How do Plato, Aristotle, and Cicero understand the purpose of politics?

First, let's define "politics" as these three would have understood or used the term. The word "political" comes from the Greek word politikos, meaning "of, or pertaining to, the polis." (What's a polis? It refers to a city-state.)

Let's begin with Aristotle, who compared the role of a politician to that of a craftsman. Like a craftsman, he wrote, a politician works within a system, producing and maintaining, keeping things running smoothly by...

First, let's define "politics" as these three would have understood or used the term. The word "political" comes from the Greek word politikos, meaning "of, or pertaining to, the polis." (What's a polis? It refers to a city-state.)

Let's begin with Aristotle, who compared the role of a politician to that of a craftsman. Like a craftsman, he wrote, a politician works within a system, producing and maintaining, keeping things running smoothly by following a certain set of rules. For Aristotle, the politician's rules are laid out in a constitution. The constitution, not the individual politician, is the ruling authority. As he writes in Politics:

Since we see that every city-state is a sort of community and that every community is established for the sake of some good (for everyone does everything for the sake of what they believe to be good), it is clear that every community aims at some good, and the community which has the most authority of all and includes all the others aims highest, that is, at the good with the most authority. This is what is called the city-state or political community. 

Now let's focus on Plato. Plato didn't believe that human beings could be trusted to make the best choices for themselves. He opposed the concept of democracy, because he believed that tyrants could easily rise to power if they exploited the public, and that too many individual people make decisions based on their own personal interests. For Plato, politics existed to provide structure for a public, and to protect the people. 

Cicero considered politics through another lens: he was interested in the relationship between philosophy and politics. Politics, he believed, were more important than philosophy. But he used philosophy as a means to achieve his own political goals. For Cicero, the point of politics was to communicate philosophical ideas and arguments to a public that wouldn't otherwise understand (or care to understand) them.