P3 (Proportional-Preferential-Personalized) is a system put forward by the Honourable M. Stéphane Dion. You can find the mechanics of this system at this link https://stephanedion.liberal.ca/en/articles-en/p3-voting-system-canada-2/
Under P3, ridings are grouped together in 4s and 5s to create a 4 or 5 member riding. In this region, you have a ballot with two votes, one for your preferred candidates, and one for your preferred party. The preferred candidate vote is a ranked ballot, so you list your preferences as 1, 2, 3 etc. There will be several candidates for each party on the ballot, so you need to indicate which ones you support. The local candidates are selected using an alternate vote method.
The “top-up” candidates are selected based on the total preferred party vote. However, it is not technically a “top-up” because the selections are completely independent of the locally elected candidate. So this is like having two different elections at the same time – one to select 5 local candidates, and then another to select 3 top-ups.
When it comes to proportionality, this system offers only marginal improvement and this improvement benefits only large parties. First, there is clear evidence that the alternate vote selection process (see alternate vote) is biased toward large parties and, in Canada, to the Liberal party in particular. Second, if people support the same party as their candidates, then what happens is that the top-up candidates will reflect the same distortion as the current voting system. Third, P3 excludes parties from participating if their popular vote is less than 17%. This essentially excludes many small parties that are trying to break into the system. Combining these three biases together means that there is a clear bias towards larger parties.
Finally, I believe that P3 is difficult to understand and I believe it would be difficult to implement. Votes would need to be entered into a computer to work through the alternate vote scenarios, and they would have to be counted independently for the regional representation. I am not sure that Canadians are ready to embrace a system which appears to be too complicated.