First and foremost csm members are largely a political stunt to make people think that ccp has interest in them, and while it may be true it is, its not in an meaningful way people expect.
To understand this further, lets look at the way development generally happens for things in a game like eve.
First a senior or lead designer (depending on what part of the game we are talking about its generally a senior content designer or the lead designer (the creative mind if you will).
Generally after this mock-up the UX designer / project manager(User experience designers) collect data, and give feedback on the design of the designer finding ways to improve the design by the feedback they got (usually by a collection of various types of research, of which the csm is one type).
After this research some review and improvements are generally made and its passed back through the ux/project manager and then put into post production.
When it comes to the CSM and their influence in all this process, you can be safe to know they probably make up no more then 10-20% of the decision that is made. Most of this is decided by the powers well above these positions (like the marketing team, corporate executive staff, and or investors approval, etc). Granted these values really depend on how extensive the UX designers are invested at ccp.
The position of UX designer is very broad, and has many sub-sections to it. Some do research, while others handle UI (which to be honest should be shifted into its own section) to name a few, and often the position is interchangeable with project manager (though they handle most of the over all process, then a part in it).
Hopefully that will clear up exactly what position the csm has in the process of the development cycle. It’s a notable amount, but its generally not anything more then a quarter of the over-all say.