Where oh where do they find these book reviewers? In the New York Times, Robert Alter writes:
Review of 'Reading Leo Strauss,' by Steven B. Smith - New York Times: Liberal democracy lies at the core of [Leo] Strauss's political views.... [P]olitics must be the arena for negotiation between different perspectives, with cautious moderation likely to be the best policy.... Smith... describes Strauss's position as "liberalism without illusions." All this may sound a little antiquated, and Smith is right to associate Strauss with cold war liberals like Raymond Aron, Isaiah Berlin, Walter Lippmann and Lionel Trilling. But it's a view from the middle of the past century that might profitably be fostered in our own moment of political polarization, when a self-righteous sense of possessing assured truths is prevalent on both the right and the left...
This paragraph obscures much more than it enlightens. A superior thumbnail summary is provided by M.F. Burnyeat:
The New York Review of Books: Sphinx Without a Secret: The leading characters in Strauss's writing are "the gentlemen" and "the philosopher." "The gentlemen" come, preferably, from patrician urban backgrounds and have money without having to work too hard for it: they are not the wealthy as such, then, but those who have "had an opportunity to be brought up in the proper manner." Strauss is scornful of mass education. "Liberal education is the necessary endeavor to found an aristocracy within democratic mass society. Liberal education reminds those members of a mass democracy who have ears to hear, of human greatness." Such "gentlemen" are... ready to be taken in hand by "the philosopher," who will teach them the great lesson they need to learn before they join the governing elite. The name of this lesson is "the limits of politics." Its content is that a just society is so improbable that one can do nothing to bring it about.... [T]he moral is that "the gentlemen" should rule conservatively, knowing that "the apparently just alternative to aristocracy open or disguised will be permanent revolution, i.e., permanent chaos in which life will be not only poor and short but brutish as well"...
What is Political Philosophy? p. 113, where Strauss indicates that when this argument is applied to the present day, it yields his defense of liberal or constitutional democracy--i.e., modern democracy is justified, according to him, if and because it is aristocracy in disguise. Cf. Liberalism, p. 24.
To say that "liberal democracy is at the core of Strauss's political view" is simply not true. However, Strauss would probably have approved of Robert Alter's saying that "liberal democracy is at the core of Strauss's political view": "philosophers" will know that Alter's sentence is false, and it would be good for "the gentlemen" to believe that Alter's sentence is true.
Strauss's position is, needless to say, not the position of Raymond Aron, Lionel Trilling, or Walter Lippman, none of whom believed that modern democracy was justified because it was enlightened aristocracy in disguise.