Think of the graph for it:
(3)l
(2) \ l / (4)
\ l /
(1) - - - - - - - - -
/ l \
/ l \
l
I don't mean to be rude, but I don't think this graph would make any sense. For instance, say that I was all the way to the right on axis (1), and all the way at the top of axis (3), but I was all the way at the bottom of axes (4) and (2). How would you display that here?
Most real world political structures can be described on 2 axes, though obviously limited to the specific goals of description. I also think that 4 axes would be a good number for descriptive purposes, but I think it would be better on two different 2-axis graphs, or 4 directional graph similar to this (ignore the labels): 
As for how it should break down, I would refer to the general principles of Great Power Relations. This is ultimately a game about nation-states, and the principles of international morality/philosophy are more descriptive of a player's choices than the strictly personal principles that we are accustomed to in RPG games. What follows is my opinion on which 4 characteristics can not only fully describe a nation, but can also be quantified within the mechanics of GalCiv as I know them. I also believe that the advantages and disadvantages I have assigned would translate approximately to how a human would react, such that they would operate similarly in multiplayer and single player. I'm sure others may have a different opinion on that, but this is mine.
Notes:
-As a general rule, the advantages and disadvantages of the following traits would grow in proportion to their extremity.
-When I say "influence" I am talking about cultural pressure which expands your borders and "votes" in the galactic council.
-When I take about ease or difficulty of diplomacy, I am simply referring to how much other races will require from you to make a deal work.
-The more similar your civ is to another on each of these, the easier it will be to conduct diplomacy with them
First, a civ should be described internally and externally. Internally, the state can be described on the axes of individualist vs. collectivist and free vs. ordered (a.k.a. individual freedom vs. freedom-from-fear/freedom-from-want). These two axes are intimately related.
The first axis is a reflection of the attitudes of the citizens. Each race would have a baseline that the orientation would gravitate toward over time. It can be influenced directly by using propaganda, producing culture and acceptance of immigrants (i.e. flipping planets using culture,) etc. A more individualist race would be more productive in science and culture, more effective at spreading culture and absorb new planets easily, but would have to spend more on military upkeep, and would get more unhappiness from taxation. Collectivism is supported by order, below, but can also be influenced by propaganda. A collectivist race would have a more effective army, and be able to maintain a large army cheaply, would be able to tax more, and would be more resistant to influence from outside cultures, but would have difficulty in diplomacy as well as taking a penalty to culture production and research. [Since players are going to naturally skew more ordered due to the nature of the game, I put more direct influences on individualism to protect it as a general strategy.]
The second axis is a reflection of the playstyle of the player, and would have a baseline of 0. This axis would be greatly influenced by tax rates and size of military. This axis would also self-perpetuate, the longer a player spends on one side or the other, the harder it is to change.
A free state would get a bonus to money generation, and would have a happier population, but would push the people to be more individualistic, with the advantages/disadvantages thereof. The society would also experience increased unhappiness for some time after the player moves towards order.
A player who is more ordered would have lower, but more stable happiness, and would suffer little to no penalties on event choices which would be "politically unpopular," and it would push his or her society to be more collectivist.
Ultimately an ordered-collectivist nation is going to give the player the best strategic control, it would be more conservative and slower to develop with a large, but less advanced military. A free-individualist nation gives the player lots of resources and power, but it would be unwieldy for the player, unable to "switch gears," respond to threats or choose optimal choices in events due to severe political penalties. A player whose ideologies do not align would be an a non-optimal state with only minor advantages or disadvantages, but a player may aim for this for a short period when their disadvantages become too much of a liability, but they don't want to fully lose their alignment. For instance a free-individualist state may need to start an unpopular war, and would "pay off" the disadvantages by slowly moving to a neutral status, taking the hits to unhappiness and production along the way, and then declare war as a neutral without those drawbacks, then drift back to free-individualist as the conflict is concluding.
Next, the state can be described externally on the axes of realist vs. idealist and isolationism vs. interventionism. Similar to the internal graph, this graph would have an inherent trait and a play-style trait, but these would be primarily based on player action, and are not linked to one another.
The first axis would have a race-specific baseline, similar to the individualism/collectivism, however this would not naturally drift. This axis would be influenced by the player's interactions with the other races. The player would become more realist by engaging in "power politics" by building up military, the use of coercion in diplomacy, entering mutual defense pacts (rather than non-aggression treaties) and contravening alliances/treaties/laws of the galactic council. A realist player will get a bonus to military combat, and be more successful in demanding action from other races, but will not be able to form alliances or trade easily and their influence will be tied directly to their military strength (i.e. no ships = no influence, but big army = huge influence for the realist.)
A player would become more idealist by using cooperative means of diplomacy, which includes having a primarily defensive military and giving gifts to other nations to build them up and curry favor. Generally most diplomatic actions which are not realist will be idealist. The idealist will naturally grow in influence regardless of military or economic might, and can easily forge alliances and pass intergalactic legislation. Since the idealists strengths come primarily from their ideology itself, their advantages can be great and very cheap, however inherent to that is a similar disadvantage to the free-individualists above: moving away from idealism can be devastating due to the opportunity costs of foregoing objectively optimal solutions for those which favor the ideology.
The second axis here is easier, and self-perpetuating. Starting half isolationist, a state maintains isolationism by avoiding entanglements with others and becomes more isolated by building defensive structures. A state becomes more interventionist by becoming involved in treaties and conflicts and building up offensive forces. The more you willingly interact with other nations, the more interventionist you become, otherwise you drift towards isolationism.
Isolationism grants the simple benefit of increased defensive combat effectiveness and resistance to cultural domination. The only drawback is a moderate reduction in influence proportionate to your isolationism.
Interventionism makes diplomacy easier, but slightly increases domestic (internal) political penalties whenever they occur.
