Perhaps a politico could be defined purely from the nature and strength of his or her political relationships.
When I was dreaming of building this game (and who hasn't dreamed of it) this was the political system I envisaged:
We can imagine a graph of nodes and arcs representing the political actors and the relationships between them. Note that this is quite separate from the institutions of government and represents the informal network of political affiliation.
Political actors are the nominated representatives of the powerful familes. Importantly, these actors recognise no nationality, only the interests of their families. So it is quite conceivable that a Roman senator might have very good relationships with political actors in Asia or Egypt or even Africa.
The arcs between these nodes are weighted. A positive score indicates goodwill and support, a negative score hostility and oppostion. These weightings change dynamically during play.
The way to change the weighting of a relationship is to do good (or harm) to the person concerned.
Patronage or the dispensing of favours to your circle of clients and friends was the fundemental stuff of politics, not just in Rome but everywhere. The ability to bestow favours is the index of a political actors power and influence. Because he can expect support in return, bestowing favours creates power.
To measure an actor's influence, reputation, auctoritas we can simply sum the weights of the actor's political relationships.
When an actor gives some benefit to another actor (loans, gifts, bequests, civic or religious office, military command, that sort of thing) the relationship weighting is improved accordingly. Likewise, lawsuits, fraud, theft and other nasty (but potentially lucrative) actions will diminish the weighting, perhaps taking it into negative territory.
Now here's the funky part...
A proportion of the weight added for a deed gets passed on to all the recipients contacts. (We can decide this proportion in various ways, it doesn't matter too much)
What is important is that the value passed on takes the same sign as the weight of the relationship between the recipient and the recipient's other contact. So that doing a good deed for someone will make their friends like you more and their enemies hate you more.
Ok, an example.
Julius fixes up Tiberius with a provincial governorship. This improves the relationship between them by (say) 12. However, Tiberius has two other relationships. One with Mithradates [weighted 32] and one with Crassus [weighted -16]. If the proportion passed on is one tenth, then the relationship
Julius-Mithradates improves +1.2
Julius-Crassus deteriorates -1.2
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There are two reasons why this system might be worth looking at:
first, I believe the dynamics of the system would inherently lead to the formation of parties/factions/interest groups. How stable those groups are, I couldn't vouch for without trying it. But I think you could tweak it till you got the right level of instability.
second, we need to ascribe to political actors no further motive than educated self-interest. The nature of an actor's self-interested actions will be coloured by the need to please his friends and to acquire the wherewithal to do so.
In many cases this will involve the interests of the ruling families of foreign powers.
The beauty is that this makes it easier for the AI to play.
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Anyway, those were my thoughts when I was dreaming.

Love this site btw.
My favorite place.