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Tom Monto

The Electoral Sweet Spot - 5 to 9 seats in a multi-member district, for STV anyway

Updated: Mar 11, 2023

he article The Electoral Sweet Spot

The author gives this rationale for why strategic voting is less under MMDs with 6 seats: political scientists of electoral systems have recognized for some time that strategic, or “tactical” voting, diminishes as district size increases, primarily because estimating how marginal votes will affect outcomes is more difficult as the number of seats, and contestants, rises. In higher-magnitude elections, shared expectations about candidate and party viability are less widely held, and therefore voter coordination around such expectations is more rare ..."

Not mentioned is this: strategic voting is less done because (as the author had previously stated) parties with 10 percent of support usually get some representation where District have 6 seats give or take so voters supporting marginal parties have good chance of seeing their vote used to elect someone even if placed on that marginal party. I think it is not so much that votes cannot calculate who has best chance of being elected - it is that many parties have a good chance of being elected so voter can take chance on voting for whom they truly want to see elected. it is directly tied to the higher rate of effective votes, represented voters under PR compared to FPTP. And - obviously being a "Proportionalist"- I query the author's statement that SMD as in UK produces high measure of accountability. If a majority of voters did not vote for the successful candidate, as often happens in any FPTP election, then how can there be accountability? Only if enough of the approx. 34 percent of voters (sometimes 18 percent/sometimes 64 percent) who elected the member decide not to vote for the member's re-election, only then will the member not be re-elected. So who exactly wields the accountability hatchet under FPTP? In many cases it is not the majority of voters, it seems, because the majority did not elect the member in the first place (in many cases). The essay is questionable on those grounds, but here's an interesting mathematical presentation of diminishing returns of larger DM: "...Figure 3 illustrates the effect of district magnitude on the dis-proportionality of an election, with predicted values derived from Model 2. There is a rapid decline in the level of dis-proportionality of an election as the district size increases beyond 1, and then a flattening out of the relationship as the district size increases beyond 5 or 6.


For example, the average level of dis-proportionality in SMD elections is 11.9, while the average in small multi-member districts (with a median magnitude of between four and six) is 5.3. Then, increasing the size of the district beyond this does not improve the representative-ness of a parliament much further: the average score for a median district size of between 7 and 10 is 4.6, for a district size of between 11 and 20 is 3.5, and for a district size of more than 20 is 3.0..."


(What 11.9 or 3.5 or 3.0 means in the real world is beyond me. But the gross perceptions seems clear - 11.9 is much worse than 3.0.

I look at more useful measures - the quota and percentage of wasted votes - below.)


As larger DM is burdened with problems of size:

- the district is geographically large (or at least larger than it would be if divided into two or more districts with smaller DM),

- the ballot is larger, carrying more choices for voters - in districts with DMs that exceed 12 ballots are sometimes almost literally blanket sized,

so the finer proportionality of an added member in a seat may not be worth the extra work that it would cause the election process. So it turns out that a DM of about the usual DM of STV is also the "sweet spot" for PR of all types, it seems. (I should point out that the sample used to determine the stats includes Ireland, which uses STV (Dail Eirean DM ranges from 3 to 5 in each district).) STV usually involved/involves DM of between 3 and 8, although even DM of 21 is not unheard of. (Aus. NSW) I think Winnipeg's use of 10-seat district to elect its MLAs, 1920-1949, is one of the largest-DM STV elections ever in the world, up to 1990s. (and it worked well for many years - without computers!).


Under STV, the quota is both the common amount of votes needed to take a seat and also approximately the number of votes wasted in a district.


At lower DM each additional member make a large change in proportionality and a large decrease in wasted votes , but as DM rises past 6 or so, the rate of change slows dramatically, as the following table shows. Quota (Droop) changes quickly at lower DM levels and changes much slower once past 6 DM.

DM 3 quota is 25 percent of valid votes. DM 4 quota is 20 percent of valid votes DM 5 quota is 17 percent of valid votes DM 6 quota is 14 percent of valid votes DM 7: quota is 12 percent of valid votes DM 8: quota is 11 percent of valid votes DM 9: quota is 10 percent of valid votes DM 10 quota is 9 percent of valid votes DM 11: quota is 8.5 percent of valid votes. ... DM 21: quota is 4.5 percent of valid votes Quota does not determine all winners under STV but it is guide to the proportionality of the system. Quota is not used in systems that use Saint Langue I think, but according to the article, increasing proportionality of all PR systems slows after DM 6, which the list of Droop quotas, shown above, shows in concrete terms. A PR system that uses all the votes of the nation as a whole is different than one where votes are divided among districts/regions or provinces (constitutional requirement in Canada for federal elections)*. A party with wide but shallow support is not likely to succeed in a district-ed system. A party that has consistent ten percent of support in every city and province would get no seats in a system that uses districts with DM of 8 or less (where no overall top-up). Luckily, things are not as normal as that across Canada. A party with ten percent average likely gets as much as 30 percent or more in some places. If that peak is just in one province, the party may take ten or 20 seats under FPTP but nowhere near the 38 that is its proportional due under PR. Let's note that: 1. in Canada we have parties that do not run across the country so for them it does not matter if PR is conducted separately in each province as one province is all that matters - they have no support across provincial boundaries that they wished they could pull together. 2. Other parties are fairly consistent across provincial borders (or at least not as inconsistent as seat counts currently pretend them to be) 40 percent of the vote is the same in every province across Canada as per recent elections 40 percent of the seats in each province proportionally would have same blend of Conservative, Lib, NDP and Green. this is definitely not the way it is when under FPTP we have one-party sweeps of whole provinces or regions. 3. even if at absolute minimum, Canada must be split into ten MDs (plus three SMDs (the Territories)), four of the provinces each have more than a seventh of the seats, Ontario having almost a full third, Quebec having a full fifth, so that the great proportionality of those four means that overall the result would be very P. even if there is no overall Proportional mechanism. ========= The article, what I read anyway, does not indicate the problem of large ballots. giving voters a choice of more than 50 names would be (or thought to be) brutal but that is what would happen if more than say ten seats are up for contest. marking preferences is made easier by use of party ID and the ballot being organized by party. and in many cases voters do not have to mark a set number of preferences -- they only mark as many as they want to. But ballots can be massive under STV if DM is large. not so bad in Ireland say Carlow where 14 ran for the five spots. Edmonton -- when it had STV, in 1955 it elected 7 MLAs and there were 30 names on the ballot But then we have an election where DM was 21. NSW Aus 2021 -- there were about 350 candidates running for the 21 seats. a party ran as much as 21 candidates although no way it would win all the seats - no party won more than 7 seats. other than limit of 21, there was no restraint on the slates, parties apparently trusting in the transferability of the votes and voters' disciplined marking of back-up preferences. So no reason to worry about votes being wasted by a broad slate. But such a large ballot is definitely jaw-dropping. if there are problems with large DM, large ballots is one of them, but party-list PR may reduce this problem -- there are only so many parties. But then you definitely have problem of accountability - if voters do not vote for candidates, then how to punish a candidate you don't like without punishing a party you like? on other tack, if there is lack of accountability under PR, it is that a small shift in votes means a small shift in seats -- and only a small shift no more than that --- but also no less (generally). This is unlike FPTP, where a small shift in votes may mean great change in the elected rep. but it can also mean no change at all or only a small change. so FPTP does not give us a dependable accountability. In Alberta, Conservatives were elected to majority government from 1971 to 2015, whether it got 62 percent of the vote (as in 2001, when it took 76 percent of seats) or 45 percent as in 1993, when it took 61 percent of seats. is that any kind of accountability?


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*when i wrote what I did (above) I had the understanding that votes in one province could not "splash" across provincial lines and that that meant there could be no overall national top-up seats or proportionality,

but now I know that overall proportionality can be created under particular conditions:

- the number of seats in the House of Commons must be allowed to fluctuate - that is, necessary top-up seats would grow the House of Commons past the pre-indicated number of district seats.

- that each province must have its due proportion of the seats in the House of Commons, both in the number of district seats and in the number of seat after top-up is added.


The process would be basically like MMP anywhere:

district seats are filled, then top-up seats are calculated at national level and then allocated to each party as needed to being a party's seats up to required proportion

but due to Confederation requirements, top-up seats wold be allocated to each province in line with the province's proportion of district seats in the HofC.


(Obviously rounding off would play a part.

Allocating top-up seats per province Could work this way: each province gets its share of top-up seats rounding down, then if any seats are left to be allocated after that, they go to province with the largest un-used fraction. This is the process shown here.)


Looking at 2021 Canadian election:

national Seats as per PR District Top-up Seats

vote share In the end

Conservative 34 pc 115 119 0 119

Liberal 33 pc 112 160 0 160

NDP 18 pc 61 25 36 61

BQ 8 pc 27 32 0 32

People's 5 pc 17 0 17 17

Green 2 pc 7 2 5 7

338 58 396

58 is 17 percent of the HofC so each province must increase by 17 percent.

seats count are

Seats Seats by New

district seats 17 pc increase RNDD OFF LGT FRCTNS total

Ontario 121 20.57 20 1 142

Quebec 78 13.26 13 91

BC 42 7.14 7 49

Alberta 34 5.78 5 1 40

MB 14 2.38 2 1 17

SK 14 2.38 2 1 17

NS 11 1.87 1 1 13

NB 10 1.7 1 1 12

NFLD 7 1.19 1 8

PEI 4 Not applicable (PEI is already over-represented pop.-wise) 4

335 58 52 6 393

Territories 3 (Territories are already over-represented pop.-wise) 3

TOTAL 338 58 396


if it happens that two provinces have the same number of seats and there is only one seat to allocate, then the larger one by population gets the extra seat.

SK and MN is tied === SK pop. is 1.174; MN pop. is 1.369 so MB gets the seat.

In the above case, there was one seat for each of them


Under such a system, the provinces (except for PEI) maintain their original proportions so it is strictly in line with Constitution. (Aside from some grandfather clauses that I did not apply, because I don't know about to apply them)


Constitutional experts or pundits will inform me if I have it wrong and that PEI should get an extra seat if its fraction of increase dictates it. They will tell me if the Canadian constitution insists that PEI should get an extra seat or not on same basis as the other provinces.

But if so, it is easy to do, Simply include PEI in the comparison allocation of seats -- base the allocation of the seats on fractions same as for the other provinces. And if it is due a seat by fraction, then some other province with less of a fractional surplus will not get that extra seat.


Then once the seats are allocated by province, then allocate the top-up seats in each province according to party shares.

give seats to un-elected candidates of the party

thus all BQ top-up, if there had been any, must be in Quebec.


Award top-up seats within each province and for each party to the most-popular un-elected candidates of the party. (as per open-list party list PR)

Like that...


So that is how national party shares can be used to set the membership of the HofC, despite the dictates of our Confederation constitutional framework.


Thus

top-up seats would go something like this:

(allocating seats to smallest provinces first,

seats in each province based on percentage of under-representation in that province

NDP PP Greens Top-up

ON 12 8 1 21

QU 9 3 1 13

BC 2 2 3 7

AB 4 2 6

MB 2 1 3

SK 3 3

NS 2 2

NB 1 1 2

NFLD 1 1

PEI 0

36 17 5 58


The percentages in each province will not be perfect proportionally compared to province party shares.

but top-up would be allocated based on national party shares and in each province, top-up would be allocated relative to under-representation of the parties that get top-up.


Despite any inconsistencies, the result would be more fair and balanced (party-wise and province-wise) than the present results.

- each party would get about its due share of the seats

- no clean sweeps by any one party across a whole province's seats as now.

-most-popular candidate(s) of each party is awarded top-up seats. (They would be candidates who ran in district contests but were not elected.)


if district seats are allocated according to district-level PR or STV, then the result would be even more fair.


I believe it would work!

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