Discussion-Based Ranking

The discussion-based ranking associates to any AF $F$ a ranking $\succeq^{\theta^{\mathsf{Dbs}}}_F$ on $A$ such that $\forall a,b \in A$: $a \succeq^{\theta^{\mathsf{Dbs}}}_F b$ iff $\mathsf{D}^F(a) \succeq_{\mathrm{lex}} \mathsf{D}^F(b)$, where $\mathsf{D}^F$ is the discussion count.