Let's take one example --
a place with 3M population, the chamber might have 100 members
(this is according to the cube root rule)
perhaps 2 M eligible to vote in an election
65 percent turnout of the voters, likely about 1.3M vote
(13,000 votes cast per member)
(low compared to Canada fed. elections but not excessively so)
list PR electoral threshold of 2 percent nation-wide would be 26,000
a SMD would have about 13,000 votes cast
(the winner might win with anything from 4000 votes to 10,000 votes.
STV at-large 100-seat district == Droop quota is 12,871.
A MMD of 20 members would have about 260,000 votes cast
Droop quota is about 12,380
A MMD of 10 members would have about 130,000 votes cast
Droop quota is about 11,800.
A MMD of 5 members would have about 65,000 votes cast.
Droop quota is about 10,833.
This effective threshold in the district is again less than half of the votes marked by a 2 percent electoral threshold.
That shows that as DM is reduced below 10, the effective threshold in the district actually becomes lower than in a DM-10 district, and even more lower than in an at-lage districting.
(but mostly Droop quota is about the same, no matter what the DM is.)
Thus, The effective thresholds in the district is less than half of the votes marked by a 2 percent electoral threshold.
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(Below find similar calculation for smaller legislature. That calculation shows same result -- STV quota is less than list PR effective threshold.)
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Comparing effective threshold/Droop to FPTP winner's portions
More interesting is that list PR and STV are similar in that it takes more votes to be elected under list PR or STV than happens sometimes under FPTP.
This can be mentioned as reassurance for those who worry that PR will give too many seats to small parties.
Here is proof for the supposition that because list PR and STV have high percentage of effective votes (80 to 90 percent of valid votes cast are used to elect members), the same number of seats (100) is spread over more votes
and thus in a scientific system (list PR or STV), the threshold is actually higher than what some FPTP winners have in FPTP contests.
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effective threshold is basic amount that ensures election to a seat, either for a party or a candidate depending on system.
Assuming fair voting where each successful candidate receive same or about same number of votes.
say where 1M votes cast for 100 seats
districting makes little difference (bear with me)
math shows that where fair voting is used
if districting is at-large, to take one seat needs 10,000 votes (1/100 X 1M)
if province is divided into ten districts, 100,000 votes in each,
to take one seat takes 1/10 X 100,000 = the same 10,000.
that is using the Hare quota.
Droop quota, the usual used in STV,
means there is some difference when districts multiply.
if districting is at-large, to take one seat needs 9901 votes (1/101 X 1M)
(this is assuming, for the sake of argument, that a STV winner takes full Droop quota, which is usual but not always the case. More on that below.)
if province is divided into ten districts, 100,000 votes in each,
to take one seat takes 1/11 of district votes = only 9090.
if province is divided into 20 districts, each electing 5, 50,000 votes in each,
to take one seat takes 1/6th of district votes = only 8333.
if province is divided into 50 districts, each electing 2, 20,000 votes in each,
to take one seat takes 1/3 of district votes = only 6667.
meanwhile converting Droop quota to an effective threshold in district, as measured by percentage,
in 100-seat jurisdiction we say that it is approx. 1/101 at-large, 9900
10 percent of vote cast in a DM-10 district. 9000
17 percent of votes cast in a DM-5 district 8333
33 percent of votes cast in a DM-2 district. 6667
so despite higher percentage (in district) as DM is reduced,
the actual quota used to determine winners under STV contains fewer votes.
and then we look at FPTP
one member in a district 100 districts so about 10,000 votes in each district
(district turnout can vary but let's assume unrealistically uniform turnout.)
depending how vote is split and how many candidates are in running.
candidate is certain to win with 5001 votes.
but often a candidate wins with 3300 votes in district with 10,000 votes cast,
some with just 2500 votes in district with 10,000 votes cast,
(and of course some with 8,000 votes cast)
so threshold under FPTP is something like as few as 3000 votes (some elected with fewer -- but not many with much fewer; most with more; some with a great deal more)
while under fair voting (STV or list PR) the necessary amount to be elected ranges from like 8333 to 10,000.
(6667 in two-member district which is too low to be truly PR in overall effect)
so point is basic effective threshold under STV or list PR is higher than under FPTP so already you prevent small parties from being elected.
while under FPTP any candidate with about 3000 votes may win in a local contest (sometimes that has happened historically) and take that one seat,
but I would not bank on it - it is just an accidental result that happens when one uses a unscientific method.
but of course a scientific system is more fair and dependable,
but why is threshold under list pr or STV so much higher than FPTP can be?
the difference is the waste of votes
under FPTP as much as two-thirds of votes in a district may be wasted.
while under List PR, the waste is perhaps half or so of Hare for each major party, and about one Droop quota under STV.
the difference is that
under list PR about 1/00th of seats goes to 1/100th of effective votes (10,000);
under STV 1/100th of seats goes to 1/101th of effective votes (9900)
or with districting, perhaps 1/6th of seats to 5/100ths of effective votes (8333)
under FPTP 1/100th of seats goes to perhaps 1/3rd of 1/100th of votes,
or 1/2 of 1/100th of votes, if district majority is used as the touchdown line.
(that is assuming that the smallest districts have 1/100th of votes,
while in real-life FPP elections, due to inconsistent district size or varying voter turnout rate, the actual voter turnout can vary by a factor of 2 -- some districts have twice the votes cast as another district, perhaps ranging from 6600 votes to 13000 votes
and the necessary winner's vote tally then possibly ranging
from 2400 (1/3rd of smallest vote turnout) to 10,000 (80 percent of largest vote turnout). )
because list PR and STV have a high percentage of effective votes (80 to 90 percent of valid votes cast are used to elect members),
the same number of seats (100) is spread over more votes
and
thus
in a scientific system -- list PR and STV -- effective threshold is higher than in FPTP.
fair but higher.
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But not all elected with full Droop...
While full Droop quota guarantees election under STV, candidates can be elected with less than that.
But historically in STV, even they are elected by not that much less than that.
There is the case of O'Gorman (West Dubllin 2024), he won in the end without quota, getting only .82 of quota in the district.
But see, he got 6080 votes (at the end), almost 14 percent of the district vote.
West Dublin had about 42,000 votes cast.
If it had been five districts, each with 9,000 votes cast, the winner of a seat might have won with only 3,000 votes.
So even that extreme case of a winner with .82 quota at the end, showed that actual effective threshold under STV was higher -- perhaps double - than what a FPTP winner might have had.
it could be that as little as .75 percent of a quota may be a winner sometimes.
That figure sometimes is said to apply to FPTP as well
As it happens, 75% of Droop in single member district is 37.5 percent.
likely if you get that, you will be elected.
most but not all who get that number are elected,
BUT some with less are elected; and
not all who get that amount are elected.
the only firm rules i see are:
someone who gets quota is elected. Droop is usually the quota used.
it is possible to be elected with .82 of Droop quota at the end when the field of candidates is thinned to the number of remaining open seats. But such winners have vea vote tally quite close to quota, generally
In O'Gorman's case, he took 14 percent of valid votes cast in that five-seat district.
Thus, he won with about about twice the number of votes that a winners might have had in a single-member district of 1/5th the size.
Under fair voting, the number of votes that a succ. cand. takes is more than is won by some winners under FPTP.
Under fair voting, the number of effective votes used to elect someone (versus wasted votes) is greater than in any FPTP results except where the succ. FPTP winner takes like four times the votes of all the others put together.
Under fair voting, because there are a larger portion of votes used effectively (actually helping elect someone), each member is elected with a larger number of votes compared to what happens under the inefficient, wasteful FPTP.
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Comparing STV quota and effective threshold under list PR,
this time with 126-member legislature
Using a 126-member legislature, instead of a 100-member chamber, does not change what we saw above.
But let's say with 2M population, chamber might have 126 members
(this is according to the cube root rule)
perhaps 1 M vote in an election (60 percent turnout of the voters, likely about 1.2M)
(8000 votes cast per member)
(low compared to Canada fed. elections but not excessively so)
list PR electoral threshold of 2 percent nation-wide would be 20,000
a SMD would have about 8,000 votes cast
(the winner might win with 2700 votes or 6000 votes)
A MMD of 10 members would have about 80,000 votes cast
Droop quota is about 7300.
This effective threshold is less than half of the votes marked by a 2 percent electoral threshold.
A MMD of 5 members would have about 40,000 votes cast.
Droop quota is about 6667.
That shows that as DM is reduced below 10, the effective threshold in the district actually becomes lower
(but mostly Droop quota is about the same, no matter what the DM is.)
Looking at a district with higher DM
A MMD of 20 members would have about 160,000 votes cast
Droop quota is about 7619, still considerably lower than 2 percent overall (20,000).
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