(I'm a little bit late, but here's my position): I believe that it is better to know P in almost all cases.
The Pursuit of Happiness
On a purely theoretical basis, one might argue that not knowing P will bring you more happiness, which is a reasonably desirable objective. However, it is important to realize that happiness is not the only objective that's desirable. For example, it's possible to take psychoactive drugs that make the user (continuously) immeasurably happy. However, wasting away as a drug addict is an existence that most people consider to be undesirable(for good reason). Clearly, this example shows that there are things more important than just happiness. Any good decision has to clearly account for the principle that happiness is not the only important value.
What you don't know can't hurt you....right?
Consider the ostrich, which sticks its head into the ground to evade predators(note 1). The ostrich would probably be very upset if it knew a predator was trying to make dinner out of it. However, no matter how enjoyable head-sticking might be, the ostrich will inevitably be turned into a tasty meal. On the other hand, if the same ostrich attempt to make a run, it has a chance to make it out alive, something that most ostriches probably value, regardless of how miserable exercise may be.
In real life, we can make changes to our environment(note 2). Of course, this isn't really possible without some information about what's going on. In addition, the environment generally affects you, whether or not you want it to(ie ostrich + predator). By having additional information, you often gain the ability to change your environment. Is it possible to cook up scenarios where this more information =/= more ability for change? Sure. But there's almost always something you can do - change your own reactions.
Reacting wisely
Oftentimes, things in the environment can't be changed - terminal cancers, supernovas, etc. But what can be changed(almost always) is how one reacts to the environment. It's possible to react in a hateful, self-destructive manner that creates negative consequences, but it's also possible to react in a positive, constructive manner that mitigates the effect of the change. What you do has a dramatic difference on your happiness.
Obligatory Terminal Cancer Example
In our hypothetical world(note 3), Person A and person B both have incurable terminal cancer - they will both die in 6 months(say July 31st). In January, A is diagnosed with cancer, but B's doctor misses it. A initially is quite sad - he spends some time lamenting his eminent demise. But then, after a while, he finally realizes(note 4) that what he's doing isn't particularly helpful. He retires, calls up his family and friends, and prepares his will and bucket list. As his friends and family enjoy the last of their time with him, he is touched by their love for him, but ultimately is a little sad by the fact that he will soon be dead. When July rolls around, A's friends and family surround him as he slowly dies in the hospital. When he dies, all of his affairs are in order, and his passing is relatively peaceful. In contrast, B checks into the hospital on July 28th and quickly wastes away until he dies. B's family and friends are all shocked by his sudden passing, and no one is prepared. His heirs then begin a fight for his inheritance, which quickly turns ugly in the absence of a will. Years later, A's family remembers their last moments(somewhat) fondly, while B's family can only remember how fast B died, and how they regret not interacting more positively with B.
In this example, both B and his family didn't know, while A and his family were aware of a very unpleasant fact. Yet, A's wise reaction, combined with his knowledge, led to a much more positive outcome for everyone involved.
Santa Claus and spoilers
So when is it better to know nothing? Is it possible that you can't even change your own reactions? Well, two examples are Santa Claus and movie/book spoilers. In both these examples, there's not only so much you can do to forget the information - and knowing won't necessarily give you the opportunity to make physical changes. At first, it might seem that not knowing these things has significant merit. But then, a deeper look might yield better understanding. In the case of Santa Claus, the damage dealt is to your sense of imagination and sense of wonder. With movie spoilers, you don't get the same opportunity to be scared, or become as engaged with the show. But there's a lot of ways to be scared, to imagine, or to be thrilled. Santa Claus or that TV series isn't the only way to get that emotion. It's possible to acknowledge that Mr. Claus isn't real - but exercise that imagination elsewhere and eventually make an amazing invention. It's possible to get spoiled, but still remain interested in TV shows. After all, you can still get a good amount of happiness from knowing - placebos still work fairly well when people know that they're fake(note 5). In return for the minor loss, you gain the ability to make changes later down the road, and we've seen how those changes can make a big difference. Are there scenarios where the loss might be too severe? - sure. Are they by far extreme and rare? - probably.
In summary, knowing more is almost always better. Very often, that knowledge allows you to make meaningful changes. Although these changes might only be mental, they can make a huge difference. Even if there is no apparent mental/physical benefit for knowing, the losses aren't terrible - you generally don't lose that much, and that knowledge might one day help you.
(note 1): ostriches don't actually stick their heads in the ground to avoid predators, though it's commonly believed to be so. The point stands though, doing such a maneuver is not very effective.
(note 2): Unless you're a complete fatalist, of course. But then, this discussion doesn't really make sense to you, because the misery you feel is already predetermined, and hypothetical questions like this one don't make sense.
(note 3): It's conceivable that this could happen, but this is not based on any single real story.
(note 4): Hey, who knows; perhaps he read my excellent post
(note 5): Seriously, yeah. http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0015591 . To be a little fair though, Plos one isn't exactly the most reputable journal, but it was done by Harvard researchers, and it's something like 60% with knowing placebo vs. 35% without, which is fairly hefty.
