Abstract: When G is a graph, L is a list assignment on G, and b is a nonnegative integer, we say that G is (L:b)-colorable if one can assign each vertex v a set of b colors from L(v) such that adjacent vertices receive disjoint sets. A graph is (a:b)-choosable if it is (L:b)-choosable whenever $|L(v)| \ge a$ for all vertices v; note that (k:1)-choosability is the same as ordinary k-choosability. This notion was introduced by Erdős, Rubin and Taylor in their first paper concerning choosability. It is known that all 2-choosable graphs are (2m:m)-choosable for all m, but the converse does not hold; in fact, it was shown by Alon, Tuza, and Voigt that every bipartite graph is (2m:m)-choosable for some (extremely large) value of m. A graph is 3-choosable-critical if its choice number is 3 and all its proper subgraphs are 2-choosable. Voigt showed that for odd m, G is (2m:m)-choosable if and only if G is 2-choosable, and conjectured that for even m, every bipartite 3-choosable-critical graph is (2m:m)-choosable. Resolving Voigt's conjecture in the negative, we determine which 3-choosable-critical graphs are (4:2)-choosable, and we conjecture a full characterization of (4:2)-choosable graphs. We also recover a weaker version of Voigt's conjecture, which we will discuss if time permits. This is joint work with Jixian Meng and Xuding Zhu.