Biproportional apportionment where districts gets seats they should and parties get the seats they should.

Biproportional apportionment is where districts are given seats only in line with the voter turnout (no longer is the population figures taken as guide) and each party is give nits due share.

Biproportional apportionment can also work to ensure ethnicities and genders get their due share.

But each voter or candidate would have to be labelled and the appropriate ones guaranteed election.

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Michael Balinski invented a form of biproportional apportionment that ensured more proportional results in U.S. elections.

Wiki says Balinski's Fair Majority Voting "is a biproportional apportionment method with single-member regions called "districts", so each district has exactly one representative. It can be thought of as the district cluster implementation of Party list. It proceeds the same as Party list except that each candidate is designated to a specific district so when a winner is elected, that eliminates the other candidates in the district from all future rounds.

It was proposed in 2008 by Michel Balinski as a way to eliminate the power of gerrymandering, especially in the United States.

(Michael Balinski also invented the election system known as "majority judgement," of which I know nothing.)

Balinski's Fair Majority Voting seems to me to be related to the "schedule plan" version of PR. But I haven't seen much on Balinski's system.

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When New York City used STV in the 1930s and 1940s, it both allocated seats to boroughs and seats to parties proportionally by using a uniform quota. Allocating seats to districts based on votes cast, not on population, allowed representation to be much more precisely proportional. However the number of city councillors fluctuated in a way that many saw as unsettling.

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Loose allocation of seats to districts

as semblance of Biproportional apportionment 

As elections taking place after adoption of PR may see voter turnout change in unexpected ways, perhaps a looser allocation of seats to districts would be a good thing in the early PR elections.

Such can be done by this method:

multi-member districts are drawn (perhaps with a smattering of single-member districts where settlement is sparse)

say in Alberta with total of about 90 seats,

80 seats are firmly allocated to districts:

40 seats in major cities (about 20 seats in each, perhaps two or three districts in each city) (This is the seat distribution basically based on population figures)

12 (or 13) 3- seat districts in countryside, based on population figures

4 (or so) single-member districts (the four largest districts drawn about the same as now, but boundaries moved to conform to counties or other existing units on the ground.

after district winners determined based on the districts' set seat count, ten seats are allocated to the "best losers", unsuccessful candidates with the highest votes tallies.

Thus districts would not initially be given a set number of seats. Their District Magnitude would not be determined until the final count. (The use of best loser compared across all the districts in the province means votes would be counted in serious way - a few hundred votes may make a difference.)

Of course in each MMD, seats are allocated to parties fairly. (using STV in a perfect world).

The ten top-up seats are allocated based on candidates' vote tallies, not on demands for party proportionality. This assumes that STV will be continued even after the original district seats are filled in the district to a point where only one unsuccessful candidate still stands. But often only one unsuccessful candidate will be standing anyway at the end.

The ten top-up seats are allocated without reference to party proportionality. But with MMDs and candidates winning by being the most-popular of the losers, the fluctuation in winners' vote tallies would be reduced, and thus each party would take its due share of seats (almost incidentally), same as occurs in all STV elections. (that is, if you base party proportionality on the location of the votes as they are finally placed, not on first preferences).

The ten top-up seats would go to districts where the voter turnout was exceptionally large, and therefore where the District Magnitude was not in line with votes cast. The quota in such a district would be larger than in a district with lower voter turnout and therefore the unused votes would be more numerous.

say 1,763,441 valid votes cast in 2023 60 percent turnout

90 seats means 19,600 votes per member.

Edmonton has 20 seats

perhaps 3 districts -- 7,7, 6

the 7-seat districts would be drawn in such a way as to get 137,000 votes each (out of 228,000 eligible voters)

Quota would be 17,125

likely the last unsuccessful candidate would perhaps have half of that (hence about 8500 votes)

(and the district would have about 120,000 effective votes)

But say voter turnout increases to 68 percent (a distinct possibility as voter turnout rate was that much in 2019)

voter turnout would then be 155,000.

Quota would be 19,000

likely the last unsuccessful candidate would perhaps have half of that (about 10,000 votes)

then with that district given an additional seat, effective votes would total 143,000.

in 2023 Alberta election, 19 unsuccessful candidates won more than 10,000 votes. This would be less common due to the use of the MMDs once PR is adopted.

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It could happen that a single-member district would get a second seat,

but likely the top-up would go to a MMD where the un-used votes (approximately a quota) is the most,

so perhaps inevitably they would be in the large city MMDs.

But wherever allocated, they would be allocated in accordance with principles of "one person one vote," that each vote should count equally as much as possible hence each winner should be elected with about the same number of votes.

Allocation of seats based on voter turnout would encourage higher voter turnout, which is also a good thing.

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