On the issue of mechanics and "yielding" in this particular context I don't know that I have all that much more to add.
The claim that "any resolution system could land on the OP's outcome, the same way the application of 5E's did" seems false to me. Prince Valiant won't, because one feature of its system for establishing consequences is that PC death should rarely be in issue. So executions are off the table. In my Prince Valiant game, when the PCs found themselves at odds with an evil and treacherous NPC, the NPC called for a joust to prove his innocence. He won, and hence the PCs rode on, later to hear news that the older brother of the NPC in question had mysterioulsy died, leaving the NPC the undisputed ruler of Fort Seahawk.
In Burning Wheel the stakes should generally be made explicit if they are not already implicit. In our game, when the PCs acccused the evil cleric in the Keep on the Borderlands of being such, the result was a duel of honour which (again) the PC (played by the same player) lost. In a scenario closer to the OP's one, the introduction of the guards, and the consequences thereof, would be handled very differently from what is described - BW invites and requires the GM to be far more thoughtful about framing than seems to have been the case in the OP.
In the 5e context I would think some of these ideas could equally be applied - hawkeyefan has sketched out a good range of possibilities already, both just upthread and earlier in the thread also.
Yes, @hawkeyefan described several ways the scene could have been handled differently. I believe he has some experience with the adventure in question, so his points are well worth considering in this specific instance. I think some of them are looking to solve what's clearly an out-of-game problem (different preferences/expectations for play) in-game, which I think is ... not the best approach, but if you're determined not to break the fourth wall here they'll serve--though I think there's still a discussion necessary, after the scene or after the session. I think his points about DM Fiat mattering less than people having fun, and the sorts of considerations that should come into play before deploying DM Fiat in this instance are important and valid.
I disagree about the situation being impossible in other resolution systems, though. I'll grant that it would probably violate the expectations of play that in Prince Valiant the PCs should be arrested and in a prison with their executions scheduled for the next day, but that doesn't in itself seem contradictory to your description of its approach to PC death--the expectation I'd think would be that there'd be a way to arrange their escape. It doesn't seem out of the mechanics' range, but I'll grant that you know the system approximately infinitely better than I do. I don't know Burning Wheel any better than Prince Valiant, but again it seems plausible (not likely--plausible) that the mechanics could lead to a situation not radically different from this, with the GM being thoughtful about the NPC and about framing, and with the stakes being explicit. I figure there are different paths to roughly the same place.
As to "yielding" and the effects of checks on the NPC: Those in this thread who know the adventure have described the tyrant in question as weak. It seems to me that a weak despot would be more likely to react poorly to being insulted, more likely to resort to executions and other strong-arm tactics than a strong one, and that those in fact might be his failure states (he loses his composure) rather than his success states. Of course, it's possible that my tendency to think backward is leading me astray here--and of course, he may be written differently in the adventure.
Aragorn in your example fails to jump the distance by the way, no roll, if his Strength is less than 20. If some special circumstance were present, he might get a check to jump an unusually long distance.
The search function is not turning up the thread for me, but some time in 2018 (I think it was) there was an extensive thread about this very issue in which I believe you participated. Your reading of those rules is not the only one. In particular, some people - including regular 5e players - think that the reference under the Athletics skill entry (Basic PDF p 59) to "try[ing] to jump an unusually long distance" establishes a framework within which attempts to jump further than a PC's STR score might be resolved; and that the statement under the Movement heading (Basic PDF p 64) that "Your Strength determines how far you can jump" should be taken to be qualified with an adverb such as "usually" or "with certainty".
I personally find that level of group coordination extraordinary. I do not think it should be taken as a given.
For my part a good deal of how I learned to run games is focused on getting players to play their characters as individuals. If a character is present on the scene during a social interaction I would expect that they would be actively involved in the negotiations. If they were not NPCs would bring that up. I might also ask them questions about how they see things.
Now if they are like not in the scene because they are doing other things or are on the other side of the room that's one thing. If they interrupt when I am specifically addressing someone else that's another. If your character is physically present you are in the scene.
Of course at the end of the day a lot of this confusion comes from the lack of instruction provided to players and GMs by the game. There is no meaningful sense of where your priorities ought to be so unless that is resolved by group explicitly you are apt to run into mismatched play priorities.
I can't (and won't try to) speak for the other two, but I'd find the behavior of the player whose character insulted the tyrant while I was negotiating with him to be literally infuriating. You're not only keeping my character from achieving the goal of the negotiation now, you're keeping my character from ever achieving that goal with this NPC. It has vibes of PvP to me--and I utterly detest PvP.
Besides my own experience, there is the experience of others. Who has had the sort of thing described in the OP happen in Prince Valiant, or Burning Wheel, or Dungeon World? That is - to be clear about the sort of thing described - who has had a session result in a player apologising for "ruining the campaign" because a confrontation between PCs and a ruler led to PCs being escorted out by guards to be executed with the GM seeing no way out but either "reward[ing] murder-hoboism and let[ting] them escape with a deus ex machina?
I'm spelling this out to make it clear that - as I read it - the problem in the OP is not the fiction. RPGing can support an incredibly varied range of fictions, including imprisonment and escape. (It happens quite often in my games, including the last session I ran - a Wuthering Heights one-off.) The problem - as best I can tell - was the process whereby the fiction was produced., this process including both framing and resolution.
In my BW campaign two PCs ended up imprisoned after a confrontation with city guards while leaving the scene of a murder carrying a severed head and some vessels filled with the victim's blood. But this did not ruin the campaign. And the game was ble to continue without rewarding "murder-hoboism" and without "deus ex machina". This is because BW has robust systems and frameworks, on both GM and player side, for resolving a whole host of action declarations - not only the ones which were attempted (and failed) to placate the guards, but such ones as "I wait to see if anyone visits me in prison" (Circles check) - and for establishing the framing of scenes (eg the design and play of BW pracically guarantees that there will be some sort of nemesis who wants to come and gloat over the imprisoned PC, or some sort of ally who will want to come and help him/her escape).
In the OP we are told that "they were given several opportunities to escape the stocks, but the would-be assassin failed and the instigator said he would rather die than let this corrupt man stay in power." @hawkeyefan, having knowledge of the module, may be able to conjecture what those opportunities were likely to have been. I infer - from the players' responses, and treating those as sincere - that these opportunities involved some sort of compromise with or concession to the tyrant. More generally, and in line with the reference to deus ex machina, it seems like the only way out of the failed attempt to defy and/or kill the mad tyrant was to follow the GM's lead.
This problem is not going to arise in systems which encourage the GM to follow the players' lead.
I'll grant that it would probably violate the expectations of play that in Prince Valiant the PCs should be arrested and in a prison with their executions scheduled for the next day, but that doesn't in itself seem contradictory to your description of its approach to PC death--the expectation I'd think would be that there'd be a way to arrange their escape.
The language of "arrangement" to me resonates strongly with "giving opportunities" and "deus ex machina".
Prince Valiant has a different mechanical framework from BW, but one option for a player in possession of a Storyteller Certificate is to Find and Escape Route or Escape Bonds. From p 45 of my imprint:
FIND ESCAPE ROUTE
Whether locked in the dank donjon prison, upstairs in a chamber inside a burning castle, or in the hold of a sinking ship with the hatches battened, this Special Effect will allow one character to find a way out. In the donjon he might discover that the wretch who brings slop owes him a favor; in the castle a hidden passage behind curtains might be found; among the dunes a deep wadi might conceal a rapid escape; a section of rotten planking might provide escape from a ship.
ESCAPE BONDS
Whenever immobilized with rope, chains, manacles, or other devices, a character can escape with this Special Effect. Maybe a rat comes and chews the bloody thongs, as happens to Val in one dramatic sequence, or a jagged edge of stone lies nearby, or a tool is smuggled in, or the lock proves to be broken.
If the escaping character has companions in adversity, he may be able to free them once free himself. But Escape Bonds does not permit a whole group of characters to miraculously free themselves at the same instant.
There are also options based around action resolution: even without a special effect a player might have his/her PC make a Fellowship check to befriend the slop-delivering wretch. Or with a Presence check have Prince Edward turn up and reveal the PC's "noble heritage" which warrrants him/her being freed. (I'm thinking of the resolution of the stocks scene in the film A Knight's Tale.)
The orientation of the system is towards player proactivity rather than dependence on following the GM's lead.
As to "yielding" and the effects of checks on the NPC: Those in this thread who know the adventure have described the tyrant in question as weak. It seems to me that a weak despot would be more likely to react poorly to being insulted, more likely to resort to executions and other strong-arm tactics than a strong one
An alternative thought is that a weak despot might yield to those who are obviously stronger than him.
This goes back to my thought that sometimes "realistic" = what the GM has in mind.
In my experience a more flexible appoach to establishing consequences and NPC behavious not only helps avoid the problems in the OP, it also produces more interesting, fleshed out and hence "realistic" NPCs. This came out in a discussion a couple of years ago about my Classic Traveller game, when @chaochou posted some thoughts about how a group of PCs might try and capture a military ship, including some respones to the suggestion that it was "unrealistic" for his plan to work:
If I was going to try and get aboard the cruiser it wouldn't be through violence, and probably not stealth either.
I'd be looking to broadcast a distress signal and claim to have a life support malfunction and multiple system failures - throw the ship into a slow awkward spin to make it look convincing. Something to get you on board the target ship with a credible reason to be there and as little suspicion as possible.
Actually the Captain was once in an emergency situation himself as a young boy and vividly remembers his own rescue. He may be researching bio-weapons, but he'll take a distress call seriously. There's no honour amongst thieves though, and three or four of the other senior crew lost patience the last time they went out to a distress beacon. This one could easily push them over the edge.
The remarks about the NPC captain were part of an explanation as to why a distress signal broadcast by the PCs might be picked up even though doing so would not be "rational" or "realistic" for the NPCs.
I can't (and won't try to) speak for the other two, but I'd find the behavior of the player whose character insulted the tyrant while I was negotiating with him to be literally infuriating. You're not only keeping my character from achieving the goal of the negotiation now, you're keeping my character from ever achieving that goal with this NPC. It has vibes of PvP to me--and I utterly detest PvP.
I don't feel the force of that ever. A fortiori I don't feel its bolded force.
Why does PC A insulting a NPC prevent PC B from ever achiving B's goal with that NPC?
In our Cortex+ Heroic vikings game, the fact that one PC (the skinchanging trickster) failed in his atempt to sell a giant chieftain his own ox after stealing it from the barn (the chieftain recognised the ox and tried to eat the offending PC) didn't stop another PC (the level-headed warthane) from first persuading a giant shaman of the importance of his mission and with the shaman's help then persuading the chieftain himself to offer help rather than eat the PCs.
I could probably think of other actual play examples, but that's the first one that came to mind.
Besides my own experience, there is the experience of others. Who has had the sort of thing described in the OP happen in Prince Valiant, or Burning Wheel, or Dungeon World? That is - to be clear about the sort of thing described - who has had a session result in a player apologising for "ruining the campaign" because a confrontation between PCs and a ruler led to PCs being escorted out by guards to be executed with the GM seeing no way out but either "reward[ing] murder-hoboism and let[ting] them escape with a deus ex machina?
I wasn't saying it was likely. I was saying it was plausible. I was kinda hoping you'd think about (and explain--thanks for doing that) how the situation could be handled if it arose in those other games.
I can see how you might understand it that way, but my intended meaning was that the game/fiction would allow for the characters (or the rest of the party) to arrange their escape--as you proceed to demonstrate. I'm not surprised that PbtA games have such mechanics, as well, given how they seem to be focused around complications--and being captured seems as though it could be a complication.
Prince Valiant has a different mechanical framework from BW, but one option for a player in possession of a Storyteller Certificate is to Find and Escape Route or Escape Bonds. From p 45 of my imprint:
Well, yes, that's apparently the more common thought. I admitted that I have a tendency to think backward and end up in strange places. I've had a player tell me point-blank he didn't ever want to play in a dungeon-crawl if I ever wrote one, specifically because I think so strangely. (NARRATOR: He's playing in a dungeon-crawl that I wrote. He has described it as "nightmare-fuel.")
As to what the GM has in mind: Maybe it's how the GM prepped the character. A GM might prep the character as reacting to insults by cowering in the corner and crying for his mommy. A GM might prep the character as reacting to the insults by havng the offending characters imprisoned or exiled. A GM might prep the character in any number of ways, and could then have that character behave according to its nature, as prepped. If the PCs know about the character's nature, they can behave accordingly; it seems from the OP that they at least had the opportunity to learn about the NPC's nature, and behaved the way they did anyway.
Aragorn in your example fails to jump the distance by the way, no roll, if his Strength is less than 20. If some special circumstance were present, he might get a check to jump an unusually long distance.
That's not entirely accurate. Strength(Athletics) allows PCs to try and jump an unusually long distance. It doesn't give how far and with what DCs, so one DM might be like for every 5 you get on the check, you go 1 extra foot, and another might be for each number higher than 15 you roll, you go 1 extra foot or a number of other methods.
You get to go your strength distance with no roll(certain). X extra feet possibly, depending on the roll and DM method(uncertain). And no roll if the distance is simply not possible with Strength + max X(certain).
Because I expect the insulted character to remember that insult, and I probably used all of PC B's good mojo not getting roped into PC A's idiocy? Because I expect goals passed up or missed not to be available again via the same path? It's clear we have pretty wildly different expectations of play in most cases, in terms of the fiction and in terms of the rules of the game and in terms of player behavior around the table.
In our Cortex+ Heroic vikings game, the fact that one PC (the skinchanging trickster) failed in his atempt to sell a giant chieftain his own ox after stealing it from the barn (the chieftain recognised the ox and tried to eat the offending PC) didn't stop another PC (the level-headed warthane) from first persuading a giant shaman of the importance of his mission and with the shaman's help then persuading the chieftain himself to offer help rather than eat the PCs.
So your trickster's actions weren't able to derail the warthane's actions that had already happened. Makes sense to me. I dunno if I'd have stepped in so readily as the warthane, though. Maybe the giant chieftain only needs to eat the one PC (the idiot trickster, in this case) and after that he'll be more willing to deal with the other PCs who had nothing to do with the idiocy.
