Gibbard's theorem is an impossibility result in mechanism design showing there is no (non-trivial) universal mechanism for extracting truthful information from players in a game. It states that for any game form (mechanism) in which players hold a set of preferences, at least one of the following three properties must hold:The mechanism is a dictatorship: a single player always dictates the outcome. The mechanism is a duple: there are only two possible outcomes. The mechanism is not straightforward: the optimal action for a voter requires strategic behavior, i.e. it depends on their beliefs about other players.