The Foreign Policy / Prospect list of "The Top 100 Public Intellectuals" states that "the criteria to make the list could not be more simple:"
Candidates must be living and still active in public life. They must have shown distinction in their particular field as well as an ability to influence wider debate, often far beyond the borders of their own country.
Rather like Time's "Person of the Year," then, there is no merit qualification; "distinction" and "influence" are value-neutral. Thus, the administration's error-prone neocons (or the "public intellectuals" whose pronouncements give their ideology the gloss of respectability) would be just as eligible for this list as real historians, economists, and political scientists (such as Eric Alterman, Jacques Barzun, Michael Berube, Harold Bloom, Eric Foner, Thomas Frank, George Lakoff, Lewis Lapham, Bill Moyers, Juliet Schor, and Andrew Sullivan, none of whom made the list).
The criticism from HTML Mencken at Sadly, No! is brutal, but not inaccurately so: "Many of the 'intellectuals' are actually something between 'stupid' and 'clueless fucktard stupid.'" He names a few names, and then concludes:
See, it's not just that political scientists and pundits are shamelessly over-represented; it's not even that contributors to Foriegn Policy [sic] seem to be "intellectuals" by definition (and thus "earn" inclusion to the list); it's that "intellectualism," for the list-makers, seems to often mean, "the capacity to fuck-up hugely and be praised for it."
[editor's note: the list of omitted intellectuals has been updated]