I would run this with the DMG's social interaction rules which would lend it some structure. If the players are just talking to NPCs, that to me is exposition or possibly color and no mechanics are necessary. If either party wants something from the other that it might not get, then the social interaction rules come into play.
This sounds pretty sensible to me. Although in some contexts (and some systems - I know you've got 5e D&D in mind but our thinking about RPGing can be helped by a range of comparisons) I think it can make sense to see if a NPC is spontaneously hostile or generous. A related idea is
@Hriston upthread referring to setting the baseline attitude via random roll.
a player could choose to play a PC who throws the tyrant's offer back in his face scornfully - but should he not expect to suffer the predictable consequences? Or should those consequences be unrelated to the established nature of the tyrant or not based on the scornful rejection? If they are, then what's the point of knowing anything or even trying to make rational choices?
<snip>
I don't assume it's a question of inferring what the DM is thinking. A meaningful choice is one that is taken with a reasonable understanding of the expected consequences - consequences that will be distinct from the ones you'd face if you made a significantly different choice. If the outcome isn't related to the choice being made, like the thin-skinned tyrant just laughing it off when insulted or the guards were too drunk to make an arrest, what kind of meaning would it have?
I've highlighted two noun phrases.
Where is it it established that the tyrant will respond to scornful rejection by calling for the guards? As far as I can tell,
in the mind of the GM. Nowhere else. This is what the players are expected to infer.
What makes a choice meaningful, in my view, is not
the consequence that follows from it but the fact that
it engages the fiction and tries to push it forward in a distinctive way. That's why choosing to confront the tyrant rather than go along with him is meaningful; just as the other choice would be also.
As for the idea that the GM
has to insist that the tyrant has obedient guards ready to hand because
otherwise s/he could not impose the "meaningful consequence" of being arrested by them after the tyrant callis for them when confronted: how is that anything but circular reasoning to justify a railroad? If the module writer hadn't included them, then the GM would have to write them in or else who know what the players might get away with!
Because in 5E the DM gets to decide. Maybe he's decided the Mad Tyrant is too Mad (MAD I TELL YOU) to be cowed. In combat I believe the DM has a good deal less freedom to opt-out of die-rolling.
If the DM cannot decide, or chooses not to decide, randomizing options is a valid way of deciding. If the DM can decide and does, so is that.
<snip>
While in 5E, the DM can decide whether an ability check needs to be rolled (can determine auto-success or auto-failure) they cannot do so with attack rolls--and a nat 20 is a success regardless of the target's AC. Deciding the orc captain is unhittable is against the rules of the game; deciding he cannot be placated is not.
So I had a quick look at the Basic PDF for 5e.
On pp 57-58, 62 I found this:
Each of a creature’s abilities has a score, a number that defines the magnitude of that ability. An ability score is not just a measure of innate capabilities, but also encompasses a creature’s training and competence in activities related to that ability. . . . An ability check tests a character’s or monster’s innate talent and training in an effort to overcome a challenge. . . .
Each ability covers a broad range of capabilities, including skills that a character or a monster can be proficient in. A skill represents a specific aspect of an ability score, and an individual’s proficiency in a skill demonstrates a focus on that aspect. . . .
Charisma measures your ability to interact effectively with others. It includes such factors as confidence and eloquence, and it can represent a charming or commanding personality. . . . A Charisma check might arise when you try to influence or entertain others, when you try to make an impression or tell a convincing lie, or when you are navigating a tricky social situation. . . .
When you attempt to influence someone through overt threats, hostile actions, and physical violence, the DM might ask you to make a Charisma (Intimidation) check. . . . When you attempt to influence someone or a group of people with tact, social graces, or good nature, the DM might ask you to make a Charisma (Persuasion) check.
Now it's true that p 58 also says that "The DM calls for an ability check when a character or monster attempts an action (other than an attack) that has a chance of failure. When the outcome is uncertain, the dice determine the results." But I would take it as obvious that the GM is meant to make that decision havng regard to the text I already quoted, as well as to what will make for satisfying play.
So the GM might decide (say) that it is impossible to influence a zombie or skeleton via threats, because they are mindless undead which have no heed to their own physical integrity. Or the GM might decide that an otyugh is not amenable to influence via tact or social graces, because it's an otyugh. But nothing there suggests to me that the GM should decide that an ordinary human being can't be influenced because
the GM thinks it would make for a better story if that doesn't happen. Or because
the GM thinks it would make more sense for the NPC not to be influenced.