You have to think about the change in Nyquist frequency between both images. If the Nyquist frequency of the original image is N, the downsampled image will have a lower Nyquist frequency, xN, where x is related to the ratio of sizes between the final image and the initial one. You would need to remove those spatial frequencies which are higher than xN in the original image before downsampling it.
The power spectrum of a Gaussian in the image space, is also a Gaussian in the frequency space. If we ignore for a moment the second dimension, the Gaussian in the image space is defined as exp(-x^2/s^2), where x represents your pixels. This is mapped to the frequency space as exp(-w^2*s^2), where w is the frequency. The sigma parameter (s) shows that a broad Gaussian in the image space, corresponds to a narrow Gaussian in the frequency space.
You would like to choose a sigma parameter that yields a very low value in frequency space at the frequency that corresponds to the Nyquist frequency of the down sampled image.