The question and Weissman's answer are good, so this is just a distraction: are utils and bits really thought of as units? The mathematical formalism of e.g. physics doesn't actually have (or doesn't require) units, but you can extract them by thinking about the symmetries of the theory: e.g. distance is measured in the same units vertically and horizontally because the laws of physics stay the same after changing some coordinates. How do people think about this in economics?