Dynamic elections and political system are the last pieces of the puzzle to make Victoria II into the really great game it has the potential to be, but it would be very easy to screw up. Drawing on my knowledge of coaltiion formation and parliaments as a political scientist and thinking about how they are relevant to the game, a good dynamic cabinet system might look something like this:
Instead of asking "How can we create a cabinet system that fits the current political system", we should be asking "How can we change the political system so that we can have cabinets?"
Possible Parliamentary model - let's take a country with the Liberal, National Liberal, Conservative, Catholic, Socialist, Communist and Reactionary parties. The election happens, and the player is presented with a broad array of possible coalitions, including {[Liberal; National Liberal; Catholic], [Conservative; National Liberal; Catholic], [Liberal; Socialist], [Communist; Socialist] [Conservative; Catholic; Reactionary]}. There's plenty of interesting research on how exactly coalitions are formed, but it's not necessary to discuss that here, other than to say that any such coalition formation would have to be minimum win-set (so the smallest number of parties to form a majority possible), and to be ideologically consistent (so liberals can form coalitions with conservatives or socialist, but not at the same time).
Each party not in government would have its own 'shadow cabinet', composed of politicians and beyond the control of the player. What's key is that we represent both the desires of individual politicians to get into government (and be head of it), and the desires of parties to be in government and carry out their policies. So, let's say the [Liberal; National Liberal; Catholic] government is formed, and the parties' composition of that coalition are 60%; 25%; 15% of the government. Accordingly, parties will want roughly that share of the ministries to go to them; but, if we take the prestige mechanic for generals and apply it to politicians, voters could also want a certain amount of 'prestige' in their government. This would reflect the need for influential politicians in the party to also be influential politicians in the government and disincentivise the player from forming coalitions with large parties that have massive majorities, with prestige for ministers being generated by holding on to different shadow cabinet positions (so being shadow minister for war generates more than being shadow cabinet minister for agriculture, for example),
It also wouldn't really make sense for politicians to have specific bonuses like generals do, otherwise you'd just end up with the Hearts of Iron problem of putting the best ministers in each position and having them sat there until the end of the game. Instead, whilst politicians should have simple general-like personalities (so pacifists immediately resign if a war is declared for example, a Francophobe means you won't be able to ally with France etc.), it also makes sense to have different but general values of competence - say military, economic and technological. So, if you have a naval minister who is top notch at military competence, but crap at economic and technological competence, naval units would become more effective in combat and cheaper to run, but both more expensive and take longer to build in less efficient factories, and also with a slower research pace in the naval school. This minister would therefore be good to have in the middle of a war, but not in peacetime. Obviously, some competences would be more important than others, as military competence in agriculture wouldn't be used at all for example. It also makes sense to have a 'leadership' competence for the head of the government - this would be a kind of meta-competence that affects the efficiency of all the other ministers in government.
Finally, parties should impose stronger constraints upon governments than they do now, and we should see more flexible governments. Returning back to the [Liberal; National Liberal; Catholic] coalition, assume that the liberal parties are free trade, and the Catholic party is protectionist. Government policy might either be then explicitly free-trade or status quo depending on how trade is weighted in the issues for the voters for those parties - if Catholic voters aren't bothered by protectionism, then the coalition policy might be free trade, whereas if they're ardent protectionists, the policy would be status quo. Under the latter, the Catholic party would have a veto over trade policy, and if tariffs are lowered by the player, the Catholic party would exit the coalition and the government would fall. Vice versa if the liberal voters are ardent free traders as well. Causing the government to fall would then present the player with a choice of either selecting a different coalition (with possible coalitions only selectable once every Parliament) or dissolving the legislature and calling a new election. This would be a much more interesting dynamic than the current silly max-mins imposed by the largest party of the largest ideology - seeing the government fall because it raised taxes or cut military spending would add a whole new dynamic to the game and economic decisions by the player.
Presidential systems could exist as a hybrid between this and the current system, without the need to build coalitions.
Interesting, Phalanxia. What about unciv? Most of those countries didn't even have political party then? Just curious to hear your thought.