 Golden ratio approximation for MAX-2SAT

When each variable appears in at most one normalized singleton clause, satisfy that favored literal with probability $p>1/2$ and choose independent variables. Every proper binary clause is then satisfied with probability at least $1-p^2$, and every singleton with probability $p$. Maximize the common lower bound by $p=1-p^2$, giving the reciprocal of the golden ratio. The method of conditional probabilities derandomizes the construction, obtaining approximation ratio $p$. Tautologies are harmless; the singleton restriction must be applied after removing repeated literals within clauses.