Decision made upon a political question by the votes of all qualified persons

One word substitute is Plebiscite.

Veto: a constitutional right to reject a decision or proposal made by a lawmaking body.
Suffrage: the right to vote in political elections.
Plebiscite: the direct vote of all the members of an electorate on an important public question such as a change in the constitution.
Franchise: an authorization granted by a government or company to an individual or group enabling them to carry out specified commercial activities, for example acting as an agent for a company's products.