From my understanding, dithering is used to mask the systematic error that one introduces by reducing the bitrate simply by truncating (i.e. chopping off) the least significant bits. This makes sense to me.
But what if instead of truncation one uses the lower bits to round instead, wouldn't that be even better for quality? So say you reduce the bit rate from 24 bit to 16 bit, use the lowest 8 bit of the 24bit sample to decide if a one is added to the truncated value (with e.g. round-to-even for the half-way point 128). That would seem like the most "correct" way to me, as it is the mathematically closest representation of the original signal in the lower bitrate.
And by using rounding instead of truncation, there may possibly be less need for dithering afterwards (when reducing to otherwise near-transparent bitrates like 16bit or above, as obviously rounding vs truncation won't matter much for easily audible quality-reducing reductions). Since the maximum amplitude of the error signal by rounding is only half of that of truncation I assume the introduced noise is more quiet, which might be quiet enough to not be noticeable at 16bit and possibly preferable over the added dither noise. So my question is, are there publicly available studies that compare the quality of truncation vs rounding (with and without dithering)?