A double majority is a voting system that requires a majority of votes according to two separate criteria. This mechanism is usually used to require strong support for any measure considered to be of great importance. Here are some examples of how double majority is used in different contexts:

• Australia: Constitutional changes must be passed at a referendum in a majority of states (4 of the 6), and by a majority of voters nationally. This means that a national majority of electors from all states and territories, and a majority of electors in a majority of the states (i.e. at least four of the six states) must vote in favor of the changes.

• European Union: Double majority voting replaced artificial voting weights for votes requiring a qualified majority in the Council of the European Union following implementation of the Treaty of Lisbon. A qualified majority requires 55% of voting EU member states, representing at least 65% of the population of voting members for a European Commission proposal to be approved.

• Switzerland: The passing of a constitutional amendment by popular vote requires a double majority; not only must a majority of people vote for the amendment but a majority of cantons must also give their consent. This is to prevent a larger canton from foisting amendments onto the smaller ones and vice versa.

• United Kingdom: A double majority vote is a House of Commons division where the agreement of both a majority of all MPs and a majority of all MPs representing is required.

• United States: Double majority is used for some initiative or referendum votes on issues such as a tax levy. For example, a law requires a majority in the House of Representatives, where participating states are represented according to size of population, and then a majority decision of the Senate, in which two senators each, independent of size of state population, represent individual states of the USA.

• Condominiums: In the context of condominiums, a double majority is a majority necessitating both a specific percentage of the votes of the co-owners and a specific percentage in number of all the co-owners.

In summary, a double majority is a voting system that requires a majority of votes according to two separate criteria. It is used in various contexts, including constitutional changes, European Union voting, condominiums, and legislative bodies.