In Federalist 39, Madison takes up the vexed question of how to define a republic. John Adams once wrote that if past usage were to be the guide, anything and everything would be the appropriate answer, so various were the definitions of previous authors. Madison’s answer was not dissimilar--writers had used the term with "extreme inaccuracy"--but a principled view had to insist that a republican government "derives all its powers directly or indirectly from the great body of the people, and is administered by persons holding their offices during pleasure, for a limited period, or during good behaviour."
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What, then, are the distinctive characters of the republican form? Were an answer to this question to be sought, not by recurring to principles, but in the application of the term by political writers, to the constitutions of different states, no satisfactory one would ever be found. Holland, in which no particle of the supreme authority is derived from the people, has passed almost universally under the denomination of a republic. The same title has been bestowed on Venice, where absolute power over the great body of the people is exercised, in the most absolute manner, by a small body of hereditary nobles. Poland, which is a mixture of aristocracy and of monarchy in their worst forms, has been dignified with the same appellation. The government of England, which has one republican branch only, combined with a hereditary aristocracy and monarchy, has, with equal impropriety, been frequently placed on the list of republics. These examples, which are nearly as dissimilar to each other as to a genuine republic, show the extreme inaccuracy with which the term has been used in political disquisitions.
If we resort, for a criterion, to the different principles on which different forms of government are established, we may define a republic to be, or at least may bestow that name on, a government which derives all its powers directly or indirectly from the great body of the people, and is administered by persons holding their offices during pleasure, for a limited period, or during good behaviour. It is essential to such a government, that it be derived from the great body of the society, not from an inconsiderable proportion, or a favoured class of it; otherwise a handful of tyrannical nobles, exercising their oppressions by a delegation of their powers, might aspire to the rank of republicans, and claim for their government the honourable title of republic. It is sufficient for such a government, that the persons administering it be appointed, either directly or indirectly, by the people; and that they hold their appointments by either of the tenures just specified; otherwise every government in the United States, as well as every other popular government that has been or can be well organized or well executed, would be degraded from the republican character. According to the constitution of every state in the union, some or other of the officers of government are appointed indirectly only by the people. According to most of them, the chief magistrate himself is so appointed. And according to one, this mode of appointment is extended to one of the coordinate branches of the legislature. According to all the constitutions also, the tenure of the highest offices is extended to a definite period, and in many instances, both within the legislative and executive departments, to a period of years. According to the provisions of most of the constitutions, again, as well as according to the most respectable and received opinions on the subject, the members of the judiciary department are to retain their offices by the firm tenure of good behaviour.
On comparing the constitution planned by the convention, with the standard here fixed, we perceive at once, that it is, in the most rigid sense, conformable to it. The house of representatives, like that of one branch at least of all the state legislatures, is elected immediately by the great body of the people. The senate, like the present congress, and the senate of Maryland, derives its appointment indirectly from the people. The president is indirectly derived from the choice of the people, according to the example in most of the states. Even the judges, with all other officers of the union, will, as in the several states, be the choice, though a remote choice, of the people themselves. The duration of the appointments is equally conformable to the republican standard, and to the model of the state constitutions. The house of representatives is periodically elective, as in all the states; and for the period of two years, as in the state of South Carolina. The senate is elective, for the period of six years; which is but one year more than the period of the senate of Maryland; and but two more than that of the senates of New York and Virginia. The president is to continue in office for the period of four years; as in New York and Delaware, the chief magistrate is elected for three years, and in South Carolina for two years. In the other states the election is annual. In several of the states, however, no explicit provision is made for the impeachment of the chief magistrate. And in Delaware and Virginia, he is not impeachable till out of office. The president of the United States is impeachable at any time during his continuance in office. The tenure by which the judges are to hold their places, is, as it unquestionably ought to be, that of good behaviour. The tenure of the ministerial offices generally, will be a subject of legal regulation, conformably to the reason of the case, and the example of the state constitutions.
Could any further proof be required of the republican complexion of this system, the most decisive one might be found in its absolute prohibition of titles of nobility, both under the federal and the state governments; and in its express guarantee of the republican form to each of the latter.