Halftone contains a number of jitters; the rotational jitter available for some of the shapes and the placement jitter. These randomly alter an aspect of the halftone effect in a repeatable and scalable way; consecutive renders will always show the same jitter deviation, independent of resolution.
The "Randomizer" setting in this panel allows the user to select different random patterns for both jitter operations at once by placing the slider at the position you prefer, based on the preview.