I'm well known to be on the side of a mechanized social conflict system, and for that system to be rigorously used and enforced throughout the game.
However, that said - if you wanted a political game without social stats, I would suggest instead leveraging resource stats. While you are eliminating the potential for a wider variety of players to play a robust series of concepts (if only highly socially competent players can play highly socially competent characters and be effective while having fun, it will reduce the overall variety of character concepts in your game, and skew the game towards combat competent characters), if you're fine with that as an opportunity cost, that's up to you. But you could attempt to compensate for that more by leaning more heavily on resources - money, land, military might, rare economic goods, and by creating specific systems that moderate the ability to trade and cash in these resources. This allows people to do the 'wheeling and dealing' aspect of politics without actually being good at sweet-talking others - you may not be able to craft a persuasive pose to save your life, but you can probably type "Count Rudolfo has 80 acres and a mule that he'll trade Duchess Tupelo, if she will make the bandits on the southern border go away". Design the domains to be diverse enough that everyone needs something from everyone, and make war risky enough that tromping over and just rolling combat dice isn't enough to steal all other people's shit, and at least some level of political play will emerge.
If someone does retain individual social skills/conflict resolution, I've become increasingly fond of incentivizing losing. Yes, if your character loses a social conflict, they have to do something that might not be in their best interest. But if you the PLAYER receive a reward for going along with that (or committing fully to it), then you have a reason to suck it up. Also, perhaps setting a hierarchy of success and what actions can be compelled. For a political game, you likely don't want huge swings in attitude to be compelled from social skills, because you want to maximize negotiation and intrigue space. At the same time, you don't want social characters to feel like they have to 'grind' someone's attitude IC. So what you might do, now that I'm thinking about it, is have social change/combat be sort of an unholy hybrid of 7th Sea 2E's story system, and CoD's Doors.
Social Character has to declare to the GM a meaningful end goal. This social system would not be useful for 'I want you to sleep with me' or other micro interactions (including fast talking one's way past a door guard, etc.) but would instead focus on larger, political play. So, say, the goal might be "I want the Empress to take her travelling court to a specific lady's landholdings, because I'm repaying a favor that lady did for me, and the Empress always awards a boon to her host."
The GM would then say, "Okay - that's not a particularly risky undertaking, so you'll have to do three tasks successfully to get the Empress to agree. The Empress is a PC, so let's rope her in. Hey, Empress-Player, what are three challenges that PC A would have to overcome to get Empress Tidypants to take her travelling court to Baronness Murzi's lands for the next season?"
Empress-Player might say, "Well, no one's requested it yet, so she's got no reason to fight the idea. First, PC A would have to have a good pitch (a scene with Charisma + Persuasion as a roll, maybe). Oh, and Tidypants loves to stay places with luxuries, so she'd have to know that she's going to be taken care of, if you know what I mean (Bribery, throwing her a party showcasing the exotic goods of Murzi-land, or a successful Intelligence + Fashion roll during a second scene might all be options here). Oh, and Empress Tidypants would need to feel safe moving her court, of course (so maybe an Intelligence + Leadership roll, or lending troops, or hiring mercenaries to protect her, could be a resolution of this)."
PC A might say, "That sounds reasonable," or they might say it's not worth it, or if one of the requirements seems excessive, the GM might step in and say, hey, "Hey, requiring that PC A arranges for the death of a rival's kid in exchange for this seems a bit excessive. How about he humiliates the rival at a public scene, instead?" To reduce GM load, you could also build in character types for players who enjoy doing this sort of balancing - a Negotiator's Order, or something, and helping people design these social maps would be one of their jobs.
But what about conflict and failure? You'd have to restrict it somehow. Perhaps you only get as many chances as you have some level of the Key Social Skill. So, like, if it's a 1-10 scale on skills in the example above, and the GM decides the Key Skill is Persuasion, and PC has 5 Persuasion, then they get 5 attempts to get those three things. If they fail, say, to make the Empress feel safe the first time, but got everything else, then they get two shots to make up for that, perhaps at a difficulty increase. If they don't get it by the end of the next two attempts? The Empress is unmoved - and keeps the bribes, of course.
Likewise, under this system, you're less likely to run into direct PC vs. PC conflict, and more into colliding gambits and plots. Which could be a plus, in a political game. I would generally say first past the post - if two people are competing for a similar goal, then the first person to achieve their goals wins. However, you also might work out a success exchange - perhaps people could take their successful scenes, and instead of applying that towards their end goal, they could instead use it to counter a success someone else has achieved towards their goal. Perhaps with some level of investigation/intrigue system so that characters can discover each other's plots and plans.
It would be a very different way of thinking of social conflict resolution, but one which might suit the slower, more narrative style of MU*s better than the "roll and resolve" system that is used in physical conflict.
