As the federal election on October 21 is approaching, it is a good time to talk about our electoral system. The momentum for electoral reform has stalled after the last election. Our current first-past-the-post (FPTP) electoral system exhibits significant flaws, but there is no consensus on how to remedy these flaws.

As I have argued before, there is a strong case for electoral reform given that a majority of our members of parliament are elected without a majority of votes in their ridings. Supporters of FPTP claim that nothing is wrong with this system, that it has worked well in the past, and thus maintain an "if it ain't broken, don't fix it" attitude. The first claim is arguably not true: FPTP is systematically biased when votes for political parties are translated into seats. The second claim on the other hand, is harder to dismiss. Canada's democracy has been stable and resilient despite the shortcomings of FPTP. The case for electoral reform hinges on the answer to the question: what is fair representation in parliament?

Under FPTP, the translation of votes into seats in parliament is biased towards large parties and also becomes unpredictable when three-way or four-way races lower the threshold for gaining a seat below an absolute majority. Strong regional clustering of support for political parties further distorts the votes-to-seats translation. If you believe that every vote should count equally in Canada, proportional representation (PR) is the electoral system that represents voters fairly no matter which constituency they live in. The apparent disadvantage of PR is its seeming disability to provide regional and local representation. My research shows a way to address this deficit of PR. I have proposed a novel electoral system that combines proportional representation with strong local representation.

Despite the apparent shortcomings of FPTP, electoral reform has gone nowhere in Canada. British Columbia had three referendums, and while one found a majority of support, it did not meet a higher threshold that had been set. Electoral reform is only possible when people realize that FPTP delivers outcomes that defy logic, for example when the NDP was reduced to 2 out of 77 in the BC Legislature despite winning 22% of the vote, or when in 1993 the federal Progressive Conservatives were reduced from 169 to 2 seats while maintaining 16% support. Memory of such episodes fade fast, and once a new election brings about a more "normal" result, the case for electoral reform drifts out of focus.

Supporters of FPTP point to two perceived advantages of this system. FPTP promotes single-partys majority governments, which FPTP supporters argue are more stable than coalitions of two or more parties that are formed under PR. However, minority governments are possible under FPTP as well, and they are not intrinsically more stable than coalition governments. The electoral arithmetic simply makes it more likely that FPTP produces majority governments with less than a majority of the popular vote.

The other perceived advantage of FPTP is effective local representation. FPTP counts votes in each constituency, and the candidate with the most votes (even if less than an absolute majority) wins. In Canada, this has meant that sometimes candidates with as little as 30% can eek out a win over their competitors when voting is fragmented among many parties. However, the member of parliament elected in a constituency is tied closely to that constituency and is assumed to advocate strongly for the local interests of the voters in that constituency.

My own research introduces a way to address the local representation deficit of the simple version of proportional representation. It is possible to have PR and strong local representation at the same time, and even improve local representation under full PR. My research contribution Electoral economics: Maximizing local representation under proportionality (Economics Letters, Volume 182, September 2019, pp. 109-113) shows how this can be accomplished effectively using new mathematical tools. Computational techniques and power have advanced to a level where we can figure out how we can actually maximize local representation under full proportionality by assigning constituencies optimally. I have dubbed this electoral system PROAC—Proportional Rrepresentation with Optimal Assignment of Constituencies. You can also refer to it as "proactive" because it solves the local representation problem by proactively assigning members of parliaments to constituencies in such a way that it maximizes local representation. Maximizing local representation means maximizing the number of voters whose preferred political party is representing the riding in which they have voted.

Under PROAC, seats in parliament are based on pure proportional representation, with each member of parliament assigned to represent either one or two constituences. Votes cast in each constituency matter twofold. Overall, votes determine the composition of parliament. Locally, the more votes are cast for one party, the more likely this party will represent the constituency in parliament.

PROAC comes in two flavours, single and dual optimal assignment. With single optimal assignment, one member of parliament is assigned uniquely to one constituency, similar to the current FPTP system. Dual optimal assignment improves upon that by assigning two members of parliament to each constituency: a senior MP and a junior MP. Allocation maximizes the number of voters who are represented directly, but with a senior and junior member a larger number of voters have local representation by their preferred candidate than under FPTP. Under dual PROAC, members of parliament will have a little bit more work as they will represent two constituencies, but the work is shared with another member of parliament. This duality may also foster greater local cooperation across party lines. With dual assignment, the senior member of parliament will typically come from one of the larger parties, while the junior member will tend to come from smaller parties. This ensures that constituents will more often have access to a member of parliament who is also in government, ensuring that ridings are not left behind because it is represented by a member of an opposition party (both under FPTP and single-assignment PROAC). Dual assignment of constituencies has a real potential for improving local representation over FPTP.

Applying PROAC to Canada, there is one important way in which our country's federal structure can be reflected in the electoral system. Party lists should all be provincial, so that ultimately only politicians from a province can represent that province in parliament. This leads to a provincial version of proportional representation: P-PR. Vote shares in each province are translated into parliamentary seats from each province.

Canadian Federal Election 2015:
Actual outcome under FPTP and hypothetical outcome under P-PR

The most apparent result of P-PR is that the Liberal Party would not have obtained a majority in the House of Commons: they would have received 137 instead of 184 seats. The other parties would have all received more seats. The Green Party, for example, would have obtained 3 seats in BC and Ontario, 2 seats in Quebec, and even one in Alberta. Under P-PR, the three northern territories would remain FPTP because they only have a single seat each.

How would dual PROAC play out in determining which party represents which riding? The table below shows the 2015 election outcome, the FPTP winner in each riding, and the parties that would have represented each riding under dual PROAC with a senior and a junior member of parliament. Let's start with small Prince Edward Island, where all four seats went to the Liberals. Under P-PR, the Liberals would have received only two seats, with one seat each also going to Conservatives and NDP. Because the Liberals came out strongest in all four ridings, they would provide the senior member of parliament for each riding. Conservatives and NDP would provide one junior member of parliament for the two ridings they represent. The Conservative member would represent Egmont and Malpeque, and the NDP member would represent Cardigan and Charlottetown.

Newfoundland and Labrador was likewise swept by the Liberals in 2015. Under P-PR, province-wide support would have given Liberals five out of seven seats, and one each for NDP and Conservatives. Liberals would have provided the senior member of parliament for each riding. Two Liberal members would have been senior members for two ridings each, and three liberal members would have been senior member for one riding each as well as junior member for another riding. As five Liberals can represent a total of seven ridings, they can divide the tasks of who represents which riding among them.

Moving to British Columbia, look at the outcome for the five ridings in Vancouver. The Liberals won in Centre, Granville, Quadra, and South, and the NDP in East and Kingsway. Based on dual PROAC, Liberals would have only won two seats, giving up one seat to the Conservatives. One Liberal would represent Quadra and South as senior member of parliament, and the other Liberal would represent Granville as senior member and Kingsway as junior member. The single Conservative member would represent Quadra and South as junior member. The two NDP members would represent East and Kingsway as senior members, and Centre and Granville as junior members.

Optimal assignment of constituencies works out rather well in practice. Note that the senior member of parliament is virtually always from the party that won the plurality in that riding, which means that voters in that riding will not be worse off than under FPTP with respect to having access to a member of parliament. No riding will have a senior member of parliament from a small party or fringe party. And it is exceptionally rare that a senior member of parliament is not the candidate with the most votes in that riding. Looking through the table, the only riding where this is the case is Edmonton Centre, where the votes for Liberals and Conservatives were virtually tied. In this case the algorithm may shift assignments in order to maximize the province-wide local representation. But, as is shown here, such cases are rare and would be limited to instances where outcomes are extremely close.

In parliament, senior and junior members have the exact same role. However, with respect to representation of constituencies, senior members will take on a larger responsibility—also in many instances because of their closer proximity to government.

During an election, parties do not yet know precisely which member of parliament will ultimately represent a riding if they win seats, as the allocation follows the algorithm. However, it will always be the case that a riding that has a plurality for one party will have a senior member of parliament from that riding. For the parties, it will be possible to narrow that down to a few possible permutations in each city, and previous election results are a good guide. There is an implicit benefit in this system. To the extent that politicians campaign locally in each riding, parties cannot simply ignore ridings in which they are unlikely to achieve a plurality: they may still end up representing these ridings as a junior member of parliament. This forces parties to engage voters in ridings that are not traditionally their "home turf".

When a member of parliament resigns, under FPTP there are by-elections that are often hamstrung by low voter turnout. Under PR, a member who resigns (or dies) is automatically replaced with the next person on the party list, which is more efficient than by-elections and preserves the voter intent of the last election. Floor-crossing of members of parliament would still be possible, although this distorts the proportional representation determined by the election. Extensive floor-crossing could upset the intent of voters, and to protect against such use of floor crossings, the electors in the two ridings represented by a floor-crossing member could be given a mechanism to object and ultimately expel the member from parliament, with a vacated seat reverting to be filled by the party that won the seat in the last election.

The dual PR-OAC electoral system that I have developed is a rare case of being able to have your cake and eat it too. It provides pure proportional representation at the provincial level (with the exception of the three single-seat northern territories). At the same time, it provides local representation that preserves party choices in each riding for the senior member of parliament, and additionally introduces a junior member of parliament for each riding. With PR-OAC, each riding now has two representatives rather than one. Ultimately, members of parliament may need to work more two represent two constituencies, but it also offers the opportunity for more competition and more local representation if two rather than just one member of parliament is charged with looking after the interests of each riding. The bottom line is thus: electoral reform that embraces proportional representation is possible while preserving strong, and even improved, local representation.

Whether dual PR-OAC will ever see the light of day in Canada or another jurisdiction around the world will remain to be seen. Perhaps it may find favour more quickly in jurisdictions that already use proportional representation and are looking at ways to improve local representation, or to simplify their ballots by moving from two-vote ballots (one each for a party and a local candidate) to single-vote ballots. Either way, my own research should put to rest the argument that local representation is incompatible with proportional representation.