  We show that the traditional concept of the uniform electron gas (UEG) --- a
homogeneous system of finite density, consisting of an infinite number of
electrons in an infinite volume --- is inadequate to model the UEGs that arise
in finite systems. We argue that, in general, a UEG is characterized by at
least two parameters, \textit{viz.} the usual one-electron density parameter
$\rho$ and a new two-electron parameter $\eta$. We outline a systematic
strategy to determine a new density functional $E(\rho,\eta)$ across the
spectrum of possible $\rho$ and $\eta$ values.
