Double majority means that two different criteria are needed to decide on an EU law or to reach a decision.
Under the “double majority” proposed in the Lisbon Treaty from 1 November 2014
<!--[if !supportLists]-->- <!--[endif]-->55% of member states must be in favour of a proposal
<!--[if !supportLists]-->- <!--[endif]-->Representing 65% of the toalt EU population.
<!--[if !supportLists]-->- <!--[endif]-->72% of member states must agree if proposals do not come from the Commission
The Commission will still have the monopoly in proposing all law, which would then be voted on in the Council.
The Treaty of Nice introduced a possibility of voting by size of population. Member states with 38% of the EU population could ask for a second counting of the weighted votes in the Council.
A decision then needed the support of member states representing 62% of the population of the whole EU. This possibility was never used because most decisions also required the support of 255 of 345 weighted votes, 260 of 352 following Croatian membership in 2013.
The number of citizens being calculated for each country is decided each year by means of a regulation from the EU.
The Democracy Forum and the SOS Democracy intergroup in the European Parliament proposed a different system of double voting, in which a decision would require the support of 75% of the member states in the Council and a simple majority in the European Parliament.
In the USA, 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. This is also a kind of double majority.
See also Voting in the Council and Blocking minority
Scadplus: Double majority http://europa.eu/scadplus/glossary/double_majority_en.htm