THIRTY polling stations in Toronto, Montreal and five other cities helped French expatriates in Canada vote in their country's presidential elections in April and May. But Canadian authorities would prefer their French guests not to cast ballots in the legislative election, which begins, outside France, on June 2nd. For the first time French citizens in North America (and in ten other new constituencies around the world) will have the right to elect their parliamentary representatives.

Canada wants the poll shut down. Since 2008 it has objected that such elections are interference and challenge its own sovereignty. It complained about polls of Algerian expatriates in May and of Tunisian emigrants last October. But the global trend is the other way. Around a dozen countries, like France, give non-resident citizens their own advocates in parliament. Since 2006 Italy has set aside 18 seats for compatriots elected in four continent-sized constituencies. Croatia, Morocco and Colombia have similar systems.

Many states allow emigrants to cast absentee ballots in their home constituencies. But migrants argue that fully fledged representatives defend the diaspora's interests better. France's global voters worry particularly about issues such as consular services, the state funding of French schools abroad (such as lycées) and taxes on earnings abroad. Julien Balkany, a candidate standing in France's new North American constituency, says emigrants want champions back home, so that they can return to a society that values their international experience, not one that sneers at their globetrotting.

The politics of extraterritorial elections are complex. Emigrants tend to be politically conservative—so right-wing governments encourage diaspora voting. But émigré communities can be meddlesome, so politicians often try to limit their influence in domestic affairs. One way is to make foreign constituencies bigger. Portugal, for example, has only two: one to represent its emigrants in Europe, and a second for those in the rest of the world. Arrangements for expat voters will attract increasing interest and controversy as migrants multiply (around 2m French live abroad, a population increasing by more than 4% a year). They may also begin to appeal to countries, like Ireland, that still disenfranchise emigrants entirely.

Few foreign governments object to featuring in another country's electoral system, and those that do have little power to prevent it. Canada cannot stop the French government placing ballot boxes in its consulates (even though it claims it has international law on its side). In any case, French citizens abroad can now vote over the internet.

Campaigning among expatriate voters is hard work. Media appearances and public rallies that might swing domestic races are much less effective when an electorate is spread across national borders, says Yannick Naud, a candidate in France's Northern Europe constituency, which includes migrants in Britain and nine other countries. Much electioneering is via e-mail lists provided by French consulates, as well as through webcasts and social-media sites.

Migrant-sending countries mostly cherish their diasporas. They hope wealthy and influential emigrants will do good at home. Providing parliamentary seats for compatriots abroad may rekindle loyalties. But political representation has not prevented plummeting turnouts among Portuguese expats (from 87% in 1976 to only 25% in 2005). Only 70,000 of the 350,000-odd French thought to live in Britain have registered to vote in the constituency there, and Mr Balkany thinks that about a quarter of the voters he meets in France's North American constituency are unaware of its existence. Some emigrants are homesick. Others are sick of home.