During the use of STV in provincial elections in Alberta and Manitoba, that is, from the 1920s to the 1950s, many voters marked only one preference or only just a few on their ranked ballots. This meant that these elections saw many exhausted votes. There were several effects of this aspect of Canada's STV elections.
During the use of STV in Canada, that is, from 1917 to 1971, voters were not required to rank a certain number of candidates. The effect of this was that many votes were declared exhausted (unable to be placed) if there were many eliminations.
In Australia on the other hand, votes have to mark multiple preferences - a first preference and many back-up preferences. This is more important for the Autralian elections than for Canadian STV elections because the number of seats to be filled in district elections in Australia (at least in some cases) are much more numerous than the number that used to be filled in Canadian STV elections.
In Canada, the District Magnitude at the most was ten. While in Australia STV district contests, sometimes as many as 21 seats are filled at one time. Such large contests mean many candidates and many eliminated candidates and many vote transfers. There were mote than 300 candidates, for example in the 2019 New South Wales election so it is conceivable that some votes were transferred more than a hundred times. But of course any votes cast for candidates who were successful in the end were not transferred at all.
In Canadian elections where District Magnitude was no greater than ten, the number of candidates and number of transfers was considerably less. A much smaller proportion of the votes were transferred four or five times, for example,and a much larger proportion were not transferred at all.
As there was less need to prepare for a great number of transfers and as governments were leery of pushing voters to do more than they were willing to do voluntarily, in Canadian STV elections voters could mark must one preference - their first preference - and mark no back-up preferences if that was their choice. That is, voters were allowed to plump - mark only one preference.
Many did just that, and in these cases when candidates were eliminated, any votes initially placed with them were unable to be transferred to another candidate and in these cases were declared exhausted.
The waste of votes was no higher than it would have been under First Past The Post. But for those votes whose ballots bore no back-up preferences, the waste was just as high as it would have been under FPTP. This was a result that could have been foreseen by the voter. Perhaps it was but the voters apparently made the conscious decision that electing a second choice was no better than helping to elect no one at all, so not worth the extra effort or that the relative merits of the other candidates was so little that the voter did not care which of them was elected.
The voter took the chance, and in some cases (but only in some) his or her vote ended up among those on the "exhausted vote" pile.
Votes marked just with one preference were never transferred if they were initially placed on a candidate who was never eliminated,
Votes marked just with one preference may not be transferred if they were initially placed on a candidate who was elected to fill the one of the last seats.
Only some of the votes placed on a candidate who was elected in an early count would be transferred; with usually most of them remaining with the successful candidate.
Ironically, some votes also wound up in the "exhausted vote" pile even if they bore multiple back-up preferences. This was the outcome for votes if they were initially marked for a candidate who was eliminated and if all the back-up preferences were for candidates who had been already eliminated or had already been elected. Either way these votes ended up on the exhausted vote pile - the difference was that in the latter case the voter had the satisfaction of seeing that someone whom the voter favoured was elected even if the person's vote itself was not used to effect that happy result.
In STV, opportunity for vote transfers arise when a candidate is eliminated and also when a person is elected. When a candidate is elected, surplus votes are transferred if seats still remain to be filled and there are still many more candidate than the remaining open seats. (Although it is usually said that achieving quota is required to be elected, candidate(s) can be elected with partial quotas as soon as the field of candidates is thinned to only the number of remaining open seats, or even to just one more than the number of remaining open seats. As well, transfers are not engaged in if the spread of vote tallies is such that transfer of votes of the least-popular candidates cannot affect the popularity of the more-popular candidates.
But when surplus votes were transferred in Canadian STV elections, exhausted votes were dealt with in a special way that is not seen in Australian elections.
Exhausted votes to a large extent were a common thing in Canadian STV elections but are not in Australian STV elections. So transfers of surplus votes are/were dealt with in a different fashion in those two countries.
John D. Hunt described in his 1923 booklet A Key to P.R. how to deal with surplus roughly like this - ballots are arranged as per the next back-up preference, then the proportions for each candidate was reduced to match the number to be transferred (the surplus). The make-up of the surplus to be transferred (based on the candidates receiving the transfer) is based on the make-up of the votes received by the successful candidate.
In the example Hunt provided, all the votes bore usable back-up preferences - there are none that do not. But this is not realistic in Canadian elections.
In the STV elections held to elect MLAs in Edmonton and Calgary between 1924 and 1956, almost every time a candidate was eliminated or elected, there were votes that bore no usable preference, votes that were declared exhausted. And it seems likely that happened all the time but that the special treatment (still to be revealed) merely hid that fact.
The special treatment varies from Hunt's mock election process in that votes are sorted based on next usable preference and there is also another pile for votes that bear no usable back-up preference.And further more that if the number of votes that bear usable back-up preferences are no greater than the surplus (the number to be transferred), they are all transferred with no math involved. Only when the number of votes bearing usable back-up preferences is greater than the number of surplus votes does math enter into the calculation of candidates' transfers.
Say there are ten candidates. No one has quota. In the second count, the least-popular candidate is eliminated. Simple reference is made to the first back-up preference. No math is required. Votes are transferred physically (or on computer) to the candidate marked on the back-up preference - if there is one. If a ballot does not bear a back-up preference, it is put on the "exhausted vote" pile and nothing more is done with this ballot. Let's say with the transfers one candidate passed quota. The next count will be to transfer that candidate's surplus. The number of votes over and above quota - the surplus - is calculated. The ballots are sorted depending on to whom the next marked preference is indicated, if any. So the ballots are sorted into eight piles - the elected and the eliminated candidate receive no vote transfers.
As well, if this was a Canadian election, there would be a pile for votes that bear no usable back-up preference. And this pile, or enough of it to equal quota, is left with the successful candidate. If the exhausted vote pile contains votes even after quota is taken out, then the rest of the votes there are recorded in the exhausted vote space on the election count sheet and the votes that bear usable back-up preferences are moved directly to the marked candidate.
But if the number of votes in the "exhausted vote" pile is less than the amount of surplus - the number of votes to be transferred - then some of the votes that bear usable back-up preference must be left with the successful candidate. These, in Canadian elections, were calculated mathematically to be fair. (But it is likely that random transfer would likely be just as fair as mathematical calculation.)
The amount of each candidates' pile to be left behind and the number to be transferred to the recipient candidate is calculated thusly: A total is calculated of all the other votes and the transfers to each of those eight candidates are calculated based on the number of ballots that bear back-up preferences. say 100 votes are received by A quota is 50, A is declared elected and the surplus is 50. of the 100 votes, 25 bear no usable back-up preference. 25 of the remaining 75 must stay with A, 50 of them are transferred. If the pile of votes that bear back-up preferences for candidate C are say 24, 16 will be transferred to C and 8 of them will stay with A. ratio of votes that will be transferred to the total number of votes able to be transferred will set the ratio for the two parts of the votes for any candidate. The fraction that the surplus of a successful candidate is to the successful candidate's total vote tally will be the same fraction of a pile set aside to be transferred to a specific candidate that will be transferred to that candidate. If one third of the candidate's votes are to be transferred, then one third of each recipient candidate's piles are transferred. Generally the number of votes bearing no usable back-up preference will be fewer than quota, so some votes bearing usable back-up preferences will have to stay behind with the successful candidate as well. But it should be under stood that it may happen that the number of votes bearing no usable back-up preference is greater than quota, in which case all the votes bearing usable preferences are transferred to whomever the next back-up preference is marked. No math is needed - simply transfer all the votes. This is a simpler arrangement than the math-heavy transfers usually entailed by transfers of surplus votes. But is something that election officials must be aware of. In cases where votes bearing no usable back-up preference surpass the quota, enough are left with the candidate to equal quota with all the rest put on the "exhausted vote" pile. And all the votes that bear usable back-up preference are transferred to the recipient candidates. As mentioned, there is no math required to calculate the amount of the transfers.
This seems to be the case in the example of Roper in 1948. In the tenth count, Roper was elected with 8869 votes. Quota was 7692. When his surplus was transferred in the 11th Count, only 185 votes were transferred. This looks like an oversight or a mistake. but I believe that that was all the votes that could be transferred - all the rest bore no usable back-up preference.
This seems likely for these reasons:
Some of the votes Roper held when he was elected in the 10th Count may already have been transferred eight times, so some might have had to be declared exhausted for that reason.
When Roper was elected he was the last CCF candidate still remaining. Voters at that point either would have their votes transferred to a non-CCF candidate or simply not mark any additional back-up preference.
In fact the vote count sheet records that Roper when his votes were to be transferred had no exhausted votes but his vote tally was not reduced to quota which was normal in other instances where surplus votes were transferred. I believe that there were so many "exhausted votes" that it perplexed the election official. In the directions for the vote count there were not instructions on what to do if the number to be transferred exceeded the number of votes that bore usable back-up preferences.
It was obvious to transfer what votes cold be transferred and this was quickly done - but how to record the remaining votes, which were more numerous than the number of votes in the quota, eluded them.
And in fact it did not matter - the votes had come to the end of their road. Bearing no usable back-up preference they could not be transferred to any other candidate so no part of them could be used anymore. Whether they were left with Roper or put in the exhausted vote pile did not matter to the reality of the vote.
It would perplex at least one later electoral historian - me - but for the sake of the vote count at the time, it did not matter where they ended up.
Interestingly, in most of the STV provincial elections held in Calgary, the count of votes did not record the exhausted votes in a special running total. When a candidate was elected, any votes bearing no usable back-up preferences, over and above the quota, were simply left with the elected candidate; and when a candidate was eliminated, any votes that bore no usable back-up preferences were simply left with the eliminated candidate. Whether listed separately or simply left where they were did not matter - the votes were past use as they could not be used where they were nor could they be transferred to another candidate because they bore no usable back-up preference.
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