M3 simply describes a measurement that is polarized and has UV filtered out. I.e. it’s intended to cut the effect of OBAs and first surface reflections. This may be useful if the instrument's reaction to UV is different than that of the human observer.
Have a look at this presentation: http://www.color.org/events/bressanone/15.Vogh-Bressanone.pdf
M3 is a useful for minimizing or eliminating the affects of ink dry-back or dry-down.
A fresh wet ink will have a much higher density, but as it dries, the density will drop lower. Maybe as much as 0.15 density units (1.90>1.75 on gloss coated paper). Using M3 polarized filter make the measurements more consistent, it always measures the ink as if it is still wet.