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Tom Monto

Plumping in Alberta STV elections meant few transfers used intricate math

Updated: Jan 31

I recently realized that plumping was very common in Canadian STV elections and something you don't see at all in Australian elections.


A big effect of this is, it seems, many transfers of surplus votes (done after a candidate is declared elected) did not see any math used - ballots that had no usable backup preferences were left with the elected candidate and often they were so many that there were not enough ballots bearing usable backup preferences to do all possible transfers In other words, the surplus of votes over quota was more than the number of ballots bearing usable back-up preferences. Therefore, no math had to be used to make many of the transfers of surplus.


Plumping and exhausted votes were more prevalent than might be thought. They were so common that in many cases they alleviated the need for intricate math calculation of transfer of surplus.

In the case of STV elections in Edmonton's history, I see that this happened in the case of Elmer Roper's surplus in 1948. I thought at first that there was a mistake or oversight on the part of the election officials that a thousand votes of Roper's surplus remained with him after the transfer of his surplus but I now see that it is likely that all transferable ballots were transferred but there were just so many un-transferable ballots. He was the last CCF candidate in the running as the other CCF candidates had been eliminated as per the STV vote-counting procedure. He was the last surviving CCF candidate and the only successful one. Most of his supporters did not mark transfers across party lines.

We must assume that the official did his duty assiduously and not jump to conclusion (like I have done until recently) that such a broad miscarriage of justice was allowed to happen. We must assume that no official would have been allowed to overlook a thousand votes. We must assume that there must have been cause and that the cause was lack of usable back-up preferences. This is backed up by directions that say that all non-transferable votes should remain with the successful candidate, thus allowing only ballots with back-up preferences to move on to other candidates. But that rule was in place with no one expecting that non-transferable votes would exceed quota!


Such a case never happens in Australia where plumping is not allowed at all or ranking at least a substantial number of candidates is required. (In Tasmania STV, voters must mark at least five, the number of open seats in each district. Australian Senate elections use STV with voters having choice of voting a party line or ranking every single candidate.


Recent use of ranked voting in North America shows very different rules - here voters are restricted to marking only three preferences and exhausted votes are a real problem. (See my blogs on the 2018 London, Ontario city election.) (But no matter howmny chocies a voer marks, in Alternative Voting no surplus transfer is ever done because when one candidate is elected, that fills the one seat so the vote counting process stops there.)


In Calgary STV provincial elections there were many instances when it came time to transfer a successful candidate's surplus where there were not enough transferable ballots to enact all possible transfers. In Edmonton not so much but still some. The transfer of Roper's surplus in 1948 was just one example.

(The old-time statements of the vote count reported this by leaving votes over and above quota with the successful candidate. While in some elections (but not all), exhausted votes had their own running total at the bottom. But ironically, in the cases where surplus votes were so common that they prevented the normal mathematical transfer of surplus, there are no exhausted votes added to the "exhausted vote" running total, because they were left with the successful candidate as per the usual standing procedure.


When that happened, when exhausted votes were more numerous than the surplus to be transferred, math did not have to be used to calculate the transfers at all - the transferable votes were physically moved to recipient candidates with no calculation.


Leaving out Medicine Hat's sole STV election in 1926, there were eight STV elections in Edmonton and Calgary, held between 1924 to 1956. 46 MLAs were elected in these elections in Edmonton and 44 in Calgary.

[some of these overall numbers might be off as later examination of vote count sheets gave me new info in some cases. Edmonton 1944 for exampe]


Almost half of these members (36) were elected through the field of candidates thinning to where there were only as many candidates as there were remaining open seats. Most of these candidates had only partial quotas at the time they were elected. A couple happened to have accumulated more than quota in the last vote transfers made but they would have been elected irrespective. Their surplus votes were not transferred. This was due to fact the vote count was finished when these candidates filled the last open seats.


About a fifth of the successful candidates (18) did not have sufficient transferable votes to cover the surplus of votes they had. The transfer of these candidates' relative few transferable votes was done without use of math. None of the transferable votes had to stay with the successful candidate.


Five MLAs were elected in the very last count in four of those elections. Due to that election, by that point in those elections there was only two candidates remaining and only one remaining open seat. The number of surplus votes involved was not enough to change the order of the remaining candidates - they were not numerous enough no matter how they were transferred to pull the least-popular candidate out of his or her lowest place. Therefore the fate of the least-popular candidates was sealed - he would be eliminated next and with this elimination the number of candidate would be thinned to only the number of remaining open seats so the other would be declared elected. Therefore no transfer of surplus votes was done as the same candidate would be eliminated in the next count no matter how the transfer was done. And that certain elimination alone would determine who would be declared elected to fill the final remaining open seats and thus end the vote-count procedure.


Only a third of the successful candidates had their surplus vote transferred according to the usual mathematical-reduction procedure. Only 31 of the 90 successful candidates had their surplus votes transferred mathematically.

These were the only cases where

- the transfer could affect the order of candidates and may have an impact on who was elected

- and where there were more than enough transferable votes to cover the surplus to be transferred so that math had to be used to determine which ballots would be transferred and which would stay with the successful candidate.

(two other conditions that apply are listed in "addtional information" below.)

Calgary STV elections

1926 three transfers used math; the two others won with partial quota at the end as field of candidate thinned to number of remaining open seats.


1930 Irwin's surplus (in Second Count, following First Count election) was transferred without the use of math. (he was left with 3495 votes. quota was 3489 so we can see that he did not have enough transferable votes to cover surplus)

Subsequently, transfer of surplus of Webster and White was also simple - no math

Farthing, Bowlen and McGill elected with partial quotas at the end

Sitting MLA Parkyn was eliminated at end without transfer as Farthing, Bowlen and McGill were declared elected to fill all remaining seats as field of candidate thinned to number of remaining open seats.

No transfer of surplus used math!

1935 Manning's surplus (in Second Count, following First Count election) used math. Subsequently, transfer of surplus of Irwin, Bowlen and Anderson used math. Gostick and Hugill elected due to thinning of field of candidates. Little was eliminated at end without transfer as Gostick and Hugill were declared elected to fill all remaining seats as field of candidate thinned to number of remaining open seats. Gostick happened to achieve quota in this round but she would have been elected irrespective. Four transfers of surplus used math; two did not transfer surpluses at all.

1940 Davison's surplus transferred (in Second Count, following First Count election), used math. Subsequently, transfer of surplus of Aberhart used math. Transfer of surplus of Anderson was simple - no math Mahaffy elected with quota but no transfer made as last seat would be filled though thinning of candidates. Bowlen elected with partial quota at end. White was eliminated at end without transfer as Bowlen was declared elected to fill last remaining seat as field of candidate thinned to number of remaining open seats. Two transfers of surplus used math; one used no math; two were not transferred at all. No transfers done in Calgary elections from 1944 to 1955 used math.

1944 Davison's surplus transferred (in Second Count, following First Count election) without using math. Subsequently, transfer of surplus of Anderson did not use math transfer of surplus of Wilkinson did not use math. MacDonald achieved quota but no transfer made as remaining seats filled though thinning of candidates. Liesemer elected with partial quota at end. Alderman was eliminated at end without transfer as Liesemer was declared elected to fill last remaining seat as field of candidate thinned to number of remaining open seats. Three elected with no math used; two were not transferred at all.

1948 Wilkinson's surplus (in Second Count, following First Count election) did not use math. Subsequently, transfer of surplus of Colborne was simple - no math Liesemer, MacDonald and Macdonald elected with partial quota at end. Hill was eliminated at end without transfer as Liesemer, MacDonald and Macdonald were declared elected to fill all remaining seats as field of candidate thinned to number of remaining open seats. Two did not use math; three were not transferred at all.

1952 Wilkinson's surplus (in Second Count, following First Count election) did not use math. Subsequently, transfer of surplus of Colborne was simple - no math Subsequently, transfer of surplus of Macdonald was simple - no math Brecken and Dixon elected in last count, by accumulating quota.

MacDonald declared elected with partial quota at the end. MacDonald was declared elected to fill the remaining seat as field of candidate thinned to number of remaining open seats. No transfers of surplus used math. Three did not use math; three had no transfers at all.

1955 Smith's surplus was transferred (in Second Count, following First Count election) without using math. Subsequently, transfer of surplus of Hugh J. Macdonald was simple - no math Subsequently, transfer of surplus of Colborne was simple - no math Subsequently, transfer of surplus of Wilkinson was simple - no math Grant MacEwan and Dixon elected at end, both with partial quota. Brecken was eliminated at end without transfer as Grant MacEwan and Dixon were declared elected to fill all remaining seats as field of candidate thinned to number of remaining open seats. No transfers of surplus used math. Four did not use math; two had no transfers at all.

Edmonton -- some surplus transfers used math but still many did not. 1926 three used math for transfer of surplus; Prevey and Duggan elected with partial quota at the end.

1930 three used math for transfer of surplus; Weaver, Howson, Atkinson elected with partial quota at the end.

1935 three used math for transfer of surplus; Duggan, Mullen and O'Connor elected with partial quota at the end.

1940 Two (Manning and Page) used math for transfer of surplus; O'Connor eliminated at end with no transfer; James, Duggan and Macdonald elected with partial quota at the end.

1944 One (Manning) used math for transfer of surplus; Kennedy eliminated at end with no transfer; Roper elected, his surplus not transferred as too small to make difference. Page elected, his surplus transferred without math. Williams and James elected with partial quota at the end.

1948 Two (Manning and Prowse) used math for transfer of surplus;

Roper's surplus transferred without math;

Heard achieved quota and was declared elected in the penultimate count. His surplus was not transferred as it would have had no effect on the outcome.

Adams elected at the end due to thinning of field of candidates. Adams had partial quota. Two had surplus transferred with math; one transferred without math; one had no transfer of surplus. One was elected at the end, ending the vote count.

1952 four (Manning, Prowse, Roper and Ross) used math for transfer of surplus; Holowach was eliminated in the last count with no transfer; Gerhart, Page and Tanner elected with partial quota at the end.

Three with math, three with no transfer.

1955 no actual election vote count chart found, but I see that four had quota at the end so their surplus transfers would have used math. Three did not so were elected at the end with partial quota, ending the vote count process.


(The options were like this:

achieved quota through first preferences and surplus transferred mathematically

achieved quota through combination of first and back-up preferences and surplus transferred mathematically (based on last parcel only)

achieved quota through combination of first and back-up preferences and surplus transferred not mathematically -- not enough transferable votes to cover surplus so math not necessary

achieved quota through combination of first and back-up preferences in last count and surplus not transferred as it would make no difference

achieved election without achieving quota but through the field of candidates thinning to number of remaining open seats -- no surplus, no transfers. Plumping and exhausted votes were more prevalent than might be thought and were so much so in Alberta provincial elections that in some elections, they, along with election by partial quota at the end, completely alleviated all the need for intricate math calculation of transfers of surplus whatsoever.

You don't see that mentioned in any book on STV! Perhaps I have something wrong somewhere... so yes where there are lots of seats to be filled and lots of candidates, and long ballots, people may not rank enough candidates to prevent ballots from being exhausted but that is not so bad, it is not a big problem. Still in Alberta STV elections, a mixed crop of reps were elected again and again and three to four parties usually had representation in each city. Much larger proportion of Effective Votes than under FPTP even despite the large number of exhausted votes Much more fair results than FPTP even despite large number of exhausted votes. and the moderately large number of rejected votes - which was used as the excuse for the abandonment of STV in Alberta elections.


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Additional Information


In Alberta's use of STV (which is fairly typical),

we see:

- the times when the complicated transfers that are done when surplus votes are transferred were actually few in number

-- only two in each election in each city (Edmonton and Calgary) on average.

- in Alberta the few times when those kind of transfers would have been done, they were done without fractions by transferring whole votes of just the surplus. (when done for surplus votes belonging to candidates elected in first count all the candiatte's votes wre considered in formulating transfers; for later transfers only the last parcel was considered.)

The relatively few times when mathematical transfers were done in Alberta's experience likely caused little effect on the results - this is not reflection of the transfers or the method of transfer that was used but due to the relatively few number of times that those surplus vote transfers were done.

in STV, transfers are done when - a candidate is eliminated due to being un-electable - no math is used here except just to move ballots from one candidate to another - or when a candidate is elected with surplus votes and then only if - the surplus is of enough votes to make a difference - there are still un-filled seats, - and there are two or more candidates still in the running more than the number of unfilled seats.

if all three conditions apply, a transfer is done, which can use somewhat complicated math. In Alberta's experience, these three conditions all applied only two times each election in each city on the average. and then the necessary transfer was done with whole votes in Alberta, not the fractions as done under Gregory method.elesewhere.


looking at Alberta prov STV elections, we see that actually the "complicated" math-reduction method had to be used much fewer times than people might think


Edmonton and Calgary

90 MLAs elected through STV 1926-1955

(Medicine Hat used STV in 1926 but not worthy of attention -- only three candidates went for two seats)


90 MLAs elected in Edmonton and Calgary 1926-1955

(not including by-elections where AV was used)


Theoretically each time a candidate is elected, his or her surplus votes are to be transferred

but a transfer is not done

if the surplus votes are not enough to make a difference,

or if all the seats are already filled (so never is the surplus of the last elected person transferred, for instance)

or if the unfilled seats will be filled right away becaause the number of remaining candidates in the running (after this person's election) are equal to the number of remaining unfilled seats or only one more than thta figure.

and even if a transfer is needing to be done, the mathemtical reduction calculation is only used if the number of votes that bear a usable back-up preference surpass the number of surplus votes.


19 times the surplus was transferred without math

(transferable votes did not exceed the surplus) 16 Calgary /3 Edmonton


40 times no transfer was done (either would have had no effect, or seats already filled or certain to be) 19 Calgary/21 Edmonton


31 times the surplus was transferred using mathematical reduction (in Alberta the whole-vote method was used) 9 Calgary/22 Edmonton


so these numbers tell us that in 16 STV contests, 8 in Calgary and 8 in Edmonton between 1926 and 1955, only 31 times was mathematical reduction calculation resorted to.

an average of only two times in each city in each election did the "complicated" mathematical reduction method have to be used.

it might be different if voters are required to give very complete rankings but in Canada the one-third of seats filled through math reduction stat was the case.


the point being that if math-reduction transfers are used as seldom as that, it does not matter what method is used to derive them, whether Gregory or the whole-vote "exact method" is used, as far as most of the seat results go.

so there would be little difference in results, whether the simpler whole-vote method or the more complicated fractional method is used. That is my surmise anyway.


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