How many major economic systems are there? One of the biggest political debates regards the best type of economic system, which usually boils down to capitalism vs socialism.

Are there other kinds of economic systems, aside from more "primitive" kinds, like barter?

To put my question in perspective, I think of economic systems as a continuum that looks something like this:

communism | socialism | "mixed economy" | capitalism | "free market capitalism" (anything goes, rampant corruption and inequality)

So "mixed economy" would be a combination of socialism and capitalism, rather than a distinct economic system.

But that's just my opinion. There may be views that are radically different than mine
Wikipedia has a comprehensive list of  economic systems.
If you want to start thinking about number major economic systems that exist I recomend looking at the section on an economy's  allocation mechanism.
In particular, Wikipedia lists the following kinds of system:

The basic and general economic systems segmented by allocation are:

Market economy (&quot;hands off&quot; systems, such as laissez-faire capitalism)
Mixed economy (a hybrid that blends some aspects of both market and planned economies)
Planned economy (&quot;hands on&quot; systems, such as state socialism, also known as &quot;command economy&quot; when referring to the Soviet model)
Traditional economy (a generic term for older economic systems)
Participatory economics (a system where the production and distribution of goods is guided by public participation)
Gift economy (where an exchange is made without any explicit agreement for immediate or future rewards)
Barter economy (where goods and services are directly exchanged for other goods or services)
Post-scarcity economy (a hypothetical form where resources aren't scarce, such as Marx's concept of a Communist society)