September 13th, 2007
MMP Primer part II: the MMP formula
By David Pal // 1 Comment
The second part of Spacing’s MMP Primer examines the mechanics and formulas that are used to provide parties with a number of seats in the legislature roughly proportional to their popular support (for some background on MMP and the terms used here, please see Spacing's MMP Primer Part 1).
The distribution of seats under MMP involves the use of the superficially intimidating but relatively simple Hare Formula [ Votes (V)/Seats (S) = Quota (Q) ], which is used to calculate how many party votes a party must receive in order to get one of the 39 party seats.
On election night, at the same times as the votes in all 90 local ridings are being counted, Elections Ontario counts all of the party votes. The local votes and the party votes are kept separate; they do not affect each other. Recall that parties need at least 3% of the party vote to get any of the 39 seats. After determining the number of votes each party has received, all of the votes cast for parties that received less than 3% of the party vote are subtracted from the vote total.
For example, imagine if 100,000 total votes were cast and a party received 2,000 votes (2%), under the 3% threshold. Those 2,000 votes would be removed from the calculations, leaving the relevant number of total votes at 98,000. The same process would be applied to all other votes cast for parties receiving less than 3%.
A party's share of the party vote will thus increase once the votes for parties below the threshold are discarded. The greater the number of discarded smaller party votes, the greater the remaining parties' share of the vote will be. In the above example, if a party has 30,000 votes (30% of the party vote) and the number of total votes is reduced to 98,000, their share rises to 30.61%. We’ll further explore the “disproportionality” and potential extra seats produced by this mechanism in the next MMP Primer post.
Once the small party votes have been subtracted and the final vote total reached, the calculations are relatively simple. All of the remaining votes (V) are divided by the total number of seats in the legislature (129), producing the number of votes one seat is worth. For example, if there were four million remaining votes, then one seat (4 million/129) would be worth 31008 votes. This number is the quota (Q), and is used to determine how many (if any) extra seats a party should receive.
The total number of votes cast for each party is divided by the quota, producing the number of seats that a party deserves. For example, if the Liberals received 900,000 party votes, we divide that number by the quota, producing 29.025. This means that the Liberals deserve 29.025 seats in the legislature. The same process is carried out for all of the other parties.
If a party already reaches or exceeds that number of seats because of victories in local ridings, they receive no extra seats. If they are short, they receive one or more of the 39 party seats. Initially, the fractions of a seat (.025) are put aside, and seat distribution is based only on the whole number (29). If the Liberals have won 20 local seats, they will initially receive 9 seats of the 39, bringing them up to 29. If another party deserves 30.83 seats and has 23 local seats, they initially receive 7 seats, bringing them up to 30.
Once all of the whole numbers of seats have been distributed, there will be a few seats remaining because of the fractions. These remaining seats are given to the parties according to who has the biggest fraction. The first remaining seat is given to the party with the largest fraction, the second seat to the party with the second largest, etc., until all of the seats have been distributed.
A party could receive multiple seats this way -- the process repeats if there are enough seats to distribute. A party could conceivably not receive any seats from the whole number distributions (i.e. have 12 local seats and deserve 12.46 overall) but qualify for a seat from its fractions. This is obviously not an exactly proportional mechanism, but is employed since parties will almost never deserve a whole number of seats.
photo by Mike Rose
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LOL.
Comment by Ben
September 13, 2007 | 2:32 pm