  Hadwiger's conjecture asserts that every graph without a $K_t$-minor is
$(t-1)$-colorable. It is known that the exact version of Hadwiger's conjecture
does not extend to list coloring, but it has been conjectured by Kawarabayashi
and Mohar (2007) that there exists a constant $c$ such that every graph with no
$K_t$-minor has list chromatic number at most $ct$. More specifically, they
also conjectured that this holds for $c=\frac{3}{2}$.
  Refuting the latter conjecture, we show that the maximum list chromatic
number of graphs with no $K_t$-minor is at least $(2-o(1))t$, and hence $c \ge
2$ in the above conjecture is necessary. This improves the previous best lower
bound by Bar\'{a}t, Joret and Wood (2011), who proved that $c \ge \frac{4}{3}$.
Our lower-bound examples are obtained via the probabilistic method.
