how does james madison define a republic
James Madison defined republic in terms of  representative democracy as opposed to direct democracy.)    A direct democracy, or  pure democracy, is where the people rule directly, voting on  every law themselves. republic is a form of government where a group of officials who represent the people vote on issues, whereas a direct democracy is a form of government where all citizens di â¦ rectly vote on issues. In a repulic, people ellect representatives to do the governing.