The main objects of this study are finite dimensional graded representations of the symmetric group \( \mathcal{S}_n\), including the (reduced) Orlik-Solomon algebra of the braid matroid as well as the Cordovil algebra of the oriented braid matroid. Explicit representations of the rings under consideration are given in an appendix to aid the reader. For graded representations of a finite group the authors expand the notion of equivariant log concavity by defining its strong form. Conjectures concerning the existence of isomorphisms among the graded \(\mathcal{S}_n\)-representations as well as their strong log concavity are made. For low degree the conjectures are proven by using representation stability to reduce to a finite number of cases and performing computer checks using SageMath.