Japan uses a system of Parallel Proportional Representation. This is a proportional system that is non compensatory. For example, if a country had 200 seats in Parliament, and 100 ridings, with 100 PR seats, and a party in this country won 40% of the vote, they would win 40 PR seats. It would not matter if they won 0 ridings or 100 ridings.
Japan in particular uses a form of this that allows the closest losing candidates to advance to the proportional list. In short, if the winner took 3000 votes and the runner up took 2500 votes, then that runner up has taken 83.33% of the winners vote total, and is ranked based on that 83.33%. This ensures that areas with a divided electorate will end up with both voices in Parliament. Additionally, it prevents parties from simply stacking the proportional list, as it only elects candidates who are popular with the voters.
I want to take a look at the kind of PR Japan uses.
For the sake of example, lets assume PEI used this kind of system in 2015. In this context, this would result in 16 additional seats. This is 0.6 multiplied by the number of ridings (27) which is the average number of proportional seats in relation to ridings seats used in Japan.
Note that in the event of an actual move to Proportional Representation, the ridings are likely to be redrawn, and so this is not a perfect nor exact comparison. Adding 16 extra seats to the existing riding map simply makes this easy to compare and understand. In reality, the legislature would not grow so much so quickly.
In the real PEI election, 46.4% of all votes cast were cast for winning candidates. The other 53.6% of voters did not have their candidate win, and their choice of MLA was not sent to the legislature. Keep that in mind.
Due to popular vote, the Liberals would win 7 of the 16 PR seats. The Tories win 6. The NDP wins 2, and the Greens win 1. Since the Japanese system of the closest loser allows us to know exactly who would win, we can determine that, and I've done so below.
As the Green with the highest loss ratio (47.75% of the votes of the winner in her riding) district 12 candidate, Darcie Lanthier, would become an MLA.
The top two NDP vote getters are, in order, Gord McNeilly and Michael Redmond, and thus both would join the Legislature.
The 6 Tories, in order, are: Mary Ellen McInnis, Rob Lantz, Brian Ramsay, Linda Clements, Major Stewart, and Daniel MacDonald.
The 7 Liberals are: Charlie McGeoghegan, Russel Stewart, Tommy Kickham, Dan MacDonald, Bertha Campbell, Ramona Roberts, and David Dunphy.
This allows 66.96% of people to have voted for an MLA in the legislature. Most districts also end up represented by more than one party, allowing for voters in these areas to have both a government and a opposition voice in the legislature. Since those elected on the list are not beholden to their original area, they can also represent larger swaths of voters.
The end results are as follows
25 - Liberal
12 - PC
2 - NDP
2 - Green
Not only does the NDP enter the legislature, but the Greens grow as well. The opposition Tories now have a caucus made up of members from across the province, and the Liberals have an MLA from all but 2 of the ridings. Unlike a pure PR system, the government is not turned into a minority.
There are many reasons to want Proportional Representation and many reasons to oppose it. Two key reasons are as follows.
1 - It allows more voices to be heard in the legislature, and ensures that the opposition is strong enough to counter the government.
2 - It ensures that only governments elected by a majority of voters are allowed to govern.
Opposition to each would say that some voices are extreme and should not be heard, and that people want stable government and are fine with governments elected with, say, 45% support.
In Canada, there are many more people who worry about the loss of stable government than worry about parties like the NDP or Greens getting elected.
Parallel systems do very well at getting a multitude of voices heard, but do not tend to result in the overturning of a majority government elected with a minority of voters.
As such, and given the worries Canadians have about PR, I feel (and have for a long time) that a Parallel system is the only path to a later and fuller form of PR that Canadians will be willing to stomach.