The United States is not a direct democracy, in the sense of a country in which laws (and other government decisions) are made predominantly by majority vote. Some lawmaking is done this way, on the state and local levels, but it’s only a tiny fraction of all lawmaking. But we are a representative democracy, which is a form of democracy.
Likewise, James Wilson, one of the main drafters of the Constitution and one of the first Supreme Court justices, defended the Constitution in 1787 by speaking of the three forms of government being the “monarchical, aristocratical, and democratical,” and said that in a democracy the sovereign power is “inherent in the people, and is either exercised by themselves or by their representatives.” Chief Justice John Marshall — who helped lead the fight in the 1788 Virginia Convention for ratifying the U.S. Constitution — likewise defended the Constitution in that convention by describing it as implementing “democracy” (as opposed to “despotism”), and without the need to even add the qualifier “representative.”
Sir William Blackstone, who was much read and admired by the framers, likewise used “democracy” to include republics: “Baron Montesquieu lays it down, that luxury is necessary in monarchies, as in France; but ruinous to democracies, as in Holland. With regard therefore to England, whose government is compounded of both species, it may still be a dubious question, how far private luxury is a public evil ….” Holland was of course a republic, and England was compounded of monarchy and government by elected representatives — Blackstone was thus labeling such government by elected representatives as a form of “democrac[y].”
And this is how “democracy” is like “cash” (and like lots of other words). If you pay cash in a store, what does that mean? It means that you’re paying with bills and coins, rather than with a check or a credit card. But if you buy your house for cash, does that mean that you show up with a briefcase full of bills or coins? Unless you’re in some peculiar lines of work, probably not.
“Cash,” like so many words, draws its meaning from context, and from contrast — what it is being distinguished from. Cash in some contexts means “not checks.” Cash in other contexts means “not borrowed money.”
Likewise, when people in the framing era were discussing popular government as opposed to government in which the bulk of the people had no voice, they often used “democracy” (or “democratic” or “democratical”) to mean “not monarchy or despotism or aristocracy,” with the “demo-” referring to popular control (what would become Lincoln’s “government of the people, for the people and by the people.” But when they were discussing representative government as opposed to direct government, they often used “democracy” or “pure democracy” to mean “not representative government,” with the “demo-” referring to popular decision-making.
The same is so today. America is a democracy, in that it’s not a monarchy or a dictatorship. (Some people claim it is too oligarchic, in which case they’d say America isn’t democratic enough — but again they’d be distinguishing democracy from oligarchy.) America is not a democracy in the sense of being a direct democracy.
If you’re asking whether to do something by direct ballot or by representative processes, you might ask whether we should be more democratic or more republican. If you’re asking whether China would be better off giving more power to Chinese voters, you might ask whether it should be more democratic or less democratic, quite apart from whether you think the democracy should be direct or representative.
To be sure, in addition to being a representative democracy, the United States is also a constitutional democracy, in which courts restrain in some measure the democratic will. And the United States is therefore also a constitutional republic. Indeed, the United States might be labeled a constitutional federal representative democracy.
But where one word is used, with all the oversimplification that this necessary entails, “democracy” and “republic” both work. Indeed, since direct democracy — again, a government in which all or most laws are made by direct popular vote — would be impractical given the number and complexity of laws that pretty much any state or national government is expected to enact, it’s unsurprising that the qualifier “representative” would often be omitted. Practically speaking, representative democracy is the only democracy that’s around at any state or national level. (State and even national referenda are sometimes used, but only for a very small part of the state’s or nation’s lawmaking.)
Democracy, then, has multiple meanings — as do so many words — and has long had multiple meanings. You might think the English language, or political discourse, would be better if democracy had just one meaning. But you can’t arbitrarily select that meaning, and label contrary meanings as linguistically wrong, even if having such a single meaning would be more convenient.
Nor should you invest so much significance, I think, into the particular word. Concepts are important; there is an important distinction between direct-democracy processes and representative-democracy processes, and among different degrees of directness or representativeness. But don’t expect that the English language as actually used by a large array of English speakers — from Adams, Jefferson, and Wilson on down — will perfectly or even near-perfectly capture such distinctions.
[This is an elaborated version of an earlier post, which I put up because I saw that (1) people were continuing to be interested in the subject, and (2) part of the confusion that I thought I saw had to do with the assumption that “democracy" had to mean just one thing — hence the “cash" analogy.]