The average degree of a multigraph critical with respect to edge or total choosability

Let G be a multigraph with maximum degree at most Δ ⩾ 3 such that ch ′ ( G ) > Δ or ch ″ ( G ) > Δ + 1 and G is minimal with this property. A new proof is given for the result (which was already known, apart from a simple calculation) that the average degree of G is greater than 2 Δ except possibly in the second case when Δ = 5 .