To secure the public good and private rights against the danger of such a [majority] faction, and at the same time to preserve the spirit and the form of popular government, is then the great object to which our enquiries are directed. (No. 10)
The goal of the Federalist Papers was to explain how a republican (or representative) government based on the sovereignty of the people could still protect rights and proceed according to the rule of law.
D. We often speak of our government as a democracy (direct rule by the people), but the truth is we have always had a republic, not a democracy. In a pure democracy, a faction composed of a majority of the citizens would be likely to endanger the persons or property of particular individuals or groups, but a republic, “by which I mean a Government in which the scheme of representation takes place, opens a different prospect, and promises the cure for which we are seeking (No. 10).” Madison argues a representative form of government (a republic) is better than a democracy because it results in a system of government which will refine and enlarge the public views, by passing them through the medium of a chosen body of citizens, whose wisdom may best discern the true interest of their country, and whose patriotism and love of justice will be least likely to sacrifice it to temporary or partial considerations. (No. 10)