A popular majority is sufficient for a vote on a law or on certain international treaties, which are adopted if the majority of voters vote yes.
Most international treaties only require a popular majority. But the decision to amend the constitution or join a supranational community requires a so-called double majority. Such a proposal is accepted only if both the majority of voters (popular majority) as well as the majority of cantons say yes.
To determine the majority of cantons, each canton provides a Yes or No vote based on its individual voting results. If the majority of voters in a canton voted Yes, the popular vote of that canton counts as a Yes. A cantonal majority means that a majority of the cantons voted Yes. The votes of the former half-cantons of Obwalden, Nidwalden, Basel-Stadt, Basel-Landschaft, Appenzell Ausserrhoden and Appenzell Innerrhoden each count as half a vote.