For example, if there is a small error in the green channel that cannot be represented, and another small error in the red channel in the same case, the properly weighted sum of these two errors may be used to adjust a perceptible lightness error, that can be represented in a balanced way between all three color channels (according to their respective statistical contribution to the lightness), even if this produces a larger error for the hue when converting the green channel.
For example, if there is a small flaw in the green channel that cannot be accurately depicted, and another small mistake in the red channel in the same case, the correct weighted sum of these two errors can be used to adjust a noticeable lightness error, which can be fairly represented across all three color channels (based on their statistical contribution to brightness), even if this results in a greater error for hue when converting from the green channel.