WASHINGTON — Does the European Union have a democracy deficit?

Leaders of the campaign for Britain to leave the European Union have proclaimed last week’s historic vote as a victory for democracy. The union, they often argue, is elitist and undemocratic. The only way for member states to regain full control is to quit outright.

The reality is more complicated. Scratch the surface, and it becomes clear that neither the European Union’s very real problems nor the criticisms of the bloc are really about anything as straightforward as elections or representation. This is a debate about democracy, but in a way that is both more meaningful and harder to define than how we usually think of it.

Technically, the European Union has quite a lot of democracy going on.

The European Parliament, often referred to as the “lower house” of the union’s legislature, is directly elected, via free and fair elections in the 28 member countries, every five years. Every European Union citizen of voting age is entitled to cast a ballot to select a representative. The legislature’s 751 seats are apportioned by the bloc’s treaties.

The Council of the European Union, or “upper house,” consists of representatives sent by the governments of member states. They are not directly elected, but the governments that send them are. Likewise, the members of the European Council, which sets the European Union’s policy agenda, are the elected leaders of member states.