What is the key to ensuring that a relatively small number of people can accurately represent the opinions of a large population?

The key to ensure that a relatively small number of people accurately represent the opinions of a large population is the free will when voting.

As you may know, there's a lot of parties that show their political ideas during a period of time before elections. People have to study and see which one of them represents them the better and vote for it. Once the party is elected and becomes government, people can criticize and replace their elected leaders if they don't perform as expected following certain instructions. In Democracy, people is the highest authority and the government is based on their needs.

People have the obligation to monitor the conduct of their leaders and they must be informed about public issues.