Answer:
Representative democracies are very common in the modern world and allow for democracy in large nations.
Representative Democracy
In a representative democracy, people vote on representatives instead of actual legislation. These representatives then vote on legislation and proposals. The representatives elected by the people are meant to represent the beliefs of the people that elected them.
On the other hand, true democracies have the people vote directly on legislation. However, this is unrealistic for larger countries. True democracies require everyone in the country to vote every single time laws or policies need to be passed. In a country that has a large area or millions of citizens, this is unrealistic.
Examples
As stated above, representative democracies are very common in the modern world. The USA, the UK, and Germany are a few examples of countries that have representative democracies.
Specifically, in the USA, there are senators and representatives in congress. The people vote on congress members, who then vote on laws. This is an example of how in representative democracies, elected officials vote on policies instead of the people.