Recently, Atobe gave a refinement of Moeglin's construction of local Arthur packets for symplectic and split odd special orthogonal groups. In joint work with Baiying Liu and Chi-Heng Lo, using Atobe's refinement, we define certain operators which determine when two local Arthur packets intersect. From these operators, we can define an ordering on the set of all local Arthur packets containing a fixed representation for which there is a unique maximal and minimal element. In this talk, we will discuss Atobe's construction, introduce the operators, define the unique maximal and minimal element, and discuss how these elements behave with respect to other orderings.