Counting Ranking

The counting ranking associates to any AF $F$ and damping factor $\alpha \in (0,1)$ a ranking $\succeq^{\theta^{\mathsf{Cnt}}}_F$ on $A$ that counts the attack paths ending in each argument, weighted by $(\alpha/N)^\ell$ for length $\ell$ , with $N = \|A\|_\infty$ the normalisation factor: defenders (even $\ell$ ) count positively, attackers (odd $\ell$ ) negatively.

Reference

Pu, F., Luo, J., Zhang, Y. & Luo, G. (2015). Attacker and Defender Counting Approach for Abstract Argumentation. In: Proceedings of the 37th Annual Meeting of the Cognitive Science Society (CogSci 2015).