Authorship for paper

[lrlrlrlrlr]

I am writing a review article with 2 others in my lab. The review is an invited review my PI told us about. The PI said we can split it into 3 parts and each write our section. The thing that concerns me is, there was no discussion of authorship. The PI will probably be last, but I don't know what will happen with the 3 of us. One person is one of the PI's favorites. This person already has 4 first author papers in the lab and has only been a member for 2 years. Everyone else in the lab things the PI will make this person first author again. I don't have any first author papers and would like to be first for this since I'm finishing my PhD and need it  more than the other person. In past situations of people writing papers in the lab, the PI decided the authors before submission and didn't say anything to them before submission, and a few people have gotten very upset about their positions.

My question is how should this have been handled? Is it the PI's responsibility to say who will be first second etc. before we started writing? Should I say something?

[Eigen]

You should have asked before you agreed to it.  Always discuss authorship at the beginning of a project, including what conditions (e.g., work shifting around) will cause a change in authorship.

It's not a PI's responsibility to decide before you started, although it's something I'd recommend to most PIs to save problems down the road. It is, in the end, the PI's responsibility to decide authorship based on who they feel contributed the most to the article. 

This kind of situation is really hard with authorship, TBH, and clear cut majority/minority contributions are much easier. 

Not having first author papers isn't a reason to get first authorship on this one- to get first authorship, you need to legitimately do more than 50% of the work on the paper. 

[ShogunT]

There should be some constraints that your professor has used to select the first author in a collaboration. Can be round-robin, or the person with the most contribution or something else. I think that one way to find out is to talk to your PI regarding your concern. Also, ask the PI what research/work/writing/etc. can be done from your side for you to be the first author of the in-progress manuscript or future works. Your PI can deny a clear answer, but he/she will probably give you some hints to improve at least.

In my opinion, as the project is coming from your PI (and I guess the PI was also the one giving the topic idea), and if you don't have any significant contribution over other two co-authors, it's not your call to make but your PI to select the first author.