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Participants in the Constitutional debate of 1787–1788 expressed varying views over exactly what constituted the "Republican Form" of government. However, there was a consensus as to three criteria of republicanism, the lack of any of which would render a government un-republican.
The first of these criteria was popular rule. The Founders believed that for government to be republican, political decisions had to be made by a majority (or in some cases, a plurality) of voting citizens. The citizenry might act either directly or through elected representatives. Either way, republican government was government accountable to the citizenry. To a generation immersed in Latin learning and looking to pre-imperial Rome for inspiration, a republic was very much res publica—the people's affair.
The second required element of republican government was that there be no monarch. The participants in the constitutional debates believed that monarchy, even constitutional monarchy, was inconsistent with republican government. In fact, when Alexander Hamilton proposed a President with lifetime tenure, the delegates so disagreed that they did not even take the time to respond.
The third criterion for a republic was the rule of law. Ex post facto laws, bills of attainder, extreme debtor-relief measures—most kinds of retroactive legislation, for example, were deemed inconsistent with the rule of law, and therefore un-republican.
Many participants in the post-Convention debates (such as James Iredell of North Carolina) suggested an additional criterion of republicanism: absence of a titled aristocracy. This criterion was not part of the consensus; other participants observed that some previous republics (e.g., pre-imperial Rome) and some contemporary republics (e.g., Holland) featured titled aristocracies. Indeed, the most influential contemporary foreign political writer, Baron de Montesquieu, had divided republics into aristocratic and democratic varieties. To assure, therefore, that the American states remained more purely democratic republics, the drafters of the Constitution inserted Article I, Section 10, which forbids states from conferring titles of nobility.