More generally, we should start by determining what we mean by "democracy". In my view, there are two very different meanings for this word, which are often confused, and even strawmaned against each other.
First, "democracy" is a method for decision taking.
The method is simple, though its application may be problematic. The steps are,
- determine what the decision is about (let's say, should we build a wall along the Mexican border, yes or not?)
- the relevant stakeholders discuss the issue freely, pointing out the pros and cons of the proposal (how much does the wall cost? will it solve the problem it is designed to solve? what collateral effects might it have?). This is where the concept of "freedom" intertwines with "democracy"; if some points are not allowed into discussion, you cannot have a "democratic decision", for not all aspects of the issue will be considered.
- once the relevant stakeholders can agree that the issue has been cleared, they take a vote on it, and the "side" that has more votes gets its proposed policy implemented. That is, if more people vote for building a wall along the Mexican border, then we build the wall; otherwise, we do not build the wall.
There are however some problems to this method:
- the delimitation and priorisation of issues: what is a wall, what is a boundary, what is Mexico? In this case it may seem obvious, but it is not always so, and it is necessary to ensure that all sides, for and against, are discussing the same thing. Then, should we vote on the issue of the wall before or after voting on the issue of whether policemen should wear a videocam attached to their uniform?
- the delimitation of stakeholders: since the wall is on Mexico's border, shouldn't Mexicans have a say about it?
- the delimitation of the discussion period; if there is no minimum/maximum time for the discussion, it is always possible for the majority to force a vote even if the issue hasn't been properly discussed, or for the minority to postpone the decision indefinitely, systematically arguing that the issue is still unclear.
There is seldom any earnest criticism of "democracy" as a method, though there are many attempts, with varied degrees of success, to circumvent, pervert, or corrupt it. The latest that had any historical importance seems to be the "Fuehrerprinzip" put up by the NSDAP, both internally in their party workings, and externally, in the German State issues, once their Machtgreifung succeded. This was, of course, intertwinned with their racialist vision of a "superior race". But such racialist views which, in themselves, are utterly anti-democratic in the sense that they necessarily deny the participation of part of the stakeholders) have also stood alone, as for instance in the intellectual defense of American Southern slavery, with no relation to any Fuehrerprinzip.
Previous alternate methods seem to stem from theocratic practices which were in place before the rise of modern "democracies" in the 19th century; as such, they weren't designed as a criticism of the democratic method (rather, the democratic method arised within a criticism of these practices), but they evolved into the traditional conservative/reactionary opposition to democracy (Burke, Chesterton), consisting, at least in part, in a criticism of democracy and markets as dissolvent agents of a proper order of society.
More modernly, there is some talk (and a lot of confusion) about "meritocracy", which is an ill defined term, which may coalesce around some kind of post-democratic criticism of democracy, but, as of now, it doesn't seem to sum up into a consistent ideological tendency.
Second, "democracy" is the name for a kind of political regime
Which kind, it is much more difficult to define than the method discussed above. But a regime that goes by the name "democracy" necessarily has to employ the democratic method for at least some decisions. We usually define it, minimally, as a regime that holds democratic methods for the choice of Executive and Legislative magistrates, and that employs democratic method in its legislative decisions, on the legal fiction that the legislative magistrates "represent" the population at large.
Thus, we also require, for a regime to be called "democratic", that the choice of magistrates is responsibility of a wide array of stakeholders, ie, "citizens". We wouldn't call a regime "democratic" if it doesn't allow women, Blacks, Jews, or left handed people to participate in the process of electing magistrates (but this is historically variable; we did consider the US a democracy in the 19th century - or Athens in Pericles' time -, though it blocked women and slaves, who were overhelmingly Black, from voting).
Also, we require, for a regime to be called "democratic", that it allows extensively free political discussion; if some political positions are not allowed, or if some issues cannot be addressed, we will probably deem the regime that excludes them anti-democratic or "semi-democratic". These precise limits are fuzzy; the military dictatorship in Brazil, which forcibly reduced all political activity to two parties isn't usually considered "democratic", while the idea that modern Germany, which bans neo-nazi parties, isn't "a democracy" for that reason isn't popular except among, well, neo-nazists.
It must be noted that no political regime allows for "democratic decision" on all decision making processes, or all kinds of decisions. We don't vote for what professions people embrace, nor (usually; there are exceptions) for judges and justices (who are more often selected by a "meritocratic" procedure). It may even be that the extension of the "democratic method" to some kinds of decisions is contradictory with the "democratic regime" as a whole (and so, talks of "pure democracy" are disingenuous, as such "pure democracy" cannot exist as such in practice).
Criticism of these regimes is nowadays mostly restricted to whether they are excessively or insufficiently "democratic", and is often rooted on the problem of which kinds of decision are proper subjects of the democratic method. It is deserving of particular notice that conservative/reactionary criticism of democracy has been superceeded by, or transformed or merged into, this kind of criticism: instead of arguing against women's right to perform abortions, they argue in favour of extending "rights" to the unborn, which is, in itself, as Žižek notes, an ideological capitulation to democratic principles.
It is also notable that we seem to be undergoing a general crisis of democracy-as-a-regime, as underlined by the growth of undemocratic neopopulist political tendencies in Europe (and the United States, let's not forget Mr. Trump) and reactionary tendencies in Latin America, but there is no increase in intellectual production of alternatives, the conservative/reactionary thinking having been subsumed into a right-wing tendency within democratic regimes, racialist and outright "authoritarian" ideas being outdated and demoralised, and a possible "meritocratic" alternative being, for the moment, embrionary at most.