  We parameterize Hubbard and spin models for EtMe$_3$Sb[Pd(dmit)$_2$]$_2$ from
broken symmetry density functional calculations. This gives a scalene
triangular model where the largest net exchange interaction is three times
larger than the mean interchain coupling. The chain random phase approximation
shows that the difference in the interchain couplings is equivalent to a
bipartite interchain coupling, favoring long-range magnetic order. This
competes with ring exchange, which favors quantum disorder. Ring exchange wins.
We predict that the thermal conductivity, $\kappa$, along the chain direction
is much larger than that along the crystallographic axes and that
$\kappa/T\rightarrow0$ as $T\rightarrow0$ along the crystallographic axes, but
that $\kappa/T\rightarrow\textrm{a constant}>0$ as $T\rightarrow0$ along the
chain direction.
