We point out that the universality and precision of the Hall plateaus of ${\ensuremath{\rho}}_{H}^{\mathrm{\ensuremath{-}}1}$ in the quantum Hall effect (QHE) can be understood if the conducting component of the two-dimensional electron gas is behaving like a degenerate, intensely magnetized ideal electron gas, whose exact equations of state enforce precisely this behavior. The ideal gas even gives a good description of the QHE behavior outside the plateaus: the spikes of the longitudinal resistivity \ensuremath{\rho} and the various ``slope'' and ``minimum'' relations connect ${\ensuremath{\rho}}_{H}$ and \ensuremath{\rho}, where it might not have been expected. Localization and delocalization of electrons in the QHE occur automatically in the ideal gas as its electrons pass into and out of a thermodynamic particle reservoir. However, renormalization of critical exponents is beyond the scope of this approximation.