The 44th federal election in Canada was held on September 20, 2021 and produced another minority government. The new parliament came again with significant distortions from proportionality. The case for electoral reform remains strong, and I have made this case on these pages since 2015:

• The case for electoral reform in Canada, July 27, 2015.
• Electoral entropy: the case for electoral reform continued, July 21, 2015.
• Electoral reform in Canada after the October 2015 election, November 11, 2015.
• Canada's growing urban-rural political divide, October 23, 2019.
• Canada's parliament with provincial proportional representation, October 26, 2019.
• Electoral reform with strong local representation, September 28, 2019.

Below I am providing the results of the 2021 federal election under the current first-past-the-post (FPTP) electoral system and compare them with the outcome under the electoral system that I have developed through my research (see article): proportional representation with optimal assignment of constituencies. The key ingredient in this system is provincial proportional representation (P-PR). Once provincial seat allocations are determined, each elected member of parliament is assigned to represent two constituencies so that representation from preferred parties in each constituency is maximized. Thus it is possible to improve local representation (more people are represented by someone from their preferred party in each riding), while ensuring a fair distribution of seats overall. The table below shows the outcome of seat allocations for each province, along with the percent vote shares.

The table and graph were updated on October 16, 2021 after Elections Canada completed validation of all results, including four judicial recounts.

Note that both the Green Party and the People's Party do not clear the 5% hurdle for entering parliament under the proposed rules of my electoral system. The graph below shows the actual and hypothetical composition of the new parliament.

The final table on this page shows the results of the 44th election for each riding, along with the winner under the current first-past-the-post (FPTP) system and the hypothetical outcome under my proposed Dual-PROAC system that is based on provincial proportional representation. To summarize, below are the key ingredients of the proposed electoral system.

• Canada will continue to have 338 electoral districts in accordance with the Constitution's representation formula for each province. Electoral districts will continue to matter.
• Parties offer ranked lists of candidates in each province in which they compete.
• Voters cast ballots for parties (not candidates) in each riding.
• Seats in parliament are allocated to parties by proportional representation separately for each province. PEI would have four seats allocated by PR, Quebec would have 78 seats allocated by PR, and so forth, while the three territories would continue to have one seat each with conventional FPTP elections. Proportional allocation follows the the Webster/Sainte-Laguë method.
• A party is eligible to gain seats in a province, in proportion to their provincial vote, if it achieves at least 5% of the vote in that province. (Effectively, this applies only to the four provinces with more than 20 seats: Alberta, B.C., Ontario, and Quebec. The threshold is implicitly higher in provinces with fewer than 20 seats.) A party must also achieve at least 5% nationwide to gain seats in any province. This dual threshold prevents fringe parties from gaining undue influence in parliament.
• Once seats for each party in each province are determined, constituencies are assigned to members of parliament from that province so that this allocation maximizes local representation by preferred parties.
• Each constituency will have a senior member from the party with more votes and a junior member from the party with fewer votes.
• If a candidate withdraws from an election, the next candidates on the provincial list of that party move up. If an elected member of parliament resigns, the party can replace that member of parliament with the next-ranked unelected candidate from the original electoral list. Byelection (often with low voter turnout) become unnecessary.
• Elected members of parliament can still cross the floor as in the past, or sit as independents, until the next election.

I have written code in the freely-available statistical language R to carry out the calculations above. The code is available upon request.