You're asking the right questions, but the problem is in reality you have to ignore the "unbiased" part of the question. GMMichael is working towards a list like:
Inherently, this is biased towards what the DM wants to reward, and the potential goals of the PCs do not necessarily correlate to XP. A "typical" goal is what the GM thinks the goals should be in this case. The language of the question doesn't match the intent.
For what it's worth, I'm zeroing in on some criteria for XP awards. This is the general idea: each challenge is worth XP. No challenge, no XP. Each award is multiplied by its expected appropriate level, and quest-critical criteria are worth twice the non-critical criteria.
Befriend NPC
Defeat NPC
Collect treasure
Discover secret
Quest-specific other
They're intentionally vague - they need to apply to a lot of different quests. As in, an NPC isn't necessarily a "monster,"* defeating doesn't have to mean killing, treasure is about anything of value (intentionally placed as a reward for PCs), a secret could be door/information/etc. The quest-specific other is basically things you need to complete the quest, as long as they're discrete and challenging.
When I look at that list, I wonder why we have (say)
befriending and
defeating NPCs but not, say,
defending a NPC or
avenging a NPC (who has been wronged) or
embarrassing a NPC, etc. And also where the
quests come from - I mean, one could think of Goals in Torchbearer (and analogous Beliefs in Burning Wheel) as
player-authored quests. Which are not foreign to D&D - the 4e PHB and DMG both discuss player-authored quests as a good idea for that RPG system.
As it stands, the list could be reduced to
Resolve a confrontation with a NPC (befriending and defeating being the two main ways of doing that) and
Learn something non-obvious about the scenario (with the collection of treasure and the discovery of secrets being special cases of this).
I also look at the list and wonder what happened to things that are common in Torchbearer and Burning Wheel, but have also been part of the assessment of the quality of D&D play for a long time (typically via the alignment rules) - like
standing up for a commitment or
fulfilling a vow. TB and BW go further than D&D traditionally has done, by also rewarding things like
straining under the burden of a commitment or
finding oneself compelled to abandon a vow. This could be added to a very generic list as
engage with your PC's value/commitment via your play of your PC. Burning Wheel and Torchbearer have their own reasons - partly principled, partly technical - for getting a bit more detailed and nuanced than that, but it would capture the gist. And doesn't seem to me to be any less objective than
resolving confrontations and
learning non-obvious things.
Allowing players to choose their own X.P. rewards can lead to something just as ridiculous as "My PC gets X.P. when they pick flowers or go out for ice cream" - while playing a fantasy-adventure campaign.
Is this "can lead to" based on experience? Or just abstract conjecture?
It's not something I've ever come across; in my experience players want to play the game (that's why they turn up!). And as
@Nytmare also posted, if a player authors a goal then it is the GM's job to set obstacles in the way of it.
The player who chooses the easier-to-achieve in-fiction goal etc. is favoured.
If your goal is to rebuild your family's farm and my goal is to become Emperor of Rome, you'll level up through goal achievement long before I will!
As
@Nytmare posted, in the advancement system being discussed, XP are awarded for
taking action in pursuit of a goal as well as for attaining it. And for
struggling with ones commitments as well as for adhering to them.
A player who (for whatever reason) wants to increase their ration of Fate points earned to Persona points earned has a reason to choose goals that are hard to achieve. (This is something I've seen in actual play.)
Additionally, a player somehow actually having a goal of picking flowers mundanely and somehow getting that XP is going to be bored to hell with all of the weird combat stuff that has nothing to do with calm cozy flower-picking in the new level they just earned. Inside D&D, this impossible motivation might as well be meaningless XP at that point anyway. Even as an analogy the example is contrived beyond credulity.
This thread is in General, but a lot of the posts seem to assume that the RPG being played is D&D (or some sort of D&D clone).
Here's an XP system that is unbiased, but quite different from both TB/BW and D&D. It's from Agon 2e (a wonderful Odyssey-flavoured RPG by John Harper): any event or conflict that is a worthy challenge for the PC heroes triggers a contest. The GM rolls (as per the relevant rules) to determine the obstacle; and each player whose hero participates in the challenge rolls (as per the relevant rules) to see if they can succeed against the obstacle. If the roll falls short, the hero
suffers and one XP (Glory) is earned; of the heroes who succeed, the one who rolls highest is the
best and earns Glory equal to the target number; the other successful heroes earn half that much Glory (round up).
Anything that would make sense within an Odyssey-like contest can be framed as a contest: I've had contests of wits; duels and battles; attempts to persuade or befriend; climbing cliffs and swimming out to sea; sacrificing to the gods and seeking their guidance; etc. I've seen heroes suffer unexpectedly (brought low by their hubris!), and the underdog emerge as the best hero. Sometimes the hero who earns the most glory is the one you would expect (given the dynamics of play, eg how hard/aggressively one player pushes things) but sometimes it's unexpected.
Prince Valiant is yet another XP system, based on Fame, which resembles Agon a little bit but without the competitive element and relying more heavily on GM judgement to set the amount of Fame earned by demonstrating one's prowess.
The list of
resolve an encounter and
learn some non-obvious thing doesn't even extend to such basic stuff as running a race or defending a besieged castle (neither of which is about defeating a NPC, at least in my experience of adjudicating them).