  We introduce and study the GIT CONE of $\bar{M}_{0,n}$, which is generated by
the pullbacks of the natural ample line bundles on the GIT quotients $(\mathbb
P^1)^n//SL(2)$. We give an explicit formula for these line bundles and prove a
number of basic results about the GIT cone.
  As one application, we prove unconditionally that the log canonical models of
$\bar{M}_{0,n}$ with a symmetric boundary divisor coincide with the moduli
spaces of weighted curves or with the symmetric GIT quotient, extending the
result of Matt Simpson arXiv:0709.4037. (Cf. also a different proof by
Fedorchuk and Smyth arXiv:0810.1677)
