How does Heart and Head work?
There are two parts to this new voting system:
Simple preferential voting in General Elections.
Weighted voting by Members of Parliament in the House of Commons.
The two parts work together: The preferential voting produces an accurate popular vote that is the basis for the weighted voting.
The major innovation is that MPs no longer have one-person, one-vote in the Commons. Instead, a portion of their vote is based on the popular vote that elected them.
Preferential voting in General Elections.
Heart and Head means you can vote for two candidates in an election: your first preference with your heart, then your second preference with your head. In the end, though, only one of your two votes will count. This solves three problems:
It eliminates strategic voting, or rather, it incorporates it into the voting system so that your preferences can be counted.
It ensures an accurate count of the true popular vote.
It keeps the voting (and the counting!) simple.
The ballots will look exactly the same as they do now. You can still vote with an Ⓧ or you can state your preferences with a ① (your heart vote) and a ② (your head vote).
The following are valid, completed ballots:
Counting the ballots.
The short answer is that your ① vote is counted until that candidate is eliminated from the election. Then your ② vote is counted.
Elections Canada does it this way: All of the Ⓧ and ① votes are added together for each candidate. The candidate who is in last place is eliminated, but then all of their voters' ② votes (the 2nd preferences) are added back in to the totals for the remaining candidates (that is, those who haven't yet been eliminated). This is repeated until there is only one candidate left: the winner.
The Ⓧ and the ① votes for each party, from all voters in the country, are added together to give the national popular vote for each party.
Weighted voting in the House of Commons.
Members of Parliament (MPs) will use weighted voting in the House of Commons. Their votes will be weighted by the popular vote their party received (across the entire country) in the general election. This solves many problems found in other electoral systems:
It provides proportional representation.
It eliminates the need for any extra MPs (and their associated costs).
It ensures all MPs are still directly elected by voters.
It doesn't require larger electoral districts.
It keeps the voting and the counting simple.
Calculating the voting weights for MPs.
Instead of 338 votes in the Commons (one per MP) there will be up to 1000 votes. Those 1000 votes are distributed to the parties based upon how many of their MPs were elected and what their party's popular vote was in the election. This calculation is performed by Elections Canada after the election. On average, each MP would receive about 3 votes.
For the 2015 general election (and ignoring the probably major effects of strategic voting) the distribution of votes in the Commons would have been:
Each party receives part of their votes from electing MPs and part from their popular vote. The votes allocated to each party are then distributed to their MPs equally.
(Note: The amount of proportionality for Canada needs to be decided. We are currently using 60% in our calculations for technical reasons.)
The numerical election results would have produced the following party votes and votes per MP:
The detailed calculation combines the popular vote with the percent of MPs elected:
party_votes = popular_vote x 60% + percent_of_MPs x 40%*
and is then adjusted so that there are a total of 1000 MP votes in the Commons.
Using the 2015 general election results as an example, each party would have received:
The Liberals —
More elected MPs than their popular vote.
(39.5% x 60% + 54.4% x 40%) x 1000 = 454.6 party votes
454.6 / 184 MPs = 2.47 votes / MP
The Conservatives —
About equal MPs to their popular vote.
(31.9% x 60% + 29.3% x 40%) x 1000 = 308.5 party votes
308.5 / 99 MPs = 3.12 votes / MP
The New Democrats —
Fewer MPs than their popular vote.
(19.7% x 60% + 13.0% x 40%) x 1000 = 170.3 party votes
170.3 / 44 MPs = 3.87 votes / MP
The Bloc —
Many fewer MPs than their popular vote.
(4.67% x 60% + 2.96% x 40%) x 1000 = 39.8 party votes
39.8 / 10 MPs = 3.98 votes / MP
The Greens —
Just one MP but noticeable popular vote.
(3.45% x 60% + 0.30% x 40%) x 1000 = 21.9 party votes
21.9 / 1 MP = 21.9 votes / MP
The finer details.
The total party votes is less than 1000 because 0.8% of citizens voted for a party that did not elect any MPs (or for an independent candidate that was not elected). Those voters are unrepresented in Parliament.
Percent ("%") means divide by 100, so 39.5% means to use 0.395 (like calculating sales tax).
The "40%" is 100% - 60%, that is, the non-proportional part of the weighting.