Let's compare the proportionality produced in actual elections using STV and party-list-style PR such as top-up in MMP elections.
STV: New South Wales elects 21 members to its Legislative Council through STV in a single contest, and has done so since 1991. 30 years!
Winnipeg elected 10 MLAs in a single contest in seven elections.
All were done successfully.
Five is no definite ceiling on size of districts under STV.
Party-list-style PR: it usually uses DM of more than 21 but it usually uses threshold of 2 to 5 percent, which mostly cancels the proportionality that such a large DM would provide. (More on this below.)
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I was surprised to see this in recent email:
MMP and list PR have multi member districts, just fewer districts and more members in each than in STV)
Note: New Zealand's MMP does not use multi-member districts.
It just doesn't. All members elected in single member districts except for top up.
for top-up seats, there is one pooling of the overall vote.
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While party-list PR and the overall top-up under MMP uses overall party tallies with high district magnitude (number of members elected in single contests), if it uses a threshold of five percent, the effective proportionality is not any different than STV in a 19-seat district.
And STV and party-list PR derives basically the same amount of proportionality (or more even) than party-list PR/MMP when the DM is approximately the same. Small parties have equal chance of being elected under STV as under party-list PR/MMP if the DM is about the same.
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For quick "apples to apples" comparison of STV and party-list PR
STV 21-seat district
NSW 2019
8 parties got some representation
no party took more than 3 seats
Additional Member System (regional-level MMP) 16-seat region
(regional top-up seats allocated according to party proportionality,
to overcome dis-proportionality of the district seats in the region)
Scotland -- 2021 Scottish Assembly election
Mid Scotland and Fife district (picked at random)
16 members
three parties took all the district seats (9)
two other parties were given the top-up seats (7)
five parties got some representation
Scottish National Party took seven seats.
So STV appears to stand up well visa vis proportionality and the chance of small parties getting seats.
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Regarding threshold,
in elections where transferable votes are not used, there is waste and vote splitting and election of lucky, leading but not majority candidates.
Effective threshold does not conform to mathematical fraction - ten-seat district does not mean 10 percent effective threshold when some are elected with less than ten percent.
Recent discussion got us to point where it was generally agreed that larger District Magnitude (number of seats in district) leads to greater proportionality.
and it was somewhat generally agreed that some systems easily provide greater DM than others.
Party-list PR and MMP can have large DM, 120 for example in New Zealand;
STV as used in practice has less large DM. 21 is largest ever; more often it is less than 11; often seven to five; sometimes two to four.
But while STV's DM is not as large as the DM under party-list PR/MMP, it is large enough for Canada and large enough to provide the representation for small parties that NZ's MMP provides.
I would say that DM of 21 (such as used in STV in elections in NSW legislative Council elections) is easily DM large enough to cover most Canadian elections, and DM of 19 would provide the five-percent threshold that is used mostly in New Zealand MMP elections.
Also STV allows voters to vote directly for candidates, at least for candidates within the voters' district, so offers benefits over the closed-list top-up and FPTP district elections used in New Zealand elections.
And recent thought led me to the idea that NZ top-up is used to produce representation proportional to "effective party votes," not to overall district vote (electorate vote) as might be generally thought.
I elaborate on these points:
STV uses smaller districts than nation-wide party-list PR or overall allocation of seats as under MMP, so is not as proportional, friendly to small parties.
STV has elected as many as 21 seats, in elections counting 4.5M votes (New South Wales, (Australia) Legislative Council 1991 to the present)
This election counts more votes than would be cast in most provincial elections and thus in most elections in the largest possible districts that could be used in federal elections (constitutionally province-wide is the largest possible districts in Canada in elections).
But provincial elections - and federal elections - elect more than 21 members in Ontario and Quebec, Alberta, Manitoba and BC.
So the members could not be elected through province-wide districts unless members there had staggered terms (to elect half, a third, a quarter or less each time). But such would possibly mean more frequent elections than once per two to five years as we have now with all members elected at one time.
Perhaps 21 is not a concrete ceiling on the number of members that could be elected under STV. We don’t know.
But actually the point is that STV never historically has been used - and would have difficulty - having District Magnitude as large as party-list PR and the top-up in MMP.
That DM is perhaps 120 as in New Zealand, and so forth.
So according to that observation, it seems party-list PR and MMP has ability to be more proportional (friendlier to small parties) than STV.
But many PR systems do not take advantage of the deep proportionality that is possible.
Many PR systems impose a threshold of 2 to 5 percent that prevents a very small party from taking advantage of the proportionality of PR unless it has more than threshold.
Under New Zealand’s 120-seat-based system, it is conceivable that any party with .8 percent of the vote would be eligible for at least one seat.
But that is thought to be too-fair, if you will, and the threshold used in New Zealand means that a party must have five percent of the overall vote (or win a district seat) to be eligible for the top-up, which means it must have at least five percent of the overall vote (or win a district seat) to get the representation that its percentage of the vote means it is due.
Wikipedia New Zealand 2020 election article says this clearly
“Political parties that meet the threshold (5% of the party vote or one electorate seat) receive seats in the House in proportion to the percentage of the party vote they receive."
implication being that those who don’t pass the test don’t get seats in proportion.
We see this here:
2019 New Zealand election Legislative Council election
New Zealand First party took 2.6 percent of the vote and got no seats - proportionally it was due 3.
Opportunities (TOP) got 1.5 percent of the vote and were due about 2 seats but got none.
This is just the facts and reflects the very high level of proportionality that is possible under the large DM possible under party-list PR /MMP.
The fact that the proportionality is dampened down by the threshold/district seat requirement means that such strict proportionality is not actually desired.
How does such a system compare to STV?
STV systems (at least historically) use a number of multiple-member districts so electorate is broken down into separate divisions.
If elections are fair in each district, the division will not be a problem, the overall rep will be fair. (gerrymandering is not effective if the rep is fair in each district.)
But the small DM of the STV district may be an issue.
It would take an STV district of 19 seats to set the quota at 5 percent. That size of district is perfectly possible under STV. (NSW elects 21 successfully)
With 19 seats, quota would be five percent of the votes.
If all the voters were in 19-seat districts, representation across the country would be five percent but the five percent would be calculated district by district.
The district by district counting of the five percent might make it easier or more harder for a party to get the threshold - you would need just five percent in any district to get at least one seat; any party with five percent of the vote overall but not five percent in any district would possibly not get a seat.
Any candidate (and thus party) that received five percent of the district vote would get at least one seat.
A seat often is taken with less than quota under STV, so the “effective threshold” in a 19-seat district would be lower than five percent for some seats.
So STV could produce rep. where every party with more than five percent equally distributed would be represented.
How large would a 19-seat district be?
In New South Wales Legislative Council, the 21-seat district takes in the whole state but that is just because the Legislative Council only has 21 members in the whole state.
There may be no actual reason why you could not elect 40 or more in a single district under STV. STV is just a matter of counting votes and moving votes around based on just a four-step algorithm - the number of votes involved may be more of an issue than the number of members.
Toronto elects 42 MPs so it could have two districts each electing 21 members, and the proportionality produced in each would be the same in each as produced by New Zealand’s MMP overall top-up (the five percent threshold, ignoring its one-district rule) and the effort needed in each district would be less than in NSW’s Leg. Council elections. So a 19- or 21-seat district could take in about a half or a third of Toronto, not a large area geographically and not large in the number of voters either compared to NSW,
But is strict proportionality of that scale as desired as having small districts that provide greater degree of local representation? is it a priority?
In Toronto a 19-seat district might work, but a 21-member district that takes in half of Alberta likely would be seen as taking strict proportionality too far.
In New Zealand. this might be true too if it was not for the single-member districts that provide local representation (although where in each district, perhaps half the voters do not elect the local member (due to FPTP)).
Two different votes used in NZ MMP
In New Zealand, parties get top-up seats based on the party vote.
And parties get the district seats based on the electorate votes.
Top-up seats in New Zealand are used to provide proportionality but also to make another correction to the representation created by the district seats - to convert the representation produced by the district seats to that needed to proportionally represent the “effective party votes”.
Party votes may be cast differently than the electorate votes and are.
Labour took 48 percent of the electorate vote and 50.01 of the party vote.
Based on the party vote, Labour would have won all but one of the districts. (Only in Epsom did Labour not have the lead in party votes.)
Under the electorate vote, it won only 46, 26 fewer seats.
It is amazing how much a two-percent difference can make in single-winner FPTP elections.
This difference does not seem to be accounted for by looking at the vote numbers - Labour took 1.44M party votes and 1.35M electorate votes. (I am not sure why those 90,000 votes, three percent of votes cast, made such a difference between the actual district seats won and the seats Labour would have won if party votes were used to allocate district seats.) That difference is 26 seats, which is alot for just a two-percent difference.
The difference does show that the party vote and the electorate vote are two different things.
Top-up is used not only to overcome dis-proportonality produced by the district seats but also to change the representation produced in the electorate so that the representation conforms to the party vote (as opposed to the electorate vote) – actually so that it conform not to all the party vote but only to the the “effective party vote,” the party vote given to the parties who got more than five percent or at least one district seat,
For example NZ 2019 election
Districts won Party vote p.c. “Effective party vote” p.c.* Seats
Labour 46 50.01 54 65
National 23 26 27.5 33
Green 1 7.9 8.3 10
ACT 9 7.6 8.3 10
Maori Party 1 1.2 1.7 2
*based on the actual final seat counts assuming that seats were given out properly based on the effective party vote.
Note: Maori Party did not have five-percent threshold but was eligible for top-up due to having one district seat. (It got just one top-up seat.)
So in the table we see how top-up addressed the dis-proportionality of FPTP, and also the difference between the district seats and the “effective party vote.”
The difference between the overall party vote and the electorate vote is also shown although it played no part in the seat allocation, except that it led us to the “effective party vote.”
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A person pointed out to me that in 2007 the Ontario Citizens Assembly discussed STV using 3- to 7-seat districts but discarded it because the proportionality in each district was not considered sufficient and even three-seat districts outside cities were thought too large..
I think:
taking an average of five-seat districts, a district of five seats under STV means than any candidate (or party) with 16 percent of the vote is elected.
so if that is considered not proportional enough, it is due to that DM of "only" 5.
STV can easily accommodate larger DM than five.
DM of 10 means that any candidate (or party) with 9 percent of the vote is elected, so pretty proportional. (Winnipeg used a 10-seat district in seven elections successfully.)
STV using DM of 21 (as NSW Leg. Council has used since 1991) means any candidate (or party) with 4 percent of the vote or so is elected. so very proportional.
Meanwhile cities are natural for multi-member districts. In fact in history of Canada most MM districts have been in cities - city-wide districts, not in rural areas.
Toronto, which has 40-52 seats, is natural place both to have a high-DM MM districts, which cover small geographic area and also preserve local representation. the "local" sports team for all of Toronto - the Bluejays, Raptors. Argonauts - are for whole city. You don't need representation of each little neighbourhood or sub-division - or for 1/40th or 1/52nd of the city - for local representation.
And any district-level PR in any district, such as STV in just one city, produces city or area level balance, and also aids overall balance (just as the top-up in MMP does).
In fact, the PR balance in MMP produces overall balance, it does not aid in local representation. (MMP's local representation is achieved by singe-winner district elections, where sometimes majority of voters are often frustrated. ("Frustrated" might be more heart-rendin and emotive/powerful term than ignored!)). It applies as each voter fundamentally wants their vote used to elect someone they prefer. If it isn't used that way - and often most are not used to elect someone in FPTP - their will is frustrated.
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Further notes:
Many people including myself use votes for candidate as measurement of party support, under any system where voter cannot vote for parties That means for analysis of FPTP and STV elections.
Party-list PR and MMP does allow voters to vote for parties so there the measurement is more direct.
It is common to assess party-proportionality even where voters cannot vote for parties by looking at candidate vote tallies and combining those whom run for the same parties, even if they are not actually vote for parties.
Under STV, each voter has one vote. it goes to the first-preference candidate or (where possible) to a back-up candidate, if the first preference candidate cannot be elected and if a back-up preference is marked on the ballot, or it is wasted (perhaps 20 percent of the votes will be not used to elect someone in a STV election)
My thanks if you recognize my main point above - that NZ does not allow the deep proportionality that its overall 120-member DM would produce.
In recent writing I introduced new term "effective party vote" remember that some parties get threshold and it might happen that a party that takes a district seat also qualifies for top-up. (The term party vote is used to clearly differentiate between the constituency votes (which allocates district seats) and the party votes under NZ's two-vote system.)
The question of overhangs. many of us electoral reformers are prepared to accept small degree of dis-proportionality through overhang.
The overhang is not why Labour got 65 seats. it was given 19 top-up seats - that is what gave it majority. Those top-up seats were allocated in line with the effective party vote (your "total qualifying party vote")
I am not sure that we want to say which parties will get representation, then limit the vote just to those parties. although such a system would ensure that most or all votes wold be effective votes, used to elect someone.
A more open way would be let people vote for whom they want, casting just one vote in a district or a pooling that elects multiple members, and then allow a vote to be transferred where it would otherwise be wasted. Winners would be determined by quota and mere plurality at the end. (and then the transfers stop when all the seats are filled.)
under such a system (STV)
no single group (party) can take all the seats,
with quota or without quota (there are quota-less STV systems), all the substantial groups elect someone (their most popular candidates)
each elected member is elected by about the same number, some at the end either with more or less than quota. this equal-number deal means that each party gets about the right number of seats, party-proportionality- wise.
some votes are used to elect the first preference on the ballot.
some votes are not used to elect the first preference but are used to elect someone the voter prefers over others
Each elected member either is elected by all first-preference votes or a combination of first-preference ballots and other ballots bearing back-up preferences on which the first preference choice was un-electable.
a large portion of the votes (80 percent or so) are used to elect someone.
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And I would say that a system that approaches this by the use of single voting in MM districts even without transferable votes (SNTV) would be better than FPTP or block voting.
under STV there would be larger portion of effective votes, and this is done without a second round of voting having to be held (as in France's two-round system)
unlike a system where vote can mark only the first preference and one back-up preference, STV opens the preferential ranking to more than just two ranked choices, the limit in your two-choice system.
under STV or any system that uses preferential voting, voters have liberty to vote for long-shots knowing (as possible) a back-up preference on the ballot will be used instead if the first choice is found to be un-electable, and the third preference will be used (as possible) if the first and second ranked candidate is found to be un-electable, and so on.
Without transferable votes, a vote goes to the one choice or not - there is no back-up.
Vote splitting can allow the election of someone over someone else that more actually preferred if given the choice.
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