I rechecked my numbers and what I gave you is what I got. When measuring out the flour I tried to do it as an ordinary person would do in the home. I cleaned the cups before each set of measurements with a given flour, tared the measuring cups, and I kept the scale surface clean but I otherwise just stirred, scooped and leveled, and noted the numbers. I did note, however, that the greatest variations in the numbers seemed to be with the 1-cup measuring cup. At the time, I wondered why this was so, but I was doing nothing different with the one-cup measuring cup than with the other measuring cups. Usually I spoon the flour into the cups rather than scooping before leveling but this time I followed the method you mentioned. I didn't shake or tamp the cups on a hard surface.
After your post, I looked at the measuring cups and saw that there were ml markings on them. For the 1-cup, it is 236 ml, for the 1/2-cup it is 118 ml, and for the 1/4-cup it is 59 ml. Clearly, the ratios are proportionate and correct. I used two measuring tapes to cornfirm my measurements of the cups themselves, trying to be diametrically accurate and not measuring the thickness of the metal itself, but maybe I wasn't close enough or accurate enough. I'm sure using the ml numbers should produce more accurate volumes, although I don't think that will account for the different densities.
Do you have any suggestions?