Simplified tight analysis of Johnson's algorithm

In their paper “Tight bound on Johnson's algorithm for maximum satisfiability” [J. Comput. System Sci. 58 (3) (1999) 622-640] Chen, Friesen and Zheng provided a tight bound on the approximation ratio of Johnson's algorithm for Maximum Satisfiability [J. Comput. System Sci. 9 (3) (1974) 256-278]. We give a simplified proof of their result and investigate to what extent it may be generalized to non-Boolean domains.