if the local electons in FPTP is strictly local, if the taking of the district sets has nothing to do with party, then comparing the overall party's vote tally (or proportion) to the number (proportion) of seats the party takes is not strictly accurate.
if we assume that each candidate runs on his or her own name independently and not due to any party allegiance, then the elected member should be accorded only the number of votes that he or she actually received.
these candidates' voe tallies added togethr then are the effective votes for that party
then we add together all the effective votes for all the parties that got some measure of representation and we get overall effective votes.
(by the way, effective votes is a goal of the electoral reform as much or almost as much as PR itself. With each successful candidate being elected with the same or nearly the same number of votes, effective votes, we can know that each party is represented in due propotion to the number of votes they take overall.
under FPTP there are many wasted votes and members are not elected with very different number of votes so FPTP fails on both measures.
party proportional representation can be produced under FPTP
Just look at Alberta today where NDP's under-representation in the rural area is balanced against Conservative total non-representation in the capital city.
each is a dis-proportional result but altogether if we look at votes cast, the parties' rep in the Legislature is very party proportional
but those sort of fair overall results cannot be depended on under FPTP, where many votes are wasted
and it could happen next time, just as likely, that the waste will not be balanced Conservative to NDP,
but instead next time one or the other might be only one to suffer the usual vote waste.
NDP with 44 percent of vote took 38 seats (44 percent of seats)
United Conservatives with 53 percent of the vote took 49 seats (56 percent of the seats)
But note these statistics:
With a shift of 300 votes, the Conservatives might have taken four seats from NDP, which would have produced a very lopsided 53-seat UCP caucus facing only 34 NDP members
With a shift of less than 2500 votes, the NDP might have taken six seats from Conservatives, which would have produced a NDP-majority legislature of 44 NDP seats to 43 UCP seats.
less than one percent of votes cast determined whether a UCP or a NDP majority government was elected in the 2023 election.
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so high rate of effective votes is best way to dependably ensure proportional results.
overall at-large contests as much as possible anyway, reduce the waste caused by small remander groups of votes left un-used in districts,
as well as raising District Magnitude to highest possible, (under STV, the quota is a set fraction of the valid votes. the quota is both the amount of vofes that ensures election and also is the ceiling (more or less) on the un-used votes in each district, the quota is smaller, the larger the DM.
at-large contests are not always possible expecially not in federal elections.
but having as few districts and as large districts as possible allows DM to be as large as possible, and quota (as a fraction) to be as small as possible,
the larger population in the larger district does mean that the number of votes in a quota might not follow that rule
for example:
100 MPs elected using Droop quota 1M valid votes
DM quota fraction quota as fraction quota votes
in district in overall valid votes approx.
1 at -large district 100 1/101th 1/101th 9900
2 districts 50 1/51th 1/102th 9800
10 districts 10 1/11th 1/110th 9000
20 districts 5 1/6th 1/120th 8300
thus for most of the range of DM under PR, DM stays very similar as to number of votes, whether five or 100 are elected in each district.
outside normal range of DM for PR, we have these figures:
50 districts 2 1/3rd 1/150th 6667
But as consistent 6667 in each district used is much more fair than the range today in FPTP of everything from less than 10,000 to more than 50,000 as vote tallies for winning candidates in Canadian elections,
and under FPTP everything from 30 percent of the district vote to more than 70 percent of the vote in the district, if we consider quota as fraction in the district.
Getting back to main point,
if we consider just effective votes won by party's successful candidates, we might see very different results than the party proportional results using all votes cast for party's candidates.
Conservative took 929,000 votes including both successful and unsuccessful candidates
NDP took 777,000 votes including both successful and unsuccessful candidates
looking some at some districts where Conservatives lost
Calgary
Acadia 11,000 Conservative votes wasted
Beddington 10,000 Conservative votes wasted
Bhullar 5000 Conservative votes wasted
Buffalo 7000 Conservative votes wasted
Currie 9000 Conservative votes wasted
Edgemont 11,000 Conservative votes wasted
Elbow 11,000 Conservative votes wasted
Fish 11,000 Conservative votes wasted
Foothills 11,000 Conservative votes wasted
Glenmore 13,000 Conservative votes wasted
Klein 10,000 Conservative votes wasted
NDP votes wasted
Bow 13,000 NDP votes wasted
Cross 7000 NDP votes wasted
East 6000 NDP votes wasted
Falconbridge 5000 NDP votes wasted
Hays 9000 NDP votes wasted
Lougheed Hays 7000 NDP votes wasted
and so on.
Edmonton Strathcona NDP won with 14,000 votes
80 percent of votes in the district
and also 1 percent of the entire party's votes across the province.
under PR each member is elected with about same number of votes
but under FPTP in 2023 Alberta election we see:
looking at winners' tallies (not the lead they won by but votes received)
those who won
with more than 16,000 votes 6 UCP, 1 NDP
between 15,000 and 16,000 6 UCP 2 NDP
between 14,000 and 15,000 7 UCP 2 NDP
between 13,000 and 14,000 13 UCP 5 NDP
between 12,000 and 13,000 2 UCP 8 NDP
between 11,000 and 12,000 4 UCP 8 NDP
between 10,000 and 11,000 4 UCP 2 NDP
between 8,000 and 10000 3 UCP 5 NDP
less than 8000 votes 6 UCP 2 NDP
totals 51 UCP 35 NDP
totals should be 49 and 34 (so not exact - must have made a mistake some place)
we see that some won with more than twice the votes that elected others.
glory and shame approx. equally shared by both parties
so no obvious benefit of FPTP's unfairness to any one party this time
but perhaps next time one or other party might use up big counts to win few seats while other party might take many seats with just a few votes - -- it could happen.
such un-balance might benefit NDP or UCP -- there is no way to know which,
either way it will be unfair and either way hundreds of thousands of votes will be wasted.
But compare those wide-ranging vote tallies with results under PR:
New Zealand results 2022 MMP
party votes
National party 1M votes 48 seats votes per seat 21,000
Labour 770,000 votes 34 seats votes per seat 22,600
Green 330,000 votes 15 seats votes per seat 22,000
so very similar party to party
Ireland Dail 2020 election STV
(including successful and unsuccessful candidates vote tallies of first-preference votes )
Fianna Fail 484,000 votes 38 seats votes per seat 12,700
Sinn Fein 536,000 votes 37 seats votes per seat 14,500
Fine Gael 456,000 votes 35 seats votes per seat 13,000
Green 156,000 votes 12 seats votes per seat 13,000
in a riding, transfers often go from one candidate to another candidate of the same party
but in Sinn Fein's case the party mostly ran just one candidate in each riding, so only in two cases could the transfer see vote go from a Sinn Fein candidae to another Sinn Fein candidate and in those cases 75 percent of vote went that way.
in all others the votes had to cross party lines or go to exhausted pile.
when vote had to cross party lines (or be exhausted), SF vote transfers went largely to an Independent, Green or Fianna Fail candidate, thus obviously contributing to its lower vote per seat total based on first preferences.
meanwhile in Cavan-Kilkenny (picked at random)
5 elected
first preference vote tallies for eventual winners ranging from 17,000 vote to 5000 votes
quota was 12,000 votes
by the end four surpassed quota, the fifth won with 10,500 votes, very close to quota.
so very equivalent number of votes used to elect each successful member.
if candidates are put in order of popularity in first count,
1st, 2nd, 3rd, 5th and 7th won in the end,
4th was the third ranked candidate of Fianna Fail
and 6th was the secondary candidate of Fine Gael
4th and 6th were not elected
the vote transfers of 6th candidate helped boost his co-runner (#5) over quota .
the 4th was eliminated at the end - he was declared defeated at the end. His votes were not transferred as his defeat meant only as many surviving candidates as the number of remaining open seats.
Fianna Fail's three candidates started with less than three quotas and they did not receive enough vote transfers from others to make up the difference, so party could only take two seats in the district, which it did,
but the failure of the 4th and 6th did not mean that those parties did not have any representation in the district - one party did elect one emember anyway and the other party did elect two others anyway.
four times quota is total of 49,000 votes
one elected with 10,500 votes (just less than quota)
so total of 59,000 votes actually used to elect someone
with 74,000 valid votes cast, 59,000 votes make up 81 percent of valid votes actually used to elect someone.
all in all, in that riding, four parties won representation among the district's five seats.
Fianna Fail. Fine Gael, Sinn Fein and Green.
That is the kind of fairness that I like to see in a PR system
- many effective votes and fair mixture of elected members.
- representation that is both local, and mixed and balanced.
(local because whole consittutency is only 3000 sq. kms in size although electing five members.
distance as the bird fles from the middle to anywhere in the riding is less than about 28 kms.)
the successful candidates of each party that won representation were the most popular in the party among the voters.
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