BERN, June 13 -- On Sunday one of the wealthiest countries on earth will vote on a question most nations never dare ask aloud: whether to cap its own population by law. Swiss voters go to the polls on June 14 to decide an initiative that would write a ceiling of 10 million residents into the constitution, and the cause behind it is the one that has reordered politics across the continent. It is immigration.

The measure, formally titled No to a 10-Million Switzerland, was put on the ballot by the right-wing Swiss People's Party, the largest party in the country, after it gathered the 100,000 signatures that Switzerland's system of direct democracy requires. If passed, it would oblige the government to act once the resident population, for...