of previously elected candidate.
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* this is sort of an application of negative plurality being used for elimination (as opposed to normal use of plurality to determine who is elected). The least-popular candidate is eliminated. as opposed to usual plurality where the most-popular candidate is elected.
Those who are not eliminated through this negative plurality/elimination process may be elected or they may not be.
In STV, the relative-popularity thing only works to find those who are dropped from the race - not to see those who will be elected. To be elected, those remaining in the race still need quota or to be the most popular when the number of candidates is thinned to the number of remaining open seats.
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