If an optional referendum (such as an amendment to an act) is on the ballot, the proposal is adopted if the number of ‹yes› votes exceeds the number of ‹no› votes.
In the case of a mandatory referendum (such as an amendment to the Federal Constitution), the cantons also play a role. The proposal is adopted only if the number of ‹yes› votes exceeds the number of ‹no› votes and the majority of the cantons also vote in favour.
The voting results in each canton are used to determine whether the majority of the cantons have accepted or rejected a law. If the majority of citizens in a canton vote ‹yes›, the canton is considered to be in favour of the proposal. A cantonal majority is achieved when a majority of cantons vote in favour.
However, when calculated whether a majority of the cantons has been achieved, the results in the former half-cantons of Obwald, Nidwald, Basel-Stadt, Basel-Landschaft, Appenzell Ausserrhoden and Appenzell Innerrhoden are counted are counted as only half a vote.
When a majority of the people and the cantons vote in favour of both an initiative and a counter-proposal, the deciding question comes into play. Voters are asked which proposal they prefer. The proposal that receives a majority of the popular and cantonal vote will be implemented.
If you do not respond to the deciding question, then you are abstaining on this question only. You are leaving it to the voters who answer the deciding question to make your decision. However, your votes on the initiative the counter-proposal will still be counted.
The result of a vote is valid even if the turnout is low. There is no quorum for the number of votes cast.