A Government that provides an illusion of a choice would be considered what type
of government?

A government that provides an illusion of choice would be considered an authoritarian government.

Explanation:

As you already know, an authoritarian government is one that does not allow its citizens to have freedom of choice and everything that concerns the country is decided with the vision of a single person, the leader.

The word "illusion" means the establishment of a mistake, of something false that is said to be true. If a government provides its citizens with an illusion of choice, instead of a real and effective choice, that government is not giving freedom to its people and this "illusion of choice" is a concept imposed on society by the government. Any government that imposes something is an authoritarian government.