On paper it looks like a no-brainer.

In the 2015 election the NDP has to beat Justin Trudeau to beat Stephen Harper. On that basis over the next year, fighting Liberals should be at least as important for the New Democrats as fighting Conservatives.

The equation is based on a domino theory that postulates that if presented with a clearly dominant opposition party, the non-Conservative majority of the electorate will fall in behind it.

If life were so simple, NDP leader Thomas Mulcair could put a tentative hold on orange paint for the prime ministerial Sussex Drive digs.

But politics involves more algebra than basic arithmetic.

Suppose for the sake of argument that Trudeau — like Michael Ignatieff and Stéphane Dion before him — flames out between now and the next election.

Under that scenario the NDP would hang on to the bulk of its Quebec seats in 2015 without much of a fight. But it might do that no matter how the Liberals perform. In most Quebec ridings, the Bloc Québécois is the NDP’s main rival and anything that weakens the sovereigntist party is good news for the nationalist-friendly New Democrats. Until further notice the sudden resignation of leader Daniel Paillé this week and the leadership void that it has opened up falls in that category.

A strong New Democrat performance in Quebec could block the path to power for the Liberals. But it does not follow that it would pave the way for decisive NDP gains in the rest of Canada.

In 2011, Layton’s orange wave had the opposite of a tsunami effect for the NDP in the rest of the country.

If anything, soaring New Democrat fortunes in Quebec ended up tipping the balance toward a Harper majority as scores of so-called blue Liberals — in particular in Ontario — decided that switching to the Conservatives was preferable to risking a Layton-led government.

Jump back now to Manitoba and two recent byelections that featured a sharp drop in Conservative support in favour of the Liberals.

In that province, the NDP has a solid government record. But it comes with a downside for Mulcair. In places where the Tories fight the New Democrats for provincial power, it is easier for a disgruntled Conservative voter to switch to the Liberals — a marginal quantity provincially — than to cross over to their arch-NDP foes.

That means that in regions such as the Prairies, where the NDP is strong and regularly forms governments, it may be hard for Mulcair to make gains at the expense of the Conservatives in 2015, unless the Liberals are strong enough to pry votes off Harper and divide the non-NDP vote.

Similarly in Ontario, a weak Liberal performance would more likely translate into a stronger Conservative hand than an NDP boost, but for a different reason.

In Canada’s largest province, the federal New Democrats have yet to convince a majority of voters that they are a worthy governing alternative.

In the larger picture, the evidence to date suggests that the NDP war on the Liberals in Quebec is at best a sideshow. And crushing them nationally could even be counterproductive.

While the conditions for a New Democrat repeat sweep of Quebec may be easier to recreate than many had initially assumed, they cannot be transposed to the rest of the country.

To win Canada, Mulcair has to break out of an opposition paradigm that is limiting the appeal of his party in suburban Ontario. As he noted at a year-end news conference on Wednesday, there are almost as many seats in the larger GTA as in all of Quebec.

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No amount of effective attacks on Harper in the House of Commons will achieve that and breaking Trudeau’s stride will do little to advance the cause of the New Democrats. It might even set it back.

At year’s end the biggest threat to Mulcair’s national ambitions is not Trudeau but a party brand that has yet to be made voter-friendly enough to appeal to a greater number of centrist Ontarians.

Chantal Hébert is a national affairs writer. Her column appears Tuesday, Thursday and Saturday.

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