Are There Only Two Types of Government?

I recently heard the argument that in the long term there are only two types of government, the oligarchy and the republic.

In a totalitarian dictatorship in which a dictator has total power, he still doesn't make 100% of the laws, he always has a group of delegates who at least advise him on what laws to make.
That is an oligarchy.
In an anarchy, the majority rules which makes it a convoluted democracy which eventually leads to a group of people with high influence making all the rules; that is also an oligarchy.

In a republic, the majority opinion is basically irrelevant. Republic means rule by the law. So even if 99% of people think that jumping on one foot should be illegal, it's not.

I think the republic is the freest form of government and I think that when politicians say "we're going to spread democracy" they should be looked down upon.
If we are going to spread a type of government, it should be the republic. Democracies fail abhorrently.

Tell me what you think about this either by responding on your own blog or in the comment section below.