Why does the American Government work?

"From this view of the subject it may be concluded that a pure democracy, by which I mean a society consisting of a small number of citizens, who assemble and administer the government in person, can admit of no cure for the mischiefs of faction. A common passion or interest will, in almost every case, be felt by a majority of the whole; a communication and concert result from the form of government itself; and there is nothing to check the inducements to sacrifice the weaker party or an obnoxious individual”(#10)

This shows that the founding father knew about the failures of a pure democracy, with the biggest problem being majority rule without minority rights. If a change had not been made to democracy, then major movements such as the civil rights movement would have not happened, or would have met much more opposition. The U.S. would become a country where all the decisions favored whites, with all other races facing discrimination.

Liberty is to faction what air is to fire, an aliment without which it instantly expires. But it could not be less folly to abolish liberty, which is essential to political life, because it nourishes faction, than it would be to wish the annihilation of air, which is essential to animal life, because it imparts to fire its destructive agency(#10)

This is saying that liberty causes and help factions form and gain strength, just like air makes fire stronger, however liberty is a necessary evil as politics cannot exist without it just as life cannot exist without air.

In framing a government which is to be administered by men over men, the great difficulty lies in this: you must first enable the government to control the governed; and in the next place oblige it to control itself. A dependence on the people is, no doubt, the primary control on the government; but experience has taught mankind the necessity of auxiliary precautions

In republican government, the legislative authority necessarily predominates. The remedy for this inconvenience is to divide the legislature into different branches; and to render them, by different modes of election and different principles of action, as little connected with each other as the nature of their common functions and their common dependence on the society will admit. It may even be necessary to guard against dangerous encroachments by still further precautions.(#51)

This is saying that the government needs a control over itself to make sure that it does not abuse its power. A check by the people can work sometimes, but another way to install a check is through multiple branches of government, which can more radially check if the power of another branch is getting too large.