The administrators of the executive power may be either elective or not; and in the former case all or only some of them may be elective. They are elective in a proper democracy, that is to say, in a democracy which recognizes representation. If all the public officials are directly elected by the whole people, the democracy is a pure democracy; if only some, it is a mixed democracy. The public officials may also fill vacancies themselves; this is the case in a pure aristocracy. But if only some of the magistrates are thus replaced by the public officers, and if the others are again directly elected by the people, then the form of government is that of a democratic aristocracy. A permanent president (monarch) may also be elected to exercise the executive power during his lifetime. In all these cases, either all citizens of the commonwealth, or only some of them, are eligible to office. Eligibility may, therefore, be limited or unlimited.