In this article we recall the interesting problem about local and global proportionalities in ball rings posed by Fishburn, Hwang and Lee in 1986. For the symmetric neighborhood case, we decrease the upper bounds (which were conjectured to be tight) by giving a uniform construction for the three subcases distinguished in the original paper. Furthermore, we describe our technique of obtaining upper bounds because it may be re-used for the study of other instances of the original problem.