My understanding is that for an RGB color profile working through a standard printer driver (not RIP), the actual gamut volume is determined by the capabilities of the printer and the particular driver settings (which type of inks to use, density, etc.) and should be independent of any profiling efforts.
While the media setting is the primary determining factor, the profile and rendering intent still has an influence.
The gamut volumes of different profiles using the same settings are just different *estimations* of the same actual gamut volume.
Yes, or you might say "ways of defining the color gamut." Problem is, different profiling packages calculate the gamut differently and come up with different results.
For the same paper and same driver settings there should just be one correct number for the gamut volume regardless of profiles.
That may be but if you profile with different solutions and make prints they can visually be very different in terms of their apparent real-world gamut. These real-world differences that we see when making prints are paramount.
In terms of gamut volume, a profile that arrives at this exact figure should be the best.
And how do you determine that? If they are all different, which one is "correct"?
A profile with an inflated gamut volune figure overestimates the gamut and would cause prints to be desaturated while a profile with too small an estimayed profile volume would make colors too saturated anf clip colors too early.
YES!! And that's why you've got to compare profiles by comparing prints made with them - and not gamut renderings. If you only look at the gamut renderings one can falsely conclude that an bad profile is the best.
Now a CMYK profile (or a 12 vector profile for a 12-ink printer? 
) working through an RIP that can actually futz with how individual ink droplets are laid would bea diff erent kettle of fish... 
Right, and a decade ago color geeks always got better results by calibrating and profiling through a RIP. These days, Epson and Canon have done an AMAZING job optimizing the calibration (ink densities, linearization, etc) that's included in the driver and you just can't beat it through a RIP.
To really geek out, CMYK profiling in a RIP really isn't much different from RGB driver profiling since the printer is doing an on-board CMYK to 12 color separation. That 4-13 color separation is highly protected intellectual property that they hold close to their chest but allow certain RIP manufactures to tap into. Because of this, very few RIPs even give you the option to perform a true 12 color calibration and profile. It's just too complicated and the printer OEM's have done such a good job at it already, there really isn't any need to.
If you want to get into complicated CMYK+ color calibration and profiling, check out Epson's new Surecolor S70 printer with metallic silver and white ink - that's fun stuff that's work the extra effort. On an aqueous printer, take it from me and stick with the driver and feel great about how fantastic the results are with RGB profiles. 13 years ago I used to spend all day calibrating and profiling aqueous printers through various RIPs to get better results than one could with the driver - I'm glad those days are gone.
