  Understanding the evolution of the Milky Way calls for the precise abundance
determination of many elements in many stars. A common perception is that
deriving more than a few elemental abundances ([Fe/H], [$\alpha$/Fe], perhaps
[C/H], [N/H]) requires medium-to-high spectral resolution, $R \gtrsim 10,000$,
mostly to overcome the effects of line blending. In recent work (Rix et al.
2016; Ting et al. 2016) we presented an efficient and practical way to model
the full stellar spectrum, even when fitting a large number of stellar labels
simultaneously. In this paper we quantify to what precision the abundances of
many different elements can be recovered, as a function of spectroscopic
resolution and wavelength range. In the limit of perfect spectral models and
spectral normalization, we show that the precision of elemental abundances is
nearly independent of resolution, for a fixed exposure time and number of
detector pixels; low-resolution spectra simply afford much higher S/N per pixel
and generally larger wavelength range in a single setting. We also show that
estimates of most stellar labels are not strongly correlated with one another
once $R \gtrsim 1,000$. Modest errors in the line spread function, as well as
small radial velocity errors, do not affect these conclusions, and data driven
models indicate that spectral (continuum) normalization can be achieved well
enough in practice. These results, to be confirmed with an analysis of observed
low-resolution data, open up new possibilities for the design of large
spectroscopic stellar surveys and for the re-analysis of archival
low-resolution datasets.
