There are lots of exploration rules to draw from all editions of the game...forced marching, environmental hazards, random encounter checks/tables, overland travel rules, guide rules for rangers, divination spells, visibility, dungeon turns/movement, etc, etc.
For interaction there's much less D&D rules precedent to draw from...skills, charm spells, morale, NPC reaction table, and...is that it?
If we want more balance between rules for the 3 pillars, then it's interaction rules that need the most development.
I agree with you here, but's what's interesting is to compare those exploration rules with the combat rules: very fiddly bitsy in comparison. For example, the rules of all editions define pretty clearly the benefits of being Blessed by a cleric in combat (+1 to hit, from memory). But the benefits of using Augury before entering a dungeon are left far more indefinite. And how does Augury help you with evasion, or improve your chance to track?
There is something to be said, in my view, for a greater degree of mechanical cohesion - although their are losses suffered because of abstraction, there can be significant gains by way of useability and integration.
Older editions of D&D have lots of rules support for exploration that the designers could take inspiration from.
However, there really isn't much of an equivalent when it comes to interacting with NPCs; that has always been more free-form.
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each of these "pillars" needs different types of rules. Exploration is well-served by rules which simulate a consistent environment, passage of time, and world paradigm. Interaction is well-served by rules which lean more to the "indie" side and engage players in the fiction.
I don't want to bang the uniformity drum too hard, but some considerations that tell in favour of a degree of uniformity are that it makes it easier to set challenges, to judge PC ability relative to a given conflict, to balance spells (Bless's +1 and Augury's +1 become functionally equivalent), and to award XP (because the difficulty of challenges can be compared).
Conversely, if the utility of Augury in exploration is obscure, or dependent in some ill-defined way on GM adjudication (contrast the somewhat more well-defined GM adjudication that decides whether or not a given fireball sets a particular forest on fire), then players may naturally tend towards Bless instead, which will undermine the design goal of putting the 3 pillars on a par.
I would also think it is good for all action resolution systems to engage players in the fiction.
Combat is well-served by rules which accommodate improvisational stunts while being tethered to hard numbers.
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I don't think it's an elegant solution because you're taking a model that works well in combat (roll and deplete points to win) and trying to apply it to scenarios that don't have clear victory conditions and have multiple possible outcomes.
What *might* be interesting is, for example, to have a stakes-setting element when interacting with NPCs. Something where the players get to influence what the victory / defeat conditions are when there's a conflict of interests.
Maybe even a stunt system for combat would benefit from more flexibility over success conditions and stakes setting! Part of the problem D&D has always had with stunts is treating "death of the opposition" as the only salient stake in combat.
Isn't that how Burning Wheel and FATE handle character traits/descriptors?
In BW character descriptors establish a type of success condition - having your PC do stuff in the fiction that riffs off your various descriptors earns Fate/Action/Hero points. This is somewhat orthogonal, although not completely orthogonal, to having your PC actually succeed at the tasks s/he attempts in the fiction.
This is one of the techniques BW uses to introduce multiple dimensions of success into any conflict, and thereby to handle common issues like players always bringing all their dice to bear, always letting the "face guy" do the talking, never taking prisoners, etc.
I don't want to see a lot of new rules to deal with exploration and roleplay since skill checks aren't a very exciting mechanic.
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Give the DM a helping hand in fleshing out NPCs and how the players could cater to them. Maybe the half-orc doorman isn't easily intimidated by the party fighter, but with a good enough insight check the party druid could infer that he might be easily flattered by the party bard.
This seems to me to be the sort of thing where mechanical systems can help: for example, some sort of robust system for chaining successes onto one another, or for using one ability to open another ability. (Like using movement in combat sets up a flank, which can then open up sneak attack.)
Having multiple dimensions other than simply rolling high on a skill check can make a big difference.
The game also needs guidelines on how to convey these dimensions to the players. In combat, for example, we use maps or descriptions of the layout to convey to players the information they need to bring the movement rules to bear. (This is part of what distinguishes GM scene-framing and adjudication from mere "Mother may I?") What is going to play a comparable role in the case of interaction encounters?
Passions, Traits, Relationships - things which you believe in, people who care about you - all things which can and probably should affect how you perform tasks where they're involved.
But imagine the outrage if relationships augmented abilities in D&D!
And there'd straightaway be a split between the simulationist and the metagame camps, which would manifest itself in debate over whether or not being a victim of Charm Person changes your relationships and therefore your available augments. (And this debate would get particularly bitter when it came to the question of whether your relationships can augment your "throw off the Charm Person" save.)
More seriously, I think they need something but I would be surprised if they go down this route. (But of course I've been plenty wrong before!)