I really like the advantage/disadvantage system in 5e.
Has it been play tested as a sole addition to the Pathfinder rules and practically or theoretically demonstrated and found to have any breaking change impact or unforeseen consequences?
How can I implement (dis)advantage in Pathfinder without breaking anything?
Practical, evidenced based answers (solid maths from the playtest or theory) rather than speculative answers please.
There are many, many effects in 5th that grant (dis)advantage. (Dis)advantage is a core part of the system, and so there are tons of things that grant either of them. Whether or not adapting this to Pathfinder will break anything depends heavily on exactly what is going to grant you (dis)advantage. Here are a few examples that I think illustrate the situation.
Before I continue, I'd like to note a few numbers (thank you, AnyDice). The mean value for an advantage roll is 13.82, and there is a 51% chance of getting a number 15 or higher. The mean value for a disadvantage roll is 7.71, and there is a 49% chance of getting a number 7 or higher. The actual increase or decrease in odds between a regular roll and (dis)advantage changes depending on your target number, but if you need to roll a 10, then advantage is 25% more likely to succeed and disadvantage is 25% less likely to succeed. Because of this, I'm going to use the mathematical shorthand that (dis)advantage is a +/-5 to the roll, unless there's a specific reason to not do this.
Inspiration as a source of advantage is basically harmless. Giving players an occasional +5 to an important roll isn't going to have any long-lasting impact on the game, since it will necessarily affect a tiny number of rolls. In my experience, Inspiration only comes once every few sessions. This will have no more effect on a game than the various Action Point rules that grant small bonuses to specified rolls, like the Mythic Surge mechanic in Pathfinder.
This is where things get a bit hairy. The next logical step from granting (dis)advantage on Inspiration is to grant (dis)advantage whenever you would normally grant a +2 circumstance bonus for a beneficial circumstance. In general, this means that players will be much more likely to try and get circumstance bonuses, because they'll be worth much more. However, this generally won't have a huge effect on the game; circumstance bonuses like this aren't super common, in my experience, so adding this kind of (dis)advantage won't likely cause many problems. Watch out for players trying to game the system to get more circumstance bonuses of you do this, because if you give out these bonuses more than once a session or so, you might find that players are getting much higher checks than the system usually accounts for.
In 5th, very few things grant a +2 bonus to a d20 roll, since that idea was phased out in favor of (dis)advantage. The logical final step for adding (dis)advantage to Pathfinder would be to replace every +2 bonus with advantage, and every -2 penalty with disadvantage. This would give you a system that looks a lot like 5th, as far as bonuses are concerned. This would have two big effects: First, there will be a much greater incentive to get those +2 bonuses, since they are almost always larger now. Flanking will be a bigger deal. Second, most effects won't stack. Since (dis)advantage doesn't stack with itself, effects that would normally stack won't under this system. That means that it's a lot harder to get the super-high bonuses that high-optimization players love. This might end up being a good thing, since stacking bonuses of various types can become a pretty big problem in some games, and this could be a good balancing factor.
There is one thing that Pathfinder has that 5th doesn't which makes adding advantage especially risky: crit-fishing builds. In 5th, it's very hard to get a large threat range. In Pathfinder, it's pretty trivial to get a 15-20 range. Normally, crit-fishing is a losing strategy, but with advantage, a 15-20 crit range means that fully half of your attacks are threats. If you only get advantage in a small number of circumstances, this isn't a big deal, but if you replace all or most +2 bonuses with advantage, this becomes a problem. This counts double if flanking gives advantage, rather than a +2 to hit. A rogue with a couple crit feats, two scimitars, and a flank buddy will be much, much more powerful with such an implementation. Basically, watch out for crit-fishing builds if you add advantage to more than a few rolls.
It isn't broken, but you would have to be careful.
Pathfinder uses a lot of situational modifiers to give you the results you use. These modifiers stack in many scenarios, and that is what the advantage/disadvantage system attempts to avoid.
Advantage gives approximately the equivalent of a +3-5 to the roll, statistically. WotC states that it is the effective equivalent of a +5 to a roll. Many monsters built with PF rules take in to account that there will be a lot of modifiers stacking with each other to form the bonuses needed to hit a huge AC or save DC.
Basically the trick is selecting what to use adv/disadv with and what not to. I would likely restrict it to only the situational modifiers, simplifying adjudication through stacking bonuses some, but allow spells and magic items to stack as they always have. This allows the core balance to be retained, removes the necessity to tinker with numbers on monsters to compensate for drastic system changes by not overusing a mechanic that the system wasn't originally built for, but the mechanic remains useful.
It would take some testing to ensure it works just right, but it can be used well. You just can't use it as liberally as 5e does in PF because they weren't built with that mechanic being intrinsic to all actions.
Thus, don't use it to replace every bonus, just those that need quick decisions on the fly. In the circumstances under which you use it, use it consistently. Apply it to all situational modifiers, for example.
It may in fact break Pathfinder... depending upon both how far you implement it, and just what parts of Pathfinder are important to you.
Pathfinder (and D&D 3.0/3.5) all rely upon large piles of modifiers. The target numbers scale based upon the assumptions that these are in play. Removing them to replace them with 5e style advantage/disadvantage doesn't do the same thing.
Mean, median and mode are the most relevant numbers for a die throw... but let's include min and max
Pathfinder presumes the shifts from a variety of sources, and so sets the range of difficulties to match for a number of things. (Just as did 3.X D&D.) If you replace most modifiers (but not all), then whichever cases you don't account for now no longer get balanced with the ones you switched over to (dis)advantage.
If you switch over ALL modifiers except attribute, base attack bonus, and skill, it probably won't be broken, but it will be VERY different. Most especially since the basic principle of the (dis)advantage system is that it's not stacked... If you have: advantages only, roll with advantage; disadvantages only, roll with disadvantage; both advantage and disadvantage or neither, roll normal.
Note that switching from to-hit bonuses to advantage means that certain high-AC monsters also become near unkillable... because the ability to accrue situational modifiers no longer increases the maximum AC you can hit. What you can hit, you hit more often, but you can't push up the maximum AC you can hit.
Also note: advantage becomes WAY more powerful when the threat range is wider than 20.
Threat 1d20 Advantage Disadvantage
20 5% 9.25% 0.25%
19-20 10% 19.00% 1.00%
18-20 15% 27.75% 2.25%
17-20 20% 36.00% 4.00%
16-20 25% 43.75% 6.25%
15-20 30% 51.00% 9.00%
This WILL screw with your game play. Advantage will make big crits massively more common. Almost twice as often for a given threat range. Especially if you allow advantage on the to-hit to be used also on the confirmation.
So, it will definitely break the encounter balance system (as high AC isn't accounted for as well) to some degree. Further, it may break the balance between spellcasters and warriors. In partial implementation, it can result in many more or many fewer crits.
It could very easily break a pathfinder campaign to simply add advantage/disadvantage because giving someone advantage/disadvantage could easily have a much greater effect than intended. I pulled this chart off http://onlinedungeonmaster.com/2012/05/24/advantage-and-disadvantage-in-dd-next-the-math/ and have seen it elsewhere.
The real problem comes in the fact that advantage/disadvantage is a one time huge help or hindrance in a system which already assumes that such helps/hindrances are calculated with the modifiers.
In many cases in pathfinder giving a character 2d20 to get a desired outcome is pretty much guaranteeing that the result the DM desires in a given situation is the one which results. For example a character with a BAB of +5 attacking a AC 17 creature will succeed nearly 70 percent of the time. This turns into 15% more rolls resulting in hits. Since an enemies challenge rating is based on both how hard it is to hit, as well as how hard it can hit back it means that giving a character advantage against an enemy would drastically change the creatures challenge rating. In this case it would be the equivalent of giving a character a +5 to hit. 
At the same time making it something that exists outside the system would mean that characters would not be able to game advantage/disadvantage. If you as the DM really want a character to succeed at something, but do not want to totally remove the uncertainty then calling for advantage/disadvantage in extreme situations could work.
If you consider the target number as DC minus the sum of all the modifiers then the effect of advantage is to give two chances to roll the target number. On the other hand disadvantage is requiring that you are requiring the player to roll over the target number twice.
