The problem is that the fields in which he is an expert have failed to provide sufficiently better predictive power over the judgement of a well-read or experienced layman[1]. I do not mean that as a criticism of the OP; this is merely a consequence of how young "social science" as a science is, and how difficult of a subject matter it attempts to study. The fact that a "2 sigma" level of confidence is considered acceptable in social science, whereas particle physics has a stand of 5 sigma, should demonstrate that judgement of experts from different disciplines should be different depending upon their area of expertise (but this has been known since the time of Aristotle).

Now it is fair to point out that medicine(as an application of biology) and counseling (as an application of psychology) are held to the same statistical standard, yet the medical community has the advantage of being able to generalize about the responses of human physiology in a way that the social sciences cannot, and counselors at least have the option of leveraging their empathy when trying to understand their clients. Public policy (as an application of sociology) has neither advantage.

But I also think he is painting a false dilemma, either that or he is being uncharitable to his opposition, which I would characterize as "populist"[2]. With regard to the governance of America, it is not simply a choice between experts and the unwashed masses. We also have the option of decentralizing power and policy decisions and letting states, counties, and cities - as well as voluntaristic organizations like professional societies, religious communities, corporations, and charities - decide more of their own rules. This does preclude a "rule by experts", but does delay their ascension until their science has fully matured.

Now, to be fair, my own discipline of computer science/software engineering has yet to grow into maturity as well [3][4]. Yet for all the griping about "techo-elitism" there are quite a number of counter-indicators of this:
- there are no legal barriers to entry in this discipline: while a degree is typically expected by employers it is not mandated by law and many enter this discipline without one.
- there is a strong culture of having an "open book", i.e. the open source community.
- a portfolio of work is typically the central piece of one's resume (rather than credentials or years of experience)

While not having a source of standards can be very detrimental[5], as Brian-Puccio pointed out[6] having a source of standards isn't going to solve the problem. As Dijkstra said, we gain respectability by limiting ourselves to the feasible, and we are successful when we allow ourselves to be opportunity-driven rather than mission driven. Only upon that foundation can we construct a source of credible authority.

[1]http://harveymansfield.org/multimedia/jim-manzi-on-science-k...
[2]which, I might add, is the really only position that is truly "democratic" in the traditional sense of the word. The author strikes me as someone who is merely paying lip service to the notion of democracy, perhaps to keep his job, while trying to carefully trying disarm it of any actual governing power. Of course, this side-note trails too far into the realm of speculation about the character of a man whom I do not know, and is in any case less relevant to the main points I am trying to convey.
[3]https://www.cs.utexas.edu/~EWD/transcriptions/EWD10xx/EWD104...
[4]http://blog.moryton.net/2007/12/computer-revolution-hasnt-ha...
[5]http://blog.8thlight.com/uncle-bob/2012/04/18/After-The-Disa...
[6]https://news.ycombinator.com/item?id=7082283