Gaussian Pyramid - How is Subsampling Rate Related to Sigma?
I've spent a bit of time searching for an answer to this as well.

I suspect since the Gaussian kernel has infinite support there will always be a little bit of aliasing, as there will always be frequencies passed that are greater than 0.25 of the sampling rate. That is, in the upper half of the spectrum.

So one would choose $\sigma$ to keep the amount of energy in the aliased bands to an acceptable level. Using $\sigma = 0.25 f_s$ would give 68%, $2\sigma = 0.25 f_s$ would give 95%, and so on.

From wikipedia: