In the last several decades, conformal blocks have been studied by many algebraic geometers who are interested in the geometry of moduli spaces of vector bundles. Recently, people have begun to study the relation between conformal blocks and the birational geometry of the moduli space $\bar{M}_{0,n}$ of stable pointed rational curves, because they give a huge family of base point free divisors on $\bar{M}_{0,n}$. In this talk, I will discuss an example of interaction between three approaches to the birational geometry of $\bar{M}_{0,n}$: stack theoretic viewpoint, GIT, and conformal blocks. This is based on a joint work with A. Gibney, D. Jensen and D. Swinarski.