This happened to me, they raised my market value by 39%, but my appraisal was capped at 10%, so there was a $60K difference between market and appraisal. I got them to lower both down to something more manageable, because frankly, they messed up.
If they messed up, it's something else. If they did things right and the appraised value is still lower than the market value because of the cap, you would not have much legs to stand on to get the appraised value lowered. If anything, they would want to raise it year after year to catch up to the market value.
