Does familiarity (or lack thereof) with subject modify the skill DC?

Question

Foreword: I am using 3 characters from Forgotten Realms, just to illustrate the scenario. The question is not about FR, but about skill mechanics and DC. Also history is used below just as an example.

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Given 3 characters with the same history skill total (same ability modifier, same proficiency), each of them alone (no assist) facing the same history skill check:

• The 1st one is from a radically different background, and shouldn't have ever even heard about the subject in his homeland.

• The 2nd one is from a neighboring background, that is indifferent to the subject.

• The 3rd character's background has intricate intimacy with the subject, and could have had several chances to learn about the subject during his early days.

The subject are the ruins of an ancient elven kingdom far in the north-west: The elven realm of Eaerlann.

Lets give a face to our historians:

• A dwarf librarian from a dwarf realm underneath Var the Golden in the far south-east. He has never left his lands until now, and had little contact with elven history.

• A human mage from Waterdeep. He traveled a bit around the region, it would not be a surprise if he learned some lore about Eaerlann.

• An elven archeologist from Evereska. His homeland is right next to where the fallen kingdom was, some survivors from that place ended up in his homeland, and has all the interest in elven lore.

Given those 3 characters, how should the DM adjucate the familiarity of each character on the skill roll:

1. Do not change anything. Everyone rolls the same DC as a standard skill check.

2. Grant advantage/disadvantage based on familiarity. The dwarf has disadvantage, the human rolls normal, and the elf has advantage.

3. Modify the skill DC. It is a hard roll for the dwarf, a moderate for the human and an easy one for the elf.

Of course you are not bound by these 3 choices above, but please do state the reasons.
_{(I also suspect that RAW has nothing on the matter)}

Answer 1

There is no right answer to this question, but there is a guideline:

I don't have the DMG/PHB right now to point you the exact quote but in short: The DM decides what to roll.

There are conditions that might favor what you're trying to do (intimidating thugs after you just rolled a critical and killed their boss), and there are conditions that makes things harder (trying to talk your way out of a murder acusation after being found with the murderer's weapon).

Note that none of this situations are defined in the rules, it all comes down to the DM's adjudicating the situation.

There are rules for combat that tells you what to roll and when to roll, there are guidelines to challenges but ultimately, it's all up to the DM, so everything I say after this is utter bullshit if your DM says otherwise but;

Option 2 sounds quite about right, but, if I were in your DM's shoes, I would just give the elf the answer right away. Yes, you DM might rule that this particular task requires no roll due to the conditions.
It makes complete sense that he should know this alredy, hell, in fact it hardly makes sense that he doesn't, if a player invested on some sor of background, he should have that reflected on his knowledge about the world and how he interacts with it.

Answer 2

DC

The DC is user-independent (DMG p.238):

think of how difficult a task is and then pick the associated DC from the Typical DCs table.

There is no indication here that you are thinking how difficult the task is for character X; just how difficult is objectively (except, of course, actually subjectively). Further, all of the examples in published materials set a fixed DC (or occasionally more than one e.g. for active/passive checks or checks using different Skills).

Proficiency

Proficiency applies if you say it does (DMG p.239):

One way to think about this question is to consider whether a character could become better at a particular task through training and practice. If the answer is no, it's fine to say that no proficiency applies. But if the answer is yes, assign an appropriate skill or tool proficiency to reflect that training and practice.

Advantage/Disadvantage

These represent situational effects (DMG p.239):

They reflect temporary circumstances that might affect the chances of a character succeeding or failing at a task. Advantage is also a great way to reward a player who shows exceptional creativity in play.

Characters often gain advantage or disadvantage through the use of special abilities, actions, spells, or other features of their classes or backgrounds. In other cases, you decide whether a circumstance influences a roll in one direction or another, and you grant advantage or impose disadvantage as a result.

For your example ...

1. The DC is the same for all PCs
2. The each have (or don't have) proficiency
3. The dwarf has disadvantage, the human rolls normal, and the elf has advantage.

In particular, note DMG p.239:

Consider granting advantage when ...

• Circumstances not related to a creature's inherent capabilities provide it with an edge.

Consider imposing disadvantage when ...

• Circumstances hinder success in some way.

Answer 3

It depends on the DMing style

Official materials support both absolute DC values and tweaked ones, as well as improvised by the DM.

Absolute DCs examples

The Starter Set adventure, "Lost Mine of Phandelver", contains many examples of absolute DCs, some of them explicitly say it works for "any creature":

Any creature on the ledge when it falls must make a DC 10 Dexterity saving throw

A character who succeeds on a DC 15 Intelligence (History) check recognize the sword

Keep in mind though, most of the adventures assume specific level range. The characters probably will have similar(ish) capabilities, due to the "bounded accuracy" principle.

Tweaked DCs examples

DMG explicitly says that it is the DM's job to "change established DCs":

It's your job to establish the Difficulty Class for an ability check or a saving throw when a rule or an adventure doesn't give you one. Sometimes you'll even want to change such established DCs.

It also says personal stats like character level should be taken into consideration:

If you find yourself thinking, "This task is especially hard," you can use a higher DC, but do so with caution and consider the level of the characters. A DC 25 task is very hard for low-level characters to accomplish, but becomes more reasonable after 10th level or so.
(DMG p. 238, "Difficulty Class")

The "Lost Mine of Phandelver" also has several examples of tweaking the DC depending on various reasons.

In LMoP, DC sometime depends on characters doing specific things:

If the wolves are given food, the DC drops to 10.

If the characters are searching for traps, the character in the lead spots the trap automatically if his or her passive Wisdom (Perception) score is 12 or higher.

It also has an example of automatic success depending on character having the proficiency:

Any character proficient in Arcana can see that ... apparatus appears to be set up to brew potions of invisibility

Answer 4

Advantage and DC are character-independent. You're looking for Proficiency.

DCs are set independently of who is attempting them (DMG 238, emphasis added):

If you've decided that an ability check is called for, then most likely the task at hand isn't a very easy one. Most people can accomplish a DC 5 task with little chance of failure... ask yourself, "Is this task's difficulty easy, moderate, or hard?"

For more evidence on this point, note that spell save DCs are determined not by the person who is saving against them, but rather the caster's stats (PHB 75). Likewise, consider this example from the DMG (239):

Let's say a door requires a successful DC 15 Strength check to be battered down. A fighter with a Strength of 20 might helplessly flail against the door because of bad die rolls. Meanwhile, the rogue with a Strength of 10 rolls a 20 and knocks the door from its hinges.

Note that the fighter who is super strong doesn't face a lower DC, and the weaker rogue doesn't face a higher DC--the door's DC is determined by its material properties, not its challenger.

First, advantage is centered around temporary advantageous circumstances (DMG 239, emphasis added):

Advantage and disadvantage are among the most useful tools in your DM's toolbox. They reflect temporary circumstances that might affect the chances of a character succeeding or failing at a task.

DMG 239:

Consider granting advantage when ... Circumstances not related to a creature's inherent capabilities provide it with an edge.

However, proficiency is centered on training and practice (DMG 239 emphasis added):

One way to think about this question is to consider whether a character could become better at a particular task through training and practice. If the answer is no, it's fine to say that no proficiency applies. But if the answer is yes, assign an appropriate skill or tool proficiency to reflect that training and practice.

Using Proficiency in practice

With these distinctions in mind, I would treat the three characters this way:

1. No proficiency bonus. While the librarian might be proficient generally, he has no training or knowledge in this particular question, so he doesn't get his proficiency bonus. This removal of the bonus is precedented by tool proficiencies, which only apply when the tool is actually being used (DMG 239).
2. Normal proficiency bonus. This is the average case, where the character might know something more than the average person.
3. Double proficiency bonus. For the purposes of this check, the elf is super-proficient and has a much higher inherent chance of success. The DMG uses doubled proficiency bonuses to represent particularly heightened abilities or special knowledge, such as the Book of Vile Darkness (DMG 223):

You can reference the Book of Vile Darkness whenever you make an Intelligence check to recall information about some aspect of evil, such as lore about demons. When you do so, double your proficiency bonus on that check.

or the Talisman of the Sphere (DMG 207)

When you make an Intelligence (Arcana) check to control a sphere of annihilation while you are holding this talisman, you double your proficiency bonus on the check.