Those who fear loss of local representation if rural STV grouped districts are established should consider that each and every group that has quota within the new larger multi-member district will elect a rep.
In the blog "A study of votes wasted under STV, or How much is a quota?", I showed how the "Save Our Mountain" group with less than one percent of the votes was pretty much guaranteed to take one seat. That applies to any other local group as well.
Under FPTP, the only way for a small group to win a seat is if it has more votes than any other group in a district, for example more than the local Liberal or Conservative candidate.
While under STV in a three-seat district, any group or party just needs a quarter of the vote in the district to take a seat. And in a five-seat district only one-sixth of the vote. And so on. (And any group close to quota may possibly win a seat as well.)
Despite the larger size of the district, the quota (as percentage of votes cast) is smaller, the more seats a district has, other things being equal.
Quota
As seen in the next table, the number of votes that makes up quota hardly grows at all as a multi-member districts is given more seats. In this discussion, I am using the Droop quota, the prevalent practice in present-day STV applications.
From a two-seat district to a ten-seat district, quota increases by only 60 votes while the number of votes in the district increases up by almost 2000.
The portion of Effective Votes grows magnificently from a minimum of 2/3rds in a two-seat district to a minimum of 91 percent in a 10-seat district, assuming all successful candidates win with full quotas, the Droop quota is used and there are no exhausted ballots.
An exhausted ballot can only happen if the voter did not mark enough back-up preferences to cover all the candidates and if the ballot has to be transferred and cannot be.
There are cases where candidates are elected without quota - they are the last remaining candidates as the field of candidates thins to a point where there are only as many candidates as the number of empty seats. This can only happen if votes are relatively evenly spread over the candidates.
The opposite case is where some candidates are so popular that they take quota in the first count and are declared elected, filling the seats before any candidates are eliminated and votes transferred. This never happened in STV elections in Canada but did happen in Alternative Voting elections where quota was 50 plus 1.
If such did happen in STV, the percentage of Effective Votes is exactly as presented in the table below.
But it is more likely that some candidates will be eliminated and some or most of the remaining ones will achieve quota and be declared elected to fill the seats. The next table applies here as well.
But it can happen that not all the seats are filled by the time the field of candidates thins to the number of remaining open seats. In that case, likely the number of votes still in play has also decreased by some votes becoming exhausted un-transferable due to not having any un-used marked back-up preferences.
In that case the number of Effective Votes may be lower than in the next table. However that is not to say that some of the votes who cast what turned out to be exhausted votes are disappointed by the election. Some of the exhausted ballots are marked for candidates already elected, so the voters in some cases sees one (or more) of his or her preferred candidates elected anyway. without his or her vote being needed.
Oddly, in cases where candidates are elected with partial quotas at the end, the number of Effective Votes may be larger than where candidates are elected with quota. They may be larger or not, but for sure there is only one candidate whose supporters did not elect anyone. The only candidate not elected at the end is the final one eliminated.
Whereas when candidate win with full quotas there may be many voters whose votes were not used to elect anyone. In both cases the number of votes cannot be more than a quota, but in one there may be a noticeable number of candidates whose supporters did not elect anyone. The supporters of this group of middle-ranking candidates may feel disenfranchised as their votes were pretty much ignored.
Luckily, most of the historical Canada STV elections came to an end with candidates being elected with partial quotas after the last elimination takes place and only the votes of one candidate are ignored. At that stage, when the last elimination takes place, the only candidates that the votes could be transferred to are going to be elected anyway.
It could happen that the field of candidates is thinned to the point of equality with the number of remaining open seats by the election of a candidate. In that case, the only ignored votes are the surplus of that winner!
Effective Votes in a FPTP district can be as low as a third of the votes and are seldom as large as 60 percent of the votes.
Math Proof for these statements
This example assumes 240 votes in the district per member
(You can look at it as single-member districts of that same size are grouped to make multi-member districts)
Effective Vote = votes used to elect winners if successful candidates all have quota.
Votes in this table can mean either:
votes bearing first preferences marked for the candidate or
a combination of votes bearing first preferences and votes bearing back-up preferences marked for the candidate.
1 district (FPTP)
240 votes 33 p.c. may be enough to be elected = 80 Min. Effective vote = 80
(although it is possible to be elected under FPP with only 18 percent of the vote even.)
2 district (STV) 480 votes 33 p.c. is quota = 160 Minimum Effective vote = 320 2/3
3 district (STV) 720 25 p.c. is quota = 180 Minimum Effective vote = 540 3/4
4 districts (STV) 960 20 p.c. is quota = 192 Minimum Effective vote = 768 4/5
5 districts (STV) 1200 17 p.c. is quota = 200 Minimum Effective vote = 1000 5/6
6 districts (STV) 1440 14 p.c. is quota = 206 Minimum Effective vote = 1236 6/7
7 districts (STV) 1680 12 p.c. is quota = 210 Minimum Effective vote = 1470 7/8
8 districts (STV) 1920 11 p.c. is quota = 213 Minimum Effective vote = 1707 8/9
9 districts (STV) 2160 10 p.c. is quota = 216 Minimum Effective vote = 1944 9/10
10 districts (STV) 2400 9 p.c. is quota = 218 Min. Effective vote = 2182 91 p.c. 10/11
It is probably easier for a small party like the Greens to get a seat when only 10 percent of the vote in a district is required to win a seat than under FPTP where a third of the vote is the usual basic minimum and the amount needed might be as large as 50 percent plus one (if only two are running).
The same likely holds true for a group running for a seat to fight a local issue. For example the fictitious "Save our Mountain" group would have better luck in a STV district than in a FPTP district. It may have 200 votes in a 1200-vote five-member district nearby the pretend mountain but is less likely to have a third of the vote in just one FPTP district near the mountain.
Thus STV gives a much better chance to most small parties, except for a hyper-localized party that has sizable support in a small FPTP district. (STV though is guaranteed to give more seats to larger parties than smaller parties, as is proportional to vote share.)
Such seems to be the case of the Western Canada Concept victory in 1982 in Olds-Didsbury. The WCC candidate won with only a minority of the votes in the district. Under FPTP he did not need any set number to win the seat but just to have more than each of the other candidates. And that he had.
The 1982 WCC victory was in a by-election. By-elections are considered to be more favourable to protest groups. The Government and other large parties do not have their full party machines in operation. There are no election-time bribes. Heck, if it was a good time for the government for an election to be held, the government might have called a general election and saved the expense of the by-election.
It seems clear that if the Olds-Didsbury by-election had been held in a three-seat district as could be used in STV, the WCC candidate would not have been elected.
Under Alternative Voting, the system used in by-elections where STV is used in general elections, the WCC man would likely not have been favoured by the necessary majority of the voters - and would not have been elected. It seems unlikely that he would have picked up many vote transfers from the second and third candidate, the Social Credit and Conservative candidates, nor from the NDP candidate and lesser candidates who would have been the first to be eliminated and their votes transferred. Likely vote transfers would have given the second-placing candidate Social Credit candidate the seat. But it is difficult to know.
But the result under Alternative Voting would have been seen differently, not just as lucky win by a small party but as the expression of a majority of voters in the district. If that is better or worse in this case is another question.
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Wasted votes
That table presents minimum effective vote (the amount that any group needs to elect one);
in MMDs, multiples of that minimum effective votes are a guide to how many seats a party will take.
That minimum effective vote, taken as just one group of that quantity, is the rough calculation of the number of votes that will not be used to elect anyone.
Thus in a district where ten are to be elected, only about 1/11th of the valid votes are not used to elect anyone.
The only other forms of wasted ineffective votes are those that are rejected by the election officials, those that are found to be exhaused and non-transferable, and those cast for candidates who are eliminated without their vote being transferred (this does not happen in every election contest but happens when there are two candidates left in the running for last seat. The most-popular one is declared elected and the other is declared defeated, with his/her votes not being transferred.)
In Calgary elections 1917 to 1926, rejected (spoiled) votes ranged in percentage from 2% to 9%. average was 4.6 percent.*
In Cleveland elections 1923 to 1928, rejected (spoiled) votes ranged in percentage from 5% to 10%. average was 7.8 percent.*
This seems small price to pay for a system where 80 percent or more of the remaining votes (valid votes) are used to elect the winners.
Under FPTP, often as much as half of more of valid votes are not used to elect anyone, and there can be rejected votes there as well.
Thanks for reading.
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*Information on rejected votes in early Calgary and Cleveland elections is taken from Harris, Practical Workings of PR in the United States and Canada
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More on Quota
(from Wiki "Proportional Representation")
In STV elections, there is no explicit electoral threshold, but there is a natural threshold based on District Magnitude.
Winning the [[Droop quota|quota]] (ballots/(seats+1), plus 1) of first preference votes assures election.
As well, the need to attract second preferences tends to promote consensus and disadvantage extremes. A candidate who attracts good second (and third, etc.) preference support may be elected while an initially more popular candidate falls behind and is eliminated.
Due to vote transfers, a candidate who attracts good second (and third, etc.) preference support may pass quota and win a seat even if they start with only half the quota of first preference votes. In those cases, it may be said that in a six-seat district the effective threshold would be 7.14% of first preference votes (100/(6+1)/2).<ref name="DMstvPdf" />
For a district magnitude of 3, the STV electoral threshold is 12.5 %, significantly higher than typical party-list PR. (Of course, in such a district, the number of votes involved is less than in an at-large contest, so quota in a MMD is lower than the natural threshold in an at-large contest.
A city election electing 8 members at-large is regulated by natural electoral threshold of 11 percent (Droop quota); if the same city is divided into four districts, each electing three members, the natural threshold would be 25 percent in the district, which is only 7 percent of the total vote.)
As well, in STV it is possible to win without passing the quota, by being neither elected nor eliminated when the field of candidates is thinned to the number of remaining empty seats.
The electoral threshold has different effects on STV than on Party-list PR. For STV many of the votes for candidates below natural threshold are not wasted but transferred to the next-indicated choice, thus many of the voters assist in electing someone even if not the voter's first choice.
In party-list PR, a vote cast for a party below electoral threshold is an unrepresented vote, in almost all cases.
Only a small portion of list PR systems allow votes to cross party lines.
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