In Single Transferable Voting (STV), the quota is an important and complicated part of the equation. But it does not have to be either of those things.
The quota has two purposes -
1. A candidate whose vote tally equals or surpasses the quota is declared elected. There is a different way for a candidate to be elected as well, as we explain below.
2. The quota is the amount of votes that remain with a candidate after election in step 1. The "surplus" votes are transferred away based on the back-up preferences, if any, marked by the voter.
The STV used in Canadian cities and to elect Edmonton and Calgary MLAs used the Droop quota. Droop was created through a somewhat complicated formula. How it is arrived at was a noted puzzlement all through the use of STV in Canada.
But an historically-earlier quota, the Hare quota, is easier to calculate and easier to explain.
Compared to Droop, Hare is less pure mathematically. It allows more votes to sit with winning candidates instead of being transferred where they could be used elsewhere.
Moving from the Droop to the Hare thus hurts the most-popular parties. It also may hurt the less-popular parties if they were barely just trying with their every sinew to get one seat under Droop and now find the quota is higher.
However, the difference is not large mathematically. Especially if the Hare quota is calculated by dividing the total amount by the number of positions to be filled, rounded down.
Back in 1930, Joseph P. Harris in the U.S. put forward the Hare quota for some of the reasons I give here. His writings are presented in the blog "Commonsense simplifications of STV urged in 1930."
The Hare quota is the calculation that prominent Australian STV campaigner, Catherine Helen Spence, used in her demonstration STV election (described in a separate Montopedia blog).
Hare is simple and easy to explain.
In her demonstration election, electing six members, she had a pretend 73 votes. Using her preferred quota, Hare, as described above, she set the quota at 12.
Under Droop, it would have been 11, so no big difference.
Extrapolated to real elections
Total votes Hare Droop
730 122 105
7300 1217 1043
29,200 4867 4172
29,200 is about the number of votes cast in Alberta's existing provincial districts.
Say if four districts were grouped together to form a multi-member district, multi-member districts being required under STV, the total vote count in the larger district might be about 100,000.
Hare quota Droop quota
100,000 16,666 (16.7 p.c.) 14,286 (14.3 p.c.)
Thus, about a two or three percentile difference between Hare and Droop.
Meanwhile, a quarter to a third of the positions are filled not by quota but by candidates that survive until the field of candidates is thinned down to the number of remaining seats. The field is thinned down by the successive elimination of the least-popular candidate - and by election of those who achieve quota.
The elections with less than quota have little to do with quota, no matter what level it is set at.
I see that in Australia, some South Australian local councils are giving up on explaining the Droop quota and thinking of switching to the bottom-up method, where no quota is used at all. Winners are those who survive to the end, with surplus votes of early winners not moving and being wasted. (Ben Raue, "South Australian council voting - back to cheap and ugly?")
Dropping the Droop and adopting the Hare quota may be the way to save STV-with-quota there.
It would also make STV an easier sell here in Canada.
Thanks for reading.
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Also note that in larger District Magnitude election contests, the difference between Hare and Droop is not significant.
when Thomas Hare was publicizing STV in 1850s, about 550,000 votes were cast in the United Kingdom, with 650 MPs being elected to the House of Commons, an at-large contest would have used almost exactly the same quota under Hare or Droop.
In 2010 Iceland elected 25 members in one contest using STV - this was, as far as I know, to date, the largest-DM contest ever conducted under STV.
As the election was thrown out for reasons unrelated to STV, record of the vote count process appears to be difficult to find. (The winners were actually appointed to the same seats that they had been futilely elected for anyway.)
But we can see that with the 82,000 valid votes cast, and the 25 members to be elected, Droop quota would have been or was - 3154
Hare quota would have been or was - 3280
so the difference between Hare and Droop was likely not significant.
Mind you, if the voters are prepared to accept the Weighted Inclusive Gregory Method -- as Icelandic voters obviously had been - they do not need to be placated by the use of the simpler-to-explain Hare quota!
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