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Publius was a pseudonym used by the three writers of The Federalist Papers; James Madison, Alexander Hamilton, and John Jay. The Federalist Papers were originally essays and articles submitted to newspapers during the ratification period of the U.S. Constitution. The collection of 85 essays were written to encourage ratification of the Constitution specifically by the State of New York. There were fears that the Anti-Federalists were influencing the direction New York was going to go regarding the new Constitution and it was believed that which ever way New York went, the rest of the country would follow. Hamilton and Jay were both residents of New York at the time, Madison was a resident of Virginia but was in New York at the time as a delegate in the Congress under the Articles of Confederation, and in turn he was recruited to also participate in the essay writing.
The pseudonym "Publius" was chosen as the collective name for the trio due to its connection to Publius Valerius, who helped found the Roman Republic. Cato and Cicero were also instrumental as statesmen during the time of the Roman Republic, the former being one of 46 pseudonyms used by various patriots during the Founding Era.
While the most astute observers recognized the writing styles of the authors, and it was widely believed the authors of the Federalist Essays were Hamilton, Jay and Madison, nobody knew for sure, or to which essay each of those Founding Fathers were attached. The identities of the authors were not revealed until after Hamilton's death in 1804, after which a list written by Hamilton tying each author to their work was found in his desk. Madison later released his own list, in which he disputes a few of Hamilton's claims as to regards of which author wrote what. Authorship of twelve of the essays remains disputed even now.
The use of Publius as a pseudonym was likely used to hide the writers' connections to the Constitutional Convention, as well as to hide their identities from the British since such writings were considered to be high treason against the British Empire.
-- Political Pistachio Conservative News and Commentary