This is based on the text in Page 5 of Xanathar's Guide to Everything:
Even if more than one factor gives you advantage or
disadvantage on a roll, you have it only once, and if you
have advantage and disadvantage on the same roll, they
cancel each other.
This would imply that an Assassin Rogue, attacking from Stealth, at a target within 5 feet who was Prone and hadn't taken a turn in Combat yet (3 circumstances that grant Advantage, which I will refer to as "instances granting Advantage"), would still only roll normally against a target who happened to be wearing a Cloak of Displacement (one "instance granting Disadvantage"), and thus wouldn't get Sneak Attack damage.
While this probably simplifies "big" encounters where there are a lot of instances granting both Advantage and Disadvantage, it seems to not reward strategic play at all, and vastly increases the power of the Cloak from being a generally-good tool for preventing getting hit for a few turns to entirely countering Sneak Attack on the first turn, meaning that, compared to a Player, an enemy never has to worry about being Assassinated (1st Turn only) or Sneak-Attacked until their later turns, especially since there is no way to Delay a turn in 5e, which means that, if an Assassin Rogue ends-up going first, they can either move and then Ready an Attack (which is a rather clumsy way to work this) or just attack and lose Assassinate.
I know some DMs whom, instead of just ruling that even one instance granting either counters every single instance granting its counterpart, will count each instance granting Advantage, and compare that to each instance granting Disadvantage, and determining which remains after all have been cancelled.
In essence, it can be distilled to the three mathematical expressions, where a is the total of instances granting Advantage, and d is the total of instances granting Disadvantage:
$$
\begin{align}
a – d > 0 & → \text{Advantage} \\
a – d = 0 & → \text{Normal} \\
a – d < 0 & → \text{Disadvantage}
\end{align}
$$
In the case of the above example with the Assassin Rogue, this would mean that, after the single instance of Disadvantage cancels with one of the three instances of Advantage, meaning that the attack ends-up going-through with Advantage because \$3 – 1 = 2 > 0 → \text{Advantage}\$.
How does this houserule change the balance of the game?
Best Answer
I want to start out mentioning the Cloak of Displacement. It's supposed to mess with sneak attack. Going back several editions, it's done a great job of it. Even thematically, it's very hard to attack a vital point when you effectively have double vision against the target (likely more like multidimensional double vision, but I digress). I don't think you need a way to "fix" that the character couldn't have snuck-attack.
With that said, we're currently utilizing this house rule in a game I'm playing, so....
Generally, it doesn't affect overall game balance
In my opinion, it's less fun, because it's more bean-counting. It very much reminds me of editions from years past where you frantically tried to add various numbers together in order to get to the magic number you needed.
"Okay, I rolled a 7, plus my 6 to hit. That's 13. Wait and I have the plus 2 from charging and another plus 1 because this is my favorite weapon. That's 16. OH OH OH Bardic inspiration! 17!"
Maybe you liked that, but I did not.
In most cases, it's a moot point because you only have one source of advantage and disadvantage anyway. In the rare case that it actually matters and you get to apply [dis]advantage in a case where you couldn't not have otherwise, it's no more or less exciting than any other scenario where you would normally get to apply [dis]advantage.
If this is something you're thinking of instituting at your table, talk it over with the players and come to a consensus. Remember that D&D is, by and large, a bad reality simulator and should not be viewed with too fine a lens, lest you see the frayed threads within.