Using close-coupling calculations of Burke and Moores for the scattering of electrons by ${\mathrm{Mg}}^{+}$ ions in the $3{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ and $3{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2},\frac{3}{2}}^{}{}_{}{}^{}$ states, Baranger's expression for the impact approximation width of an isolated line is implemented for the components of the resonance doublet. These widths are extrapolated to below inelastic thresholds and averaged over elastic resonances according to theoretical threshold laws. In the experimental energy range, results compare reasonably with semiclassical approximations and with a semiempirical method involving effective Gaunt factors extrapolated to zero electron energy.