There are a lot of explanations of consequentialism and utilitarianism out there, but not a lot of persuasive essays trying to convert people. I would like to fill that gap with a pro-consequentialist FAQ. The target audience is people who are intelligent but may not have a strong philosophy background or have thought about this matter too much before (ie it's not intended to solve every single problem or be up to the usual standards of discussion on LW).
I have a draft up at http://www.raikoth.net/consequentialism.html (yes, I have since realized the background is horrible, and changing it is on my list of things to do). Feedback would be appreciated, especially from non-consequentialists and non-philosophers since they're the target audience.
Fair enough. Though I can grant this only for consequentialism in general, not utilitarianism -- unless you have a solution to the fundamental problem of interpersonal utility comparison and aggregation. (In which case I'd be extremely curious to hear it.)
I gave it as a historical example of a once wildly popular bad idea that was a product of consequentialist thinking. Of course, as you point out, that was an instance of flawed consequentialist thinking, since the consequences were in fact awful. The problem however is that these same patterns of thinking are by no means dead and gone -- it is only that some of their particular instances have been so decisively discredited in practice that nobody serious supports them any more. (And in many other instances, gross failures are still being rationalized away.)
The patterns of thinking I have in mind are more or less what you yourself propose as a seemingly attractive consequentialist approach to problems of public concern: let's employ accredited experts who will use their sophisticated models to do a cost-benefit analysis and figure out a welfare-maximizing policy. Yes, this really sounds much more rational and objective compared to resolving issues via traditional customs and institutions, which appear to be largely antiquated, irrational, and arbitrary. It also seems far more rational than debating issues in terms of metaphysical constructs such as "liberties," "rights," "justice," "constitutionality," etc. Trouble is, with very few exceptions, it is usually a recipe for disaster.
Traditional institutions and metaphysical decision-making heuristics are far from perfect, but with a bit of luck, at least they can provide for a functional society. They are a product of cultural (and to some degree biological) evolution, as as such they are quite robust against real-world problems. In contrast, the experts' models will sooner or later turn out to be flawed one way or another -- the difficulty of the problems and the human biases that immediately rear their heads as soon as power and status are at stake practically guarantee this outcome.
Ultimately, when science is used to create policy, the practical outcome is that official science will be debased and corrupted to make it conform to ideological and political pressures. It will not result in elevation of public discourse to a real scientific standard (what you call reducing politics to math) -- that is an altogether utopian idea. So, for example, when that author whose article you linked uses sophisticated-looking math to "analyze" a controversial political issue (in this case immigration), he's not bringing mathematical clarity and precision of thought into the public discourse. Rather, he is debasing science by concocting a shoddy spherical-cow model with no connection to reality that has some superficial trappings of scientific discourse; the end product is nothing more than Dark Arts. Of course, that was just a blog post, but the situation with real accredited expert output is often not much better.
Now, you can say that I have in fact been making a consequentialist argument all along. In some sense, I agree, but what I wrote certainly applies even to the minimalist interpretation of your positions stated in the FAQ.