Now, on to the long-winded explanations!
Improved Judgement (2 ranks) reduces the cooldown of Judgement by 1 second per talent point, up to 2 points. The normal cooldown is 10 seconds, so you can reduce this to an 8 second cooldown. For a protection paladin, this means that you should be able to do 25% more Judgement of righteousness, and that's a big deal; Judgement of righteousness is approximately 15% of your total threat. So it's great, it's 25%*15% = 3.75% more overall threat, and it's a great value per point, right?
The problem is that this doesn't take into account the tanking rotation. If you're tanking a main boss, you must keep holy shield up at all costs. Every 10 seconds it must be recast. It is the highest priority to cast. The next highest priority is consecrate; consecrate is the best source of threat and the best scaling threat a paladin has. What these things end up doing is creating an infinite cycle that most prot paladins call the standard ten-second cycle:
Cast Holy Shield
Seal of Righteousness (these last two steps are done together)
Because Judgement is on a 10-second cooldown and you can reseal immediately, there's never a conflict in times. Sure, consecrate comes up when holy shield does, but that's unavoidable. You never have an unsealed melee swing, you never have to worry about casting holy shield or casting Judgement . You even have another 5 seconds and another 3 GCDs to do something else, like exorcism or avenger's shield.
However, with an 8-second cooldown on Judgement , that all changes. Judgement can never directly conflict with holy shield - Judgement doesn't take a GCD. But resealing does, and that's what conflicts. At that point, you have one of two choices: judge whenever you can and reseal at the next best opportunity or wait to judge and lose the benefits of Improved Judgement . Based on that, here is a 40-second cycle keeping in mind these issues that is optimal for the situation (taken from Lore)
3.0 SoR <- lost 3 seconds of SoR
33.0 SoR <- lost 1 second of SoR
40.0 Judge <- back to where we started
Based on this, we lose out on 4 seconds of sealed swings in a 40 second period. That doesn't account for lag either and it requires perfect timing and reflexes as well as odd things like a holy shield/Judgement macro. This is the absolute best case scenario. Let's assume some more things, like 100 damage per SoR hit, and 400 damage per Judgement . This is the value, roughly, when you're around 200 spelldamage. It scales upwards, but SoR scales more with spelldamage than JoR does over an 8 or 10 second period. At that level of damage, and with a standard 1.8 speed tanking weapon, we're looking at 55 DPS for SoR - or those 4 seconds are equivalent to about 210 Damage.
That means that in a 40 second cycle, you're gaining about 190 total holy damage. Even with improved righteous fury this is a net gain of only 9 TPS - which at the above spelldamage levels is about 1.8% more total threat. And again, this is the best case situation, with the perfect cycle and with odd things like judging when you cast holy shield and no lag. When you factor in lag, it becomes worse. When you factor in that spell hit (which isn't particularly good for paladins) controls JoR but hit and expertise controls SoR, it becomes worse. And none of that factors in the very complicated cycle to maximize the effectiveness here; if you find that you missed a judgment when you could've judged, you've basically wasted that extra threat.
1 point in Improved Judgement makes this much better by comparison; you don't conflict much at all (once every 80 seconds) but you can still judge more often. Still, it results in a complicated threat cycle that must be optimized. I may talk about the 1-point cycle in the future if there's interest.
At this point I should mention that Improved Judgement has its uses. It is stellar when for whatever reason you do not need to optimize for having holy shield up at all costs or cannot consecrate. (an example of not having holy shield up against a boss might be something like Illidan, where you only need holy shield up on shears and know exactly when those will happen) If you need to judge against multiple mobs separately, it's great there too. But this is more of a utility argument than anything else; it is not as good as reckoning or precision for threat.
What should you take instead? Well, Reckoning is roughly equivalent to 1% more threat per point against single target bosses over time, has the advantage of triggering other procs, and requires no messy cycles. It also helps more for grinding and triggers often. The disadvantage of reckoning is the parry gib, but this turns out to be not so special for paladins compared to warriors thanks to the mechanics of paladins and the advantages of holy shield over shield block. Precision, if it's not maxed out, is also better; it ends up being close to 1% extra threat (consecrate is not affected much by spell hit) and has an advantage of increasing your chances of taunting. 1hws is simply an increase to all threat by 1%. My recommendation in general would be to take all of them if you can. 3 points in precision, 5 in 1hws, and 2 in reckoning. 2 points in reckoning will keep it up most of the time against trash while keeping it up a reasonable amount of time against bosses, especially ones that hit with dots.
And clearly, a lot of this is up to personal preference. Reckoning and Improved Judgement and precision and 1hws are all very close to each other in value, and none of them will make or break you as a paladin tank. But the notion that improved judgment is ideal and far better than any other threat talent a prot paladin has is...a myth.
Next up: the effects of expertise on mitigation and avoiding parry gib.