Immunity to credible deviations from the truth

We introduce a notion of non-manipulability by groups, based on the idea that only some of the agreements among a set of potential manipulators may be credible. The derived notion of immunity to credible manipulations by groups is intermediate between individual and group strategy-proofness. To prove that our new requirement has bite, we provide characterizations of strategy-proof social choice functions that separate those rules that satisfy it from those that do not for a large family of public good decision problems