Social welfare functions generating social choice rules that are invulnerable to manipulation

Any social welfare function f - whether transitive-valued or not - induces a social choice function g as follows: If at profile p in the domain of f there is a feasible alternative x that is "strictly greater than" every other feasible alternative according to f(p) then we set g(p) = x. The domain of g is the set of all such profiles p, whether or not f(p) is acyclic. We specify a condition on a social welfare function that is necessary and sufficient for the induced social choice rule to be invulnerable to manipulation by any individual or coalition, and we generalize to an arbitrary collection of coalitions - including the family of singleton coalitions.