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All the Best,
Welsh Dragon.
So, the reason that the figures aren't adding up is because the number next to the icon of a marble bust represents that character's Gravitas, rather than the number of Senators. While that Gravitas contributes to the number of Senators (or equivalent in other factions) it isn't just a straight equivalent.
Influence isn't just a case of checking the total Gravitas of each party each turn and basing it on that, as one might expect. As I understand it, instead it's looking at the change in Gravitas for each character and each party each turn, and then adding that change to the total Gravitas that's accumulated over all the previous turns.
To use the lovely lady Salvia Pacila from your second screenshot as an example, on the current turn her Gravitas is 12. If next turn her Gravitas is 15, she contributes 3 Gravitas to the total (because 15 - 12 = 3.) If on the turn after that she has 20 Gravitas, she contributes 5 (because 20 - 15 = 5.) Turn after that, if she stays the same, she contributes 0 to the total (because 20 - 20 = 0.)
It's essentially like if I had a very large jar, and an infinite supply of different coloured marbles. Lets say, for the sake of argument, that I have 4 different colours, Green, Blue, Red and White, representing the 4 different parties in your screenshot.
Each "turn" I'm adding marbles to that jar, based on the change in Gravitas. But I'm not taking any of the marbles already in the jar out, so the total number of marbles increases each turn. That total number is the total Influence, and the proportion of that total that is each colour is that party's influence.
If I'm just adding one of each colour each turn since I started, the proportion of the marbles in the jar of any one colour remains the same, at 25% (one in four.) However as I put more or less marbles of each colour in, the percentage will over time change.
If after a while I suddenly stop putting in white marbles (House Papiria) it won't have much of an effect immediately, as there's already a lot of white marbles in the jar. But if I keep adding marbles of other colours, but not white, over time the overall colour of the marbles in the jar changes, as does the proportion of the total which is a specific colour.
So the reason House Papiria doesn't suddenly drop their influence when the old general dies, is because while he's no longer contributing his Gravitas, the Gravitas he already contributed still counts for the totals.
Just to complicate matters further, we also have Ambition which acts as a multiplier for Gravitas. I believe it's just a simple multiplication. So if we go back to lady Salvia again, she has an Ambition of 3, which is pretty high (she obviously has plans to be more than just a wife to G. Severus.) This means her Gravitas is worth more than someone who only has 1 or 2 ambition. So in the example earlier, instead of contributing 3, 5 and 0 Gravitas, she's actually contributing 9, 15 and 0 Gravitas.
Sorry, that's quite long, but hopefully you get the idea.
In the immediate future you aren't going to be able to suddenly take back a load of Senators from House Papiria because their Influence is just too high. But over time it should start to swing back towards the other parties as long as the Gravitas change for the House Papiria is less than that for other parties like yours.
You can help that by increasing your characters Gravitas and decreasing the other party's (especially House Papiria) character's Gravitas. If you can, try to make sure that it's Generals from your Party that are winning battles and leading the armies seeing the most action, while giving House Papiria the boring jobs (or none at all.) Use Intrigues which increase the Gravitas of the initiator (you) or the target (if used on members of your party,) while using ones that decrease Gravitas of the target (the other party member.) Check characters for traits and household members that increase gravitas, and with the latter make sure they're on your characters, not the other party's.
Just keep in mind that you also want to try and keep the other parties, and especially those with a lot of influence, loyal. In your screenshots you've already got a 10% risk of Secession/Civil War, which means every turn there's a 10% chance someone (by the looks of it House Papiria) could secede. If they do that they'll take all the territory they control (which with that influence will be a lot,) and any armies they have generals leading. So you really want to get their loyalty up as a first step.
The other way to handle this, which could be very painful in the short term, but may be worthwhile long term, is to cause House Papiria to secede intentionally. But I wouldn't advise it except as a last resort, as you would end up losing a lot of territory with their influence being that high.
Hope that helps.
All the Best,
Welsh Dragon.
Glad I could help.
Rome 2's politics is quite complex, and has changed a lot over the years, so it's no wonder you're having trouble. Heck, I've been playing since launch and I still don't entirely understand it.
One thing I would say is that keeping the senator proportions equal isn't as good a strategy these days as it once was. Previously it was you having high influence that could cause a Civil War, but in the current system (since they added the Party Loyalty stat) it's actually low loyalty that triggers it.
So these days you're better off increasing your own influence as much as possible (for the bonuses and to minimise the territory that you lose if a party secedes,) just as long as it doesn't cause other party's loyalty to drop too low.
It's also worth taking a look at this guide.
https://steamcommunity.com/sharedfiles/filedetails/?id=1237207803
I'm not sure it's completely up to date (EDIT: it isn't I just checked and there's a couple of things from Patch 20 which aren't included,) but it covers a lot of the mechanics of Politics, and is where I picked up quite a bit about the systems.
All the Best,
Welsh Dragon.
Happy to help.
All the Best,
Welsh Dragon.
Despite this, the poor Patricii are at 0% and the Proletarii now at 4%. Viri Egregii are now at 14%, and they are growing 1-2% per turn at the cost of the influence of the other parties, and not my own... yet.
I can find no valid reason for this happening. The patricii remain at 0% despite their huge successes and incomparable gravitas gains, and 3 ambition on everyone.
So... a party with 1 general who has 92 gravitas, 2 ambition and gains 2 grav per turn.
His party keeps growing by 1-2% influence per turn, taking from the other parties, which in turn has like 2000+ gravitas, and also massive continuous increase from active high level generals and admirals.
It's getting weird.
This does slightly piss off the other parties though. However, since gravitas is irrelevant and you will always gain influence just by spending a modest amount of funds, you can make the other parties as happy as you want. (This gets expensive though...) Hire a bunch of characters for them, seek spouse to get even more characters and promote them all. (Promote yours first early game, the influence bar swings wildly the first few turns) Use them as generals and use them to organize games or send diplomats etc. You can make your politics succession proof while keeping max influence in this way. If in a pinch there is also a secure loyalty action on the politics screen itself for a moderate amount of funds. You can only use that once every few turns per party though.
Promotions does most of the work since it is a long term passive loyalty boost. Anyone still trying to manage politics by keeping other factions at one character is laughably mistaken at this point. You need as many characters per party as needed to counter all negative traits and difficulty modifiers. Once you have that use the much cheaper seek spouse to keep their numbers stable as people die. The first level of promotions is free, other levels cost money.
And yes it is safe to use generals from other parties like this. It is even safe to get a bunch of them (or a bad trait faction leader) killed in battle if you have enough of a loyalty buffer.
Secure influence is super cheap. Seek spouse is super cheap. The first promotion is free.
The main cost comes from outright recruiting characters. This can be done over a long period of time though, like one every few turns. Seek spouse turns that character into two characters, and when one dies seek spouse again brings the number back to two. So the expensive initial recruitment only has to happen once to have the needed characters for an entire campaign. Once those characters are in place the player needs very little funds to keep it going. You probably won't need to do more than one (if that) other political action per turn unless something goes wrong, and that action can be something useful like sending diplomats to other factions (which tends to pay for itself) or sending emissaries to fix food shortages (which is the best temporary fix for that anyway.)
Also I tend to have very strong economies in my empires, throwing money at politics every turn isn't a big deal by mid game unless character recruitment is at 10k or something.