Probabilistic Ranking

The probabilistic ranking associates to any AF $F$ a ranking $\succeq^{\theta^p_{\sigma,\circ}}_F$ on $A$ such that $\forall a,b \in A$: $a \succeq^{\theta^p_{\sigma,\circ}}_F b$ iff $P_{\sigma,\circ}(a) \geq P_{\sigma,\circ}(b)$ in the PAF $F[p]$ that gives every argument probability $p \in (0,1)$ and every attack probability $1$. Here $P_{\sigma,\circ}$ is the credulous ($\circ = c$) or skeptical ($\circ = s$) acceptance probability under a semantics $\sigma$.