Answer: Hobbes felt that society naturally correspondent to a State of Nature, and that this State of Nature is a State of War, a war of “all against all”. In order to avoid living in a State of Nature, and therefore avoiding a State of War, which can only be done by submitting some mutually recognized public authority.
Anything related to: that the only right people give up in order to enter into civil society and its benefits is the right to punish other people for violating rights. No other rights are given up, only the right to be a vigilante