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Tom Monto

Basic building blocks of PR - MMDs/vote pooling and single voting

Updated: Jan 11, 2023

Multi-member districts (MMDs) are critical to Proportional representation --

Or a general pooling of votes such as country-wide as in the NZ top-up.


Where we are used to local representation or where constitutional requirements insist, a general pooling of votes country-wide is impractical.


MMDs then are critical (or a upper level of district is sometimes proposed - multi-district sub-provincial regions for example).


and single voting is critical. Let's applaud the S in STV!


Sometimes it is said,

"MMP uses two votes, But only one counts to deciding makeup of the parliament. The second is about which person takes which seat for a party."

It might work that way in say Finland but in NZ it works differently, like this.


MMP in NZ uses two votes. The first is for the local district member - and just as in Canada, often a majority of the district vote is ignored in the local election.


The second counts to deciding make-up of the parliament (the proportion of seats taken by each party). And more than 90 percent of the votes are used in that result.


Which person takes a top-up seat for a party is set by the party list.

Unfortunately in NZ they do not use MMDs to fill local district seats, and thus the local contests suffer from the usual problems of FPTP.


Examples from 2020 election:

among the first 12 districts alphabetically:

Auckland Central winner of district seat had 35 percent of the vote.

Bay of Plenty winner of district seat had 45 percent of the vote.

Coromandel winner of district seat had 45 percent of the vote.

Epsom winner of district seat had 47 percent of the vote.

Hamilton East winner of district seat had 47 percent of the vote.


winners in the other 7 of the first 12 districts (alphabetically) did take seats with majority of votes, but still representation was not proportional --

not proportional until the top-up seats were applied, that is.


Under a different PR system,

MMDs with single voting (esp STV) could achieve crude proportionality even before top-up seats, if any, are applied.

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Pro-rep systems require either a general pooling of votes or multiple-member voting districts.

Pooling may be either at-large (as in most party-list systems) or in multi-district regions (as in Additional Member Systems).


Some MMP systems use at-large pooling in conjunction with single-member districts (New Zealand); others use at-large pooling in conjunction with multi-member districts (Denmark).


Multiple-member voting districts are used whenever Single transferable voting or Single non-transferable voting is used.


The thing is: there are multi-member districts and there is wider pooling.


I would not call an at-large pooling an MMD, although it elects multiple members - I don't see it as a district, especially if the country is also divided into single-member districts as in NZ's MMP. There are single-member districts (in MMP)


There are also multi-district regions as in Scotland's Additional Member System.


To say that MMDs are pooling of votes does not quite cover the matter. To say "multi-member regions (as in most party-list systems)" raises questions. Do we know that most PR systems use regions? I would think most use at-large pooling. Only AMS uses regions as far as I know.


one description of PR states "SMDs + pooling in MMDs or at large (MMP)

But "pooling" in MMDs does not make sense to me.


I see

- pooling at large, ie single country-wide district (list PR)

- pooling in MMDs (STV, list PR (where subdivisions of the country are used))

- pooling in MMDs (list PR) + pooling at large (list PR leveling seats) Denmark

- SMDs + pooling at large (NZ MMP)

- SMDs + pooling in multi-district multi-member regions (Scottish AMS)


A multi-district multi-member region used in Scottish AMS is not a MMD to my mind. as it itself is a grouping of districts.


Districts can be thought to be in tiers:

lower tier is either SMD or MMD

upper tier is regional or at-large.


I don't know of any system that uses both types of upper-tier pooling.


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Other discussions of details of STV

I have been referred to two downloadable references on STV:


==============

22 NI STV election.pdf

about Northern Ireland's 2022 STV election


Northern Ireland result shows me that

4 or 5 first-count front runners in each district (each district electing 5 members) won in the end after transfers.

only in 6 districts was a front-runner not elected.

In 12 districts, the result was same as it would have been under SNTV (unless votes would have been cast differently).


Single voting in MMDs is what is most important, not transfers or preferential voting.


Oddly, directions to voters in the piece say voters can vote for as many as they want - although STV is very clearly single voting!


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Transferring surplus vote in the Western Australia Legislative Council


haven't yet studied in depth


but notice appendix 2 is flawed in that it does not tell how many seats in each district filled each election

NSW is a particularly glaring oversight --- although there are 42 in the district (at-large state-wide) as stated, only 21 are elected in each contest.


also the comparative method analysis is weak, it seems to me.


Random example (page 28) does not suppose the effect of the random transfer but only how a random transfer is recorded or something.

(at least that is what my quick look tells me)


"random" whole vote transfers are capable of producing various transfers so a range or a few different possible outcomes may be necessary

say take or leave 5 percent of votes for each party, that kind of variation.

But I did not see it so far.


Interesting to me is the effect of different methods on ultimate outcome even if only imagined or guessed at.


I plan to look at the piece more, in particular looking for actual presentation of the different outcome under mock election (pretend case) due to diff transfer method, if any.


===========================

More discussion on how various PR systems works, with emphasis on New Zealand's MMP


These are the facts as I see them:


Proportional Representation needs groups of voters who together elect more than one representative.

In each PR contest, each voter has just one vote.

Some semi-PR systems votes have more than one vote - such as Limited Voting used in Toronto in 1896.


In some MMP systems, voters cast two votes but each is used in a different contest.

in some city elections, voters cast one vote for mayor and one for local councillor if single-member ward is used.

These are separate contests but the one voter, one vote rule is obeyed because the two votes are used in separate contests.


in some city elections, voters cast one vote for mayor and several for local councillors if multi-member ward or at-large contest is used (Block Voting). the one voter, one vote rule is obeyed in that each voter has the same number of votes.


in each PR system

there are measures to ensure party proportionality and fairness and high ratio of votes used actually to elect someone.

These mechanisms are:

- MMD or pooling of votes to elect multiple members using single voting.

District Magnitude (number of members elected in one contest) may be as many as a hundred or more. (Angola has an at-large district where 130 members are elected through party-list PR. (as well the country has 5-member province-wide districts).


- MMDs to elect multiple members and single transferable vote. (the most DM the world has seen in STV is 21 in NSW, in every election since 1990.)


Proportional Representation can be:

- party-list PR where votes are pooled in one wide group and party seats allocated based on overall party tallies


- party-list PR where votes are pooled in separate large groups and party seats allocated based on party tallies in each group.


- where some are elected in local district elections and others are elected through top-up party seat allocations based on overall party tallies and applied in compensatory style NZ


- MMP where some are elected in MMDs through party-list PR and others are elected through top-up party seat allocations based on overall party tallies and applied in compensatory style Denmark


- STV where votes are cast for candidates and the most popular (either by passing quota or by relative popularity in the end) are elected. (Surplus votes of some of the successful candidates, and votes cast for all or only some of the unsuccessful candidates are transferred to ensure party proportionality and fairness and high ratio of votes used actually to elect someone) Ireland Malta


and hybrid systems

such as

STV/IRV some are elected through STV and others through IRV (Alberta 1924-1955; Manitoba 1924-1953)

or STV/FPTP (Manitoba in 1920)

or FPTP/Block Voting (every Canadian federal election prior to 1968) (not PR but it was a hybrid system so I mentioned it here)


As well, some countries use parallel system where some members are elected in one way and other members in another way. with a vote cast being used in both.

Some (most) of these have some aspect of proportionality.

Angola has 18 5-member districts (elected through SNTV or party-list PR) and 130 elected through party-list PR across the country.


Election contests can be conducted

at-large

Single-member at-large contest - mayor elected by voters across the city

Multi-member at-large contest - Legislative Council in NSW Australia -- where 21 are elected in one single state-wide contest through STV


or

in districts, etc.

the members can be elected in separate contests through use of districts or other pooling of just some of the votes.

Districts can elect one member or multiple (2 or more). Single-member district by themselves cannot produce proportional representation.


Districts can be geographical units mixing votes of all those who live there.


Districts (or electorates if you prefer) can be such things as university graduates in old Britain, where University seats (Cambridge, Oxford, etc.) were elected through STV. The graduates whose votes are mixed together were living anywhere.


(At least theoretically, districts could be voluntary grouping of votes of like-minded people, or at least each member could be elected by a different group of voters (such as is achieved in a MMD with a fair voting system - STV for example). Geographical districts seldom or never produce that unity of thought.

A system can use districts "layered" on districts, with different votes voting in one district system but not another. This guarantees that the votes of voters of type A are not used to deny seats to members of Group B.


New Zealand has seats dedicated to Maori to ensure they get seats that reflect their voters.


NZ uses two types of geographical districts -

the system of 65 single-member districts covering whole country -- a non-Maori voter votes in one of these.

the system of 7 Maori single-member districts covering the whole country -- a Maori voter votes in one of these.


as well there are various top-ups or additional members added at the end:

in NZ, parties that are due more seats than they won in local districts are given top-up seats if possible.


Malta to ensure that a party with more than half the vote has more than half the seats


NZ when a party takes a local seat when its vote share would not have given it a seat. (un-necessary in my view - see below)


Iraq, I think it is, gives seats to the most popular women candidates who did not win seat.

etc.


NEW ZEALAND

in New Zealand each voter may casts two separate votes. they are used separately. so it is still one voter one vote.


in New Zealand voter has oportunity to cast an electorate vote. Electorate votes are used to determine local winner.


in New Zealand in 2020 -- Auckland Central district --Chloe Swarbrick was elected due to getting more district votes than any other candidate. (This was separate from any PR effect of MMP. Even if her party did not have enough vote share to get a seat, she won this seat. (see overhang below))


in New Zealand, each voter also has right to cast a party vote. These are used to assess the number of seats a party should be given. This (hypothetical) figure is compared to the number of seats it has taken in local seats (such as Chloe Swarbrick's seat), and if possible, additional seats are allocated to parties whose district seat count is too small based on overall party vote tallies.


I looked at "NZ election night 2020" and found that the election coverage was about as good as it is in Canada. which is to say, it is overly excited and not very informative! I saw no reference to local district contests although likely local voters were curious as to who got in to represent them (or were looking to be elected to do so).

I laughed seeing the running stats across bottom show Labour as having 50.5 percent of votes when only 24 percent of the votes were as yet counted.

maybe 50.5 percent of votes as yet counted were for Labour but that is different from saying that Labour had 50.5 percent of votes cast. (which it turned out that it did have but you can't say that with 24 percent of the vote counted!)


OVERHANG

I have seen information on the problem of overhang -- those arise when the winning of district seats gives a party more seats than it deserves based on its vote share.


But it had not occurred to me that on occasion a party that is not due any seats at all may win a local seat. (But it is well known that under FPTP a party with just 35 percent or less in a district may win a seat, even if not popular outside that one district and even if it does not have support of a majority of the people in that one district. So it should not be a surprise that such un-balanced results occur in some MMP elections.)


Wiki (2014 New Zealand election) says

If a party wins more electorates than seats it is entitled to under the party vote, an overhang results; in this case, the House will add extra seats to cover the overhang. The 2014 election saw a one-seat overhang where Peter Dunne won the Ōhāriu electorate when his United Future Party was entitled to zero seats under the party vote.

UFP got .22 percent of the vote. Aside from the 5 percent threshold, the Party needed about .8 percent of the vote to be due a seat in the approx. 120-seat Assembly anyway.


But with only 37 percent of the district vote, with only 14,000 votes out of the country's 2.4M, the local UFP candidate in Ohariu won a seat - taking 1/121st of the country's legislature. (that is the effect of FPTP!)


That supports my view that local seats are filled, then top-up is applied in compensatory fashion to ensure where possible that party gets seats it is due based on party share.


In this case, due to the overhang, one seat top-up was also applied to allow the other parties to get their "fair" share of the 120 seats, aside from the accidental UFP victory, it seems.


Or at least it allowed the parties that took threshold to take their fair share of 120 seats.


This one-seat top-up seems un-necessary to me. The difference between 94 percent of the votes (those cast for parties over threshold) spread over 119 seats or 94 percent of the vote spread over 120 seats seems trivial to me.


There was already other unfairness in the 2014 election that was not created by UFP's win:


the Conservative party with almost 4 percent of the vote was ignored -- it got no seats although due about 5 seats.


Six percent of the votes got no representation.


And with the 121-seat legislature, the National Party with 47 percent of the vote was allocated half a seat less than half of the seats in the chamber.


So there is unfairness even in NZ MMP.

of course, less so than in Canada


So what difference to proportionality did UFP's one seat make?

Not much I think.

The UFP candidate was elected to the local seat. Even with the 121st seat added to the chamber, he was still the only local winner. The district did not get two electorate members.


This question of the one-seat top-up is likely clouding my basic point that NZ does not have just one district. That in fact it has 72 districts plus overall top-up seats,

but it came to my mind so I wrote it down.

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