Research bleg:

I have a couple of these, which I'll post separately. This first one is about the Clean Water Act: Are there any good sources out there arguing that stricter NPDES permit requirements would have perverse (i.e., bad for the environment) effects?

UPDATE: By "stricter NPDES permit requirements," I mean "making more activities subject to NPDES permit requirements."

Research bleg 2:

Well, my first research bleg kind of came up a bust, but maybe I'll have better luck on this one. My understanding is the prison guards union in California pushes for tougher criminal law. (1) Do prison guards unions do this in places other than California? (2) Are prison systems themselves, perhaps Departments of Corrections?, also active in lobbying for tougher criminal law or enforcement, either openly or behind the scenes?

Math bleg:

Can anyone recommend to me any simple functions with the following properties: f(0)=0, f(infinity)=1, and f'(0)=infinity? I.e., a function that could be used for the probability of getting a policy change as a function of your lobbying expenditures; but I'd like to have that first-derivative condition so I'm guaranteed to have an interior solution when I maximize af(x)-x for any a.

UPDATE: Oops! I meant f(0)=0, not f(x)=0. That's corrected now.

UPDATE 2: Thanks, folks. Aaron Bergman suggested 1 + e^(-x^2)(sqrt(x)-1). Unfortunately, I forgot to specify that I also wanted f'(x)>0 for all x; and that function goes above 1 and then dips back down so f(infinity)=1. While I'm at it, I also wanted f"(x)<0 for all x. Syd suggested sqrt(x)/(sqrt(x)+1)), which works fine. Chrismn suggested 1-e^(-sqrt(x)), which also works fine. Maniakes suggested the logistic function, but I don't think I can make that match all three of my conditions. Chrismn suggested the constant absolute risk aversion -e^(-ax)+1, but that violates f(0)=0. Aaron Bergman, finally, suggests (2/pi) atan(sqrt(x)), which looks cool.

UPDATE 3: Aaron Bergman also suggests an ingenious method, which I was unaware of, to generate all the functions like that you want! Just take a function g such that g(0)=0, g(infinity)=1, and g'(0) is finite (he doesn't say it, but perhaps you also need it to be nonzero). Then for any r in the interval (0,1), define f(x)=g(x^r). That way, first, f(0) = g(0^r) = g(0) = 0. Second, f(infinity) = g(infinity^r) = g(infinity) = 1. And, third, f'(x) = r x^(r-1) g'(x^r), so f'(0) = r 0^(r-1) g'(0^r) = r infinity g'(0) = infinity. All three functions I liked above are special cases of this. Thanks, Aaron!

UPDATE 4: Reader Paul Edelman suggests another function: sqrt(x/(1+x)). This illustrates a similar way of generating such functions: Take a function g defined as in Update 3, then define f(x)=[g(x)]^r. That way, f(0)=0 and f(infinity)=1 obviously. Also, f'(x) = r g'(x) [g(x)]^(r-1), so f'(0)=infinity. Now that's not the way Paul found the function. He used yet another way, which is also nice: Look for a function g such that g(0)=0, g'(0)=0, and g has a vertical asymptote at 1. Then take the inverse of that function, and that's your f. So x^2 definitely has value and first derivative 0 at 0, and if you stick a (1-x^2) denominator on it, you get yourself an asymptote. So g(x)=x^2/(1-x^2) works, and f(x)=sqrt(x/(1+x)) is its inverse function.

UPDATE 5: Sadly, these functions don't have closed-form solutions, if, say, I want to take the inverse of the derivative!

Antitrust research bleg:

One of the reasons for the enactment of the antitrust laws was to safeguard political freedom by preventing the formation of large corporations powerful enough to control the government. Taft, in his book The Anti-Trust Act and the Supreme Court (written in 1914, after his presidency but before he joined the Supreme Court), said the Sherman Act had attacked methods of "suppressing competition and controlling prices" which "had resulted in the building of great and powerful corporations which had, many of them, intervened in politics and through use of corrupt machines and bosses threatened us with a plutocracy" (p. 4).

Does anyone know of an economicsy, perhaps public-choicey, treatment of the same point, where antitrust emerges as a second-best optimum to prevent corruption or excessive corporate political influence?

Political preferences research bleg:

I can think of various reasons why people might favor policies that favor their industry. For instance: (1) Naked self-interest. (2) False consciousness: They wrongly come to believe that what's good for the industry is good for America ("What's good for GM..."). (3) True consciousness: They've learned how important their industry is from the experience of working in it. (4) Self-selection: They were more likely to join the industry in the first place because they sympathized with its interests. (5) Coincidence.

Have these reasons been systematically categorized? Do they have "official names"? (I just made up the names in the list above.) Are there scholarly papers discussing this? (Responsive comments only please.)

A second, somewhat related question: How do people feel about a group pushing a policy if that group would benefit from the policy economically? I can think of two possibilities: (1) Self-seeking bastards! (2) If you disagree with the policy: Self-seeking bastards! If you agree with the policy: Thank goodness someone has an incentive to stand up for the right policy!

Note: I don't really care how you, the readers of the Volokh Conspiracy, feel about such groups. I do care what social scientists have discovered about how people feel in general about them. Any scholarly papers discussing this perception issue?

Kant bleg:

"Out of the crooked timber of humanity, no straight thing was ever made." Does anyone know the actual source for this in Kant, and the actual quote in German? A Google search for "krummen Holz" yields a number of different formulations and no actual citation. Does Isaiah Berlin (whose book I don't have on hand) give a citation?

UPDATE: Well, that was quick. Thanks, all!

Isaiah Berlin's translation:

In a previous post, I mentioned Kant's phrase, which Isaiah Berlin translated as: "Out of the crooked timber of humanity no straight thing was ever made." This is a loose translation from Kant's original "Aus so krummem Holze, als woraus der Mensch gemacht ist, kann nichts ganz Gerades gezimmert werden"; Berlin seemed to have valued pithiness over accurate translation.

But now a copy of Berlin's book The Crooked Timber of Humanity: Chapters in the History of Ideas (1991) has just arrived, and it does seem that, as an epigraph (p. xi), Berlin does translate the Kant fairly accurately:

Out of timber so crooked as that from which man is made nothing entirely straight can be built.

This is in addition to the pithy translation, which is on p. 19. For an intermediate translation, see Against the Current: Essays in the History of Ideas (1980), p. 148: "Out of the crooked timber of humanity no straight thing can ever be made."

Irving = Isaiah?

Talking about Isaiah Berlin the other day, I almost said Irving Berlin. But has anyone ever seen them together?

For instance, consider the lost first draft of the lyrics to the American standard "Let Yourself Go" from Follow the Fleet. (Note: Before doing this, you may want to read the comments to this post.)

Crooked timber
Means that all things built are limber
Nichts Gerades wird gezimmer'
Let yourself go

I'm just saying, is all.

Labor-management pop culture bleg:

Scenario: Workers are trying to do something collectively against their boss -- for example, get him to agree to some policy that benefits them -- but they have no union. They try to keep each other in line (prevent each other from working, induce each other to contribute money) by using informal sanctions, like ostracism or violence.

Is there some famous book or movie or other cultural text that deals with this?