> In a democratic society, government is the representative of the people.

Representative of who exactly? Generally governments around the world win with <50% of the vote. Those who vote make up a small fraction of the population. Of those who voted for the winning party, only a small fraction of them actually feel fully represented by their party - often people vote strategically, or they vote for the "lesser evil" rather than voting for a representative who wholly represents their views.

The rest have a government who are not representative of them in power over them. Hardly representative of the people.

That might be a problem of the specific state you live in. Some systems are better at representing the people than others.