The Imperiali quota is considerably smaller than even the Droop (which is smaller than the Hare quota).
The Droop is the absolute smallest portion of the valid votes that never can allow more to pass quota thna the number of open seats. However if even one vote is taken out of the game, then the quota can be even lower than Droop with no fear of having more pass quota than the number of open seats.
If a portion that some are calling exact Droop (slightly smaller than Droop) is used and there are no exhausted votes, the only way for more to pass quota than the number of open seats would be through a tie, and in any STV system (or any electoral system at all) there are mechanisms to deal with ties.
Imperiali is even smaller than Droop, and it, being smaller, is even more likely to allow too many to pass quota. But again a mechanism can be set in place to deal with that situation.
Here are the mathematical formulas for the different formulas:
Hare number of valid votes in district/number of seats
Droop number of valid votes in district/(number of seats plus 1) plus 1 (or rounded up)
Exact Droop number of valid votes in district/(number of seats plus 1)
Imperiali number of valid votes in district/(number of seats plus 2).
Imperiali looks scary as it looks like it can see two more candiates pass qota than the number of open seats
But where voters are not required to rank all candidates, there are many exhausted votes and at most, one more candidate will pass quota than the number of open seats.
Even if voters are required to rank twice the number of open seats, there will be still some exhausted votes.
Even one exhausted means no more than one more can pass quota than the number of open seats.
And meanhile having a small quota means two things --
-large parties get more seats, and
-a small party has more chance to take a single seat.
Michael Gallager in his study states that the smaller the quota, the easier it is for large parties and where largest remainder systems are used, then a smaller quota is very good for larger parties. (so Imperiali is better than Droop or Hare.)
A small party that does not have quota wants a large quota so that large parties have few remaining votes to make up a remainder and the small party may take a seat.
However, a medium-popular party that has an Imperiali quota of votes is happy to take a seat where under Droop or Hare it may not take a seat.
(Michael Gallagher Comparing P.R. Electoral Systems. ...
I have conducted the 1926 Edmonton provincial election using Imperiali quota and it produces the same winners as far as I can see, but perhaps one or two winners might have been different.
Difference arises as soon as the first transfer of winner's surplus votes or even sooner when a winner is declared winner earlier due to the smaller Imperiali quota compared to the Droop quota that the Edmonton election used in 1926.
Generally a 1st-Count winner has his or her surplus votes transferred in the second Count.
However in 1926 Lymburn achieved the Deoop quota in the 1st Count but his surplus votes were not transferred until the 12th Count. This becasue his surplus was only about 20 votes.
When Imperiali quota is used, Lymburn's surplus is much larger and the trasfer would have been done much earlier, and woud have been larger. This might have helped Bowen or Clarke to survive longer and perhaps win a seat.
Bowen might have benefitted from more surplus votes from Prevey, and therefore the Liberal party might have taken two seats, instead of one.
In 1926, two were elected with partial quota at the end so we know very little of where their vote might have gone if subsequent marked preferences had been considered.
But under Droop in the actual 1926 election, there were more than 1500 exhausted votes.
This was more than half of an Imperiali quota (2564 votes). That alone prevented one extra winner.
Under Imperiali quota, six candidates achieved quota by the end.
At that point plurality could be used to measure the candidates' relative popularity and award the last seat to Duggan, instead of Bowen who achieved quota but had fewer votes.
So we see Imperiali produce the same winners as Droop.
Is it easier to explain dividing the valid votes by seats plus 2 than it is to explain dividing it by seats plus 1 plus 1?
and under Droop STV, at the end, the vote tallies of the last remaining candidates are compared to allocate seats.
Likewise in the use of the Imperiali quota, candidates' vote tallies are compared to allocate seats, but in this case the candidates have achieved quota.
so plurality is used under either system.
The Imperiali quota is used in the Czech Republic and Belgium.
Formerly Italy and Ecuador used the Imperiali quota.
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