The best solution I've found for this is broadly applicable, but came through another game entirely: Exalted.
Exalted player characters are so influential on the setting that they warp its internal reality. This is laid most thoroughly bare in leading groups/cities/nations: any setup works. If the PCs set up capitalism, it works. If they set up communism, it works. If they set up a theocracy, it works. Kleptocracy, gerontocracy, radical anarchism, totalitarianism, whatever, it all just works because their personal puissance makes it so. They can even set up joke societies, like Friend Computer's, if tat's what they're into, and those societies will work! They still need to explain how they are ordering their society, but only so the storyteller can describe the results appropriately. (I've simplified this description significantly, but it's essentially accurate)
Exalted also has "social combat," which operates in a way that parallels physical combat. You make arguments, you can flurry multiple arguments, you can study your opponents' arguments (aim), etc. This is all resolved using pure dice pools, just like regular combat. Like the nation-building stuff, you do need to describe what arguments you're making for narrative continuity, but whether those arguments are effective is resolved by the dice, not by the storyteller's willingness to accept them. This can lead to some silly moments, but that's okay! Sometimes very persuasive people (or regular people with gullible followers) will convince people of zany, off-the-wall ideas, and it is a natural and correct that they be able to do so.
(I personally, in real life, once convinced someone that all steak is made of coconuts. Steak. The thing defined by its origin in cows.)
You should import this approach wholesale to any game crunchy enough to support it. Ask your players to describe what arguments/bluffs/diplomacy/jokes their characters are making, but let the dice decide whether those arguments are effective.
(For intra-PC roleplay, just stay out of it. If the smart bard somehow finds the dumb barbarian very convincing, consider it a character choice and move on.)