Nonlinear Utility

(By Andrew MacKie-Mason)

An ongoing debate in my hometown just hit the "newspaper" again, provoking another round of arguments over the city's decision to install an expensive work of public art next to the newly renovated City Hall. The sculpture ended up costing the city $750,000, and many people are taken aback by the price. (There's a smaller sub-issue caused by about 20% of the money going to a German design artists, but I won't address that here.)

A few of the anonymous comments on the story provide a good picture of the main complaint:

Benjamin: "This is a testimony to the condescending city government and their attitude toward the hard working citizens of Ann Arbor. They reduce our services (fire/police, leaf pick-up, parks etc.) and then they waste our money on this "art". How in the world was there room in the budget for this ahead of other city services?"

f4phantomll: "How many potholes can you fill for $750,000? How many cops or firefighters can you rehire for $250,000? Sheesh."

GoBlue: "I'm embarrassed and ashamed. What does this say about us as a city? Our economy is in shambles, what is crucial is ignored (bridge for example), key safety elements (police and fire) being reduced and council uses our tax dollars for this and could not even use local artists, to add insult to injury. Our city has sunk to new lows."

AlwaysAmazed: "How many hungry children and homeless families could this money have helped? You've got to be kidding me!"

grye: "We should put one of these on every street corner, then get rid of all the city employees, police officers, firemen, shut down all the utilities, no garbage pickup. Get rid of everything so we can sit on our collective behinds and admire expensive art. Who needs anything else? And with such art and no city services, millions will flock to this city to enjoy the art and wish they could move here because it is such a wonderful place.

Is our mayor and city council ever going to get it?"

mun: "$750,000 could have paid for how many police officers, how many fire fighters, how many school buses?"

The root of all of these complaints is that the money spent on this project could have been put to better use in other ways: that is, there are other ways the money could have been spent that would give us a higher ratio of utility to cost.

The problem with this kind of simplistic cost-benefit analysis, though, is that it implicitly assumes that the utility of a certain scalable choice is linear in the chosen magnitude of the choice. That is, if we are calculating the utility of hiring x firefighters, the assumption seems to be that U(x) = mx. That translates to each additional firefighter giving us m units of utility. We could have a similar equation for the utility of spending $y on public art, and have that U'(y) = m'x. (Throughout this discussion I'll make the simplifying assumption that the money is being spent most efficiently on each project independently: the best firefighters are being hired for their salary, and the best art is being purchased for its cost. Altering that assumption would lead to a different, though also interesting, issue.)

On that model, it makes sense to ask, like 'mun' did, how many firefighters could have been hired for the cost of the public art. If we had that number, we could do a pretty simple comparison between U(x) (with x being the number of firefighters) and U'(750,000). Whichever utility is greater is where we should spend our money.

The problem is that this is a horribly inaccurate approximation of what our utility functions should look like. This approximation not only leads to slightly incorrect answers (as is inevitable with any approximation), but it actually causes us to ask the wrong question. To see why, consider the following simple example:

You have $2, and you go to a nearby store, that sells two items: loaves of bread and bottles of water. Each loaf and each bottle cost $2, and for whatever reason saving the money isn't an option. It's logical to assume that, faced with this choice an individual will perform an approximate evaluation of the utilities of a loaf of bread versus a bottle of water, and pick the one that gives a higher utility. Assume that, for some underlying reason, that ends up being the loaf of bread.

Now, hold everything in the example constant, but assume that you actually have $4. The linear utility model tells us that you'll buy two loaves of bread — but does that make sense? Of course not. The right answer is that we don't know what you'll do. It could well be that you're extremely hungry and not at all thirsty, so two loaves of bread is more attractive than one loaf and one bottle of water. But maybe you were somewhat hungry and also a bit thirsty. If you can only buy one thing, you'll get the loaf...but that one loaf is enough to satiate you, and so with the second $2 you'll buy a bottle of water. The reason is that the utility of the second loaf of bread is not equal to the utility of the first loaf of bread. As you get more food, additional food has a much smaller marginal benefit.

There are different ways to talk about this issue. You can frame it as a collection of choices which are not independent of each other, but instead I'd like to talk about it as an example of scalable goods whose utility functions are nonlinear. The graph at right is a decent approximation of what a reasonable utility function might look like.

Returning to the debate over city services versus public art, it's reasonable to think that both of those will have a utility function that follows a similar style to the one at right. A city with no investment in public art, for instance, can see a marked increase in quality of living from a relatively small amount of investment in improving the appearance of the area. Once the city looks nice, however, additional installations will have less and less of an effect.

Similar logic applies to hiring firefighters. A city with no firefighters is basically screwed, so hiring that first team is very, very useful. But given that there are only a certain number of people that can effectively help in any given emergency, the increases in utility fall off as you hire more and more firefighters. The first team gives you a certain percentage chance of putting out a fire. The second team gives you (probably) the same percentage chance of putting out a fire, but only if two fires happen at once. So on and so forth.

After that excessive explanation, we can finally return to the angry local commentators. Why, they moan, are we paying for this public art when we could hire more firefighters? The city obviously didn't compare the value of a single art installation to that of x firefighters.

They probably didn't, but such a comparison would also be the wrong one — or, at best, a nonsensical one. 'AlwaysAmazed' shouldn't be interested in just how many families could be fed; he should be interested in how many families could be fed and how many already are. 'mun' shouldn't be concerned with a straight translation between the amount of money spent and the cost of buses, firefighters, or police. He should be concerned with that, and how many buses, firefighters, and police officers Ann Arbor already has. Correct cost-benefit analysis can't compare different choices for marginal spending decisions without also considering the current state of the world. If the current levels of spending were actually as irrelevant as the angry people would have you believe from their questions, then we would end up spending all of our money on that single, perfect, utility maximizing project.

A Direct Democracy Jury?

(By Andrew MacKie-Mason)

Ethan Leib had an interesting proposal on PrawfsBlawg the other day, one I could swear I've written about before, though I can't find anything on this blog about it. It's worth reading in full, but here's a taste:

Instead of asking nearly 40 million people what they think about a question of policy, ask a much smaller random subgroup of “the people” what they think. When we want criminal defendants judged by a jury of their peers, we don’t ask everyone to vote: we ask a cross-section of the whole—12 people—to take time out of their private lives and serve their governments to decide if an individual in their midst should lose his or her liberty or life. When we ask “the people” to decide policy in direct democracy, it should be done by a scientifically stratified random sample of 535 people that is empanelled into jury service for the task at hand.

One issue that I see with the proposal is that we would need even stricter controls on people who can influence the "jurors" than we have in a criminal jury: since the issues will generally be of greater public interest than any individual criminal trial, there's much more risk of bribery or corruption. That control, though, would have to be balanced by a desire to let the jurors freely research the issues. We obviously wouldn't want a trial like atmosphere where one group of proponents and one group of opponents are given certain amounts of time to convince them.

Logistically, I'm not sure how it would work. But is the idea worth fleshing out more?

Posner on Recording the Police

(By Andrew MacKie-Mason)

Eric Johnson has a post about troubling comments made by Circuit Judge Richard Posner, also a professor at the Chicago Law School. It centers around a case brought by the ACLU to challenge the application of Illinois' eavesdropping statutes to interactions with public officials, and Posner seems to think that public officials somehow have a right of "privacy" in their conversations with the public.

For what it's worth, this should be an open-and-shut case — recording and publishing conversations with police officers is clearly protected under the First and Fourth Amendments (and their application to the states through the Fourteenth Amendment) — and it would be shameful if Posner fails to see that.

Bernstein's Disturbing Anti-intellectualism

(By Andrew MacKie-Mason)

David Bernstein, in a recent post on the Volokh Conspiracy, advances an unfortunately common form of anti-intellectualism. As part of an ongoing controversy involving Professor Mearshimer's blurbbing of a book written by Gilad Atzmon, Bernstein attacked Professor Mearshimer's defense of his blurb by pointing to what he views as evidence that Atzmon is an anti-Semite. As to the relationship between Atzmon's alleged anti-Semitism (the debate over which I have no desire to enter) and Mearshimer's blurb, Bernstein writes:

Mearsheimer is not content to argue, as he does, that he didn’t know Atzmon from a hole-in-the-head, and endorsed the book because he found it provocative and interesting. If he had limited himself to this, he could have then added that he wasn’t aware of Atzmon’s anti-Semitic background and didn’t read the book in that light. Now that he knows, he regrets his association with Atzmon and the book.

But this line of thinking begs what should be a very controversial point: if Atzmon is an anti-Semite, should Mearshimer "regret his association with Atzmon and the book"?

Anyone who respects the ideals of academic freedom and intellectual inquiry would quickly and easily answer: no. Even people whom we abhor can have interesting, provocative, and valuable things to say, and an intellectual work should not be marginalized just because of other characteristics of the author. Just like the value of studying Marx's work or Hitler's Mein Kampf is independent of our moral evaluation of those individuals, any anti-Semitism that Atzmon may exhibit in interviews or on his blog is separate from any evaluation of his book.

It's one thing for critics to say that the book itself is anti-Semitic, and that by calling it "interesting and provocative" Mearshimer is inappropriately endorsing an anti-Semitic work. That's hardly an open-and-shut argument, but at least it's one that doesn't undermine intellectual inquiry. But suggesting that approving of a single work by a distasteful individual should make one guilty by association is a dangerous road to go down.

If Mearshimer comes to "regret his association with Atzmon and the book," it will be because people like Bernstein abandon academic inquiry in favor of partisan sniping. The blame will rest fully on those people, such as Bernstein, who are unable to think with a degree of nuance.

There's one more point about Bernstein's post that's worth mentioning. He claims:

Mearsheimer actually defends Atzmon from the charge of anti-Semitism.

That is a blatant mischaracterization of Mearsheimer's post, in which he states:

Before I examine the substance of that charge, there is an important issue that needs to be addressed directly. Goldberg's indictment of Atzmon does not rely on anything that he wrote in The Wandering Who? Indeed, Goldberg's blog post is silent on whether he has actually read the book. If he did read it, he apparently could not find any evidence to support his indictment of Atzmon. Instead, he relied exclusively on evidence culled from Atzmon's own blog postings. That is why Goldberg's assault on me steers clear of criticizing Atzmon's book, which is what I blurbed. In short, he falsely accuses me of lending support to a Holocaust denier and defender of Hitler on the basis of writings that I did not read and did not comment upon.

This tactic puts me in a difficult position. I was asked to review Atzmon's book and see whether I would be willing to blurb it. This is something I do frequently, and in every case I focus on the book at hand and not on the personality of the author or their other writings. In other words, I did not read any of Atzmon's blog postings before I wrote my blurb. And just for the record, I have not met him and did not communicate with him before I was asked to review The Wandering Who? I read only the book and wrote a blurb that deals with it alone.

Goldberg, however, has shifted the focus onto what Atzmon has written on his blog. I discuss a couple of examples below, but I will not defend his blog output in detail for two reasons. First, I do not know what Atzmon may have said in all of his past blog posts and other writings or in the various talks that he has given over the years. Second, what he says in those places is not relevant to what I did, which was simply to read and react to his book.

Mearsheimer does not, nor should he be expected to, defend Atzmon's entire record and personality. Instead, he focuses on a few specific claims and, apparently, convincingly refutes them: Bernstein, after all, makes no attempt to claim that any of those defenses are wrong. Instead, he seizes on completely unrelated statements by Atzmon and attempts to shame Mearsheimer with those. The tactic, for those who aren't interested in fawning over Bernstein, is transparent, but those who only read Bernstein's side of the story may well be fooled.

CNN and the Tea Party

(By Andrew MacKie-Mason)

While we're on the topic of the recent Republican debate, Common Dreams (h/t Leiter) raises a good question: why would CNN partner with the Tea Party Express to put on a debate? Have there been any debates where analogously liberal groups have co-sponsored a presidential debate with a non-partisan news agency?

A Thirst For Blood

(By Andrew MacKie-Mason)

Even though most people have probably already seen it, this video is worth passing on again.



Setting aside Rick Perry's claim that capital defendants get a fair hearing (ask yourself whether Duane Buck got a fair hearing in 1997,  and why Rick Perry refused to grant a reprieve), I wonder whether it's indicative of partisanship, purposeful blindness, or just plain old stupidity that Rick Perry said he doesn't worry at all that some of those executed in Texas may be innocent.

There have been numerous high-profile cases where investigation after an execution presents compelling evidence that some victims of the Texas "justice" system have been innocent: Ruben Cantu, Cameron Willingham, David Spence, Gary Graham, and Claude Jones. Rick Perry cannot wash his hands of blood by pointing to the "process" that defendants may take advantage of before being executed, because – as governor – he is part of that process. He has an obligation to insure that every victim of the Texas executioner is guilty beyond a reasonable doubt, and that is an obligation that would cause any morally competent individual some sleepless nights. While it is true that the Texas Constitution doesn't allow him to give pardons or commutations of sentence on his own initiative (a ridiculous and outdated rule acting against the interests of justice), he can still put the full weight of his office behind a plea for clemency.

Also worth mentioning is, of course, the disgusting response the crowd had to the mention of Rick Perry's record bloodbath. As I pointed out in the wake of Osama bin Laden's death, it's disturbing to celebrate anyone's death. But it undoubtedly points to a deeper disease in elements of our country that these debate viewers – all relatively normal people themselves, we can assume – would cheer for the murder of their fellow citizens. That is not evidence of a citizenry that "understands justice." It is a glimpse into modern, 'civilized' blood lust. Our execution rooms are our modern day colosseums, and the men and women at the Republican debate were the fans cheering the death below.

A Theory of Parental Rights

(By Andrew MacKie-Mason)

Eugene Volokh has a post about the leading case on the constitutional theory behind so-called "parental rights." I'm grateful for the exposure to the case, because it confirms my previous impression: there is no way to find a constitutional guarantee of parental rights that is faithful to the constitutional text.

O'Connor's reasoning rests on the rather astounding claim that the Due Process clause protects our "liberty" interests in controlling other individuals. Such a self-contradictory argument requires little other criticism, but the objections in Scalia's dissent are also rather convincing.

There is a legitimate way, I think, to support some of the specific claims of "parental rights" advocates, though the theory is significantly different. Rather than focusing on the ridiculous "liberty" right-to-control, we should acknowledge the true possessor of the liberty right (the children) and construct the constitutional theory around determining when parents are the better proxy for free choices than the government is. Such a theory, I suppose, would support government standards for education, but parental choice between different qualifying institutions; it would support government mandated health measures except in the presence of real health concerns; it would defend most religious choices made on behalf of a child, though it would look with suspicion as the choices have more significant and permanent effects; and most clearly, it would disfavor efforts by parents to restrict access to information, especially as children get older.

The results of such a theory would meet with mixed approval among parental rights advocates, youth rights advocates, and statists alike. But at least it would be intellectually honest and founded on the text of the Constitution.

Teaching Philosophy to Prisoners

(By Andrew MacKie-Mason)

Brian Leiter linked to a Washington Post story about a marine-turned-college student who started a course in ethics for inmates at a maximum security prison. It's well worth reading, and this line in particular struck me:

But the inmates were intrigued. More than that, they were grateful for a break in the monotony of prison life, the opportunity to exercise their minds and the chance to be taken seriously as thinking adults.