Alright, so since we're roleplaying we can assume there are three cases. There is solo roleplay (this exists, and while considered self-mastubatory should be considered), one on one, and party based roleplay. Let's go through each case.>Solo
This is the one where I can see first and third person working equally well, as the same rules for writing any literature apply and the flow of information won't be broken. Second person is not viable as you're essentially telling the reader they are the character while making decisions and deductions on their behalf.>One-on-One
I've seen this done in one of two ways. Both parties doing third person or one party using second person and the other using third. The reason first person isn't viable for the 'other' party in the latter example is due to the fact that re-reading the roleplay in post is made all the more confusing when transitioning from post to post. >Party
The only real option here is everyone using third person. The problems with first in one-on-one are only exacerbated here. Imagine each player writing 'I swing...' 'I look...' and so on. Assuming a party between the sizes of three to five a gamemaster is goign to be seeing stars twenty minutes in. Second person doesn't work on the gamemaster's part due to having to give information to multiple players at the same time (with niche cases such as 'You all...' being the exception).
This might be just because of my own style of playing, GMing, and writing, but I think Third person is the best catch all for roleplaying in almost any form as it allows for easy reading in post and keeping information from being misconstrued during play.