OTTAWA — Imagine Canada's current first-past-the-post electoral system is changed so that each party's share of the popular vote is more closely reflected in the number of seats it wins in the House of Commons.

How would seats be allocated, based on those fractional percentages? Afficionados of proportional representation will tell you there's any number of possibilities.

Now suppose one party wins 37.3 per cent of the vote, another 28.2 per cent, a third 23.4 per cent and a fourth 11.1 per cent.

In FPTP, the candidate with the most votes wins, often with considerably less than 50 per cent of the vote; everyone else loses, leaving supporters of other candidates to feel their votes may have been "wasted." Critics complain the system produces "false majorities" and unfairly rewards smaller parties, like the Bloc Quebecois, whose support is heavily concentrated in one region, and disadvantages those, like the Greens, whose support may be greater but is more thinly spread across the country.

First-past-the-post, two-round voting and ranked ballot systems are examples of "majoritarian" voting systems, which are characterized by having one winner per electoral district.

Leaving the more arcane complexities for MPs to ponder, here's an electoral-reform-for-dummies primer on the options the committee — and Canadians — will have to consider:

If citizens in most OECD countries can wrap their heads around the complexities of PR, Carmichael is confident Canadians can too.

Still, Kelly Carmichael, executive director of Fair Vote Canada, says 85 per cent of the 34 countries in the Organization for Economic Co-operation and Development have adopted some form of proportional representation "because it's more democratic" than the Canadian system, wherein the governing party has routinely won the majority of Commons seats with less than 40 per cent of the vote.

That mind-numbing complexity may well account for why Canadians in the three provinces that have held referendums on electoral reform — British Columbia, Ontario and Prince Edward Island — have opted for the devil they know.

This is the type of complication that the soon-to-be-constituted all-party committee on electoral reform will have to grapple with as they strive to deliver on Prime Minister Justin Trudeau's promise that the 2015 federal election be the last conducted under FPTP.

There's the "largest remainder method," although that could lead to an "apportionment paradox." Alternatively, there's the St. Lague method, the Webster method, the Schepers method or the modified St. Lague. There are pros and cons to each, fully understood possibly only by mathematicians.

Justin Trudeau expressed his preference for ranked ballots during the Liberal leadership race in 2013. (Photo: Adrian Wyld/CP)

In the two-round or run-off system, a second round of voting is conducted if no candidate receives more than 50 per cent of the vote, with trailing candidates dropped from the ballot. It is the most costly of electoral systems, according to a 2004 Law Commission of Canada study of electoral reform, and has not been seriously advocated in Canada.

A cheaper route to the same end is the preferential or ranked-ballot system, in which voters rank their choices in order of preference. If no candidate wins 50 per cent of the vote, the last-place candidate is dropped from the ballot and the second choices of his or her supporters are counted. This continues until one candidate emerges with more than 50 per cent.

Ranked balloting would encourage parties to be less adversarial as they court second choice support. But it would not ensure proportional allocation of seats and supporters of losing candidates could still feel their votes were wasted.

During the 2013 Liberal leadership race, Trudeau expressed his personal preference for ranked ballots but he promised during last fall's election campaign to strike a committee to consider other options as well, including proportional representation, or PR.

PR systems are characterized by having multiple members representing electoral districts and are designed so that a party's share of the vote produces a roughly equivalent share of the seats in the legislature.

Critics argue that PR is more likely to produce unstable minority or coalition governments. Advocates maintain it encourages parties to be more collegial and less adversarial, while making every vote count.

There is a wide variety of different PR systems in use around the globe, including New Zealand, Scotland and Germany. They can involve an element of ranked balloting.

Mixed Member Proportional

MMP was proposed in Ontario and P.E.I. and rejected in referendums in 2007 and 2005 respectively. It is the preferred option of the federal NDP.

Under the Ontario model, voters would cast two ballots, one for a local candidate and one for a party. Each riding would continue to elect a member using the existing FPTP system but those winners would be supplemented by members chosen from province-wide party lists, apportioned according to each party's share of the popular vote.

For a country-wide electoral system, The Law Commission recommended adoption of the MMP system used in Scotland, where voters cast a ballot for one candidate in a single-member constituency and another ballot for a party list in a multi-member regional riding.

Open List vs. Closed List

The Ontario model involved closed party lists, with candidates chosen strictly by party brass. Closed lists would allow parties to put members of under-represented groups, like women or ethnic and religious minorities, high on their lists, increasing their chances of winding up in the Commons.

But critics, including Trudeau, object to the potential of party elites rigging the lists to suit themselves and to the notion of list MPs not being directly elected by or accountable to voters in specific constituencies.

That could be addressed by adopting an "open" party list approach, giving voters a chance to endorse one or more candidates on a party list. However, the Law Commission report noted that such a system can encourage unhealthy competition and infighting within a party — a problem that became so acute in Italy that it scrapped the open list concept.

Single Transferable Vote

STV is another PR option that would minimize the influence of party elites. It is used in Ireland and to elect the Australian Senate. It was also proposed — and rejected in two referendums — in B.C.

Under the B.C. proposal, the province would have been divvied up into multi-member regions, for each of which a party could nominate multiple candidates. Voters would be invited to rank their favoured candidates in order of preference. A mathematical formula called the "Droop quota" would be used to determine who wins a seat, based on voter turnout and the number of seats available in each district. Candidates who met that quota would be elected.

The proposal involved a complicated procedure — called the "weighted inclusive Gregory method" —for counting the second preferences of voters whose first choice candidate garnered more votes than necessary to meet the quota.

The biggest drawback of STV, the Law Commission concluded, is its complexity. It would also be a "signficant depature" from the "seemingly cherished principle" of one MP representing one riding.

Custom-made PR System

The all-party committee could develop a unique PR system custom-designed for Canada. Foreign Affairs Minister Stephane Dion has already produced one such model: "P3 — proportional, preferential-personalized."

Under his proposal, voters would elect up to five MPs per riding (which would be larger and fewer in number). They would cast two ballots: one ranking their party preferences, the second selecting their preferred candidate from the list put forward by their top-choice party.

Parties with the fewest first choice rankings would be eliminated and their supporters' second choices counted and so on until all the seats in the riding were won by various parties. A party that won one or more seats in a riding would be obliged to fill those seats with the candidates on its list who won the most votes.

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