29 Apr 2011

## Eat My Shorts, Landsburg

Steve Landsburg has started a new series called “D’oh,” in homage to Homer Simpson. Steve explains:

When something is wrong on the Internet, bloggers love to pounce. But since no blogger is infallible, most of us can find ample fodder in our own past writing, if we go back and reread it with a sufficiently critical eye. Over the next few weeks, I plan to revisit some things I got wrong the first time around. (You’ll recognize those posts by the Homer Simpson logo.) I hope others will be inspired to do the same.

OK if you insist Steve, I will bring up a huge mistake I think you made several years ago…

In my all-time favorite example of Neoclassicals Gone Wild, Steve made the argument that “more sex is safer sex.” The gist is that when a person decides whether to take somebody home from the singles bar, he is just weighing the private costs (like the girl could be a psycho, she might get pregnant, she could have an STD, maybe there is something to this whole “morality” thing after all, etc.) against the private benefits (use your imagination).

But this utility maximizer, according to Steve, is ignoring the positive externalities of his actions (assuming the guy doesn’t himself have an STD). By throwing himself into the hookup pool that night, he increases everybody else’s odds of not contracting an STD that night. Here’s Steve’s numerical illustration:

Suppose the bar contains two people with infection probability 5% and two with infection probability 85%. Then your chance of a bad draw is 45% (the average of 5%, 5%, 85%, and 85%). But if you replace the two 5’s with four 10’s, your chance of a bad draw goes down to 35% (the average of 10%, 10%, 10%, 10%, 85% and 85%).

Just to make sure we get what Steve is saying here: The people who were originally 5%’ers were the prudes. But if those prudes would follow Steve’s advice to go forth and multiply, then they would put themselves at more risk, it’s true. So if they doubled their activities, their own risk of getting something (and then passing it on to others) would be doubled to a 10%. (We’re speaking in averages across all the population types.)

But, Steve is saying that since there are people out there who are high risk, it actually makes the whole hookup pool safer on average if the prudes would double their activity. Any particular prude would be twice as dangerous as before, but there would be twice as many (former) prudes in the available pool on any given night at the bar.

Now in my response, I listed several objections to Steve’s analysis. But I think I overlooked what might be the most fundamental, given that Steve himself called his argument “more sex is safer sex,” rather than “more sex is Pareto efficient.” (If you don’t get that, don’t worry.)

When my article ran, at least one person emailed me and pointed out what he claimed was a huge flaw in Steve’s own numerical example: Yes, it’s true that any given person’s probability of contracting an STD would go down, if the two 5%’ers were replaced by four 10%’ers.

BUT, the expected amount of disease transmission would go up. Now Steve gave a (fairly contrived) example later on in his article where every man in town goes to the same prostitute, versus a scenario in which there are lots of free-spirited women so that doesn’t happen. And yes in those two scenarios, the spread of the disease would be slowed in the second one, because in the first scenario, if just one guy has it, then pretty soon the whole community will have it.

But in general, it would seem to me that if the goal is to minimize the ability of STDs to spread from person to person, then the robustly correct strategy is to tell everyone, “Stop sleeping around!” In the limit, if every “prude” person saved him or herself for marriage, then the STDs would be strictly confined to the high-risk group whose behavior Steve is taking as given for the purposes of the argument (I think).

Last point: I believe that Steve didn’t just dream this up from scratch, and that there are people who model disease dynamics on computers and agree with him. But I’m pointing out that strictly speaking, Steve’s first numerical example didn’t really make the relevant point (perhaps it COULD make the relevant point, if we spelled out more assumptions). So if Steve is going to give such incredibly counterintuitive advice–that the way to slow the spread of STDs is for prudish people to sleep around more–then I think he should spell it out a bit more carefully.

#### 9 Responses to “Eat My Shorts, Landsburg”

1. Steven E Landsburg says:

First, you’ve acknowledged only one of the two positive externalities that occur when prudes become a bit more active. As I’ve said many times, the second externality is empirically the more important one. It’s this: The prude who gets infected might go home and die with the disease, in which case the virus dies with him. This is (socially) better than having the same infection passed to Promiscuous Pete, who spreads it to 17 other people before he dies.

Second, despite the flamboyance of the title, I’ve stressed, every single time I’ve written about this example that there are two separate statements here. One is that more sex is more efficient, which follows from pure theory (and very simple theory at that): Whenever there’s a positive externality, we get inefficiently little of the activity. The second is that more sex leads to a lower rate of disease transmission, which is a model-dependent statement, but turns out to be true in the most detailed and careful models we’ve got (i.e. Michael Kremer’s). Kremer finds you can slow down HIV transmission substantially if you can bring everyone with fewer than 2.25 partners a year up to 2.25.

From the point of view of someone who’s trying to help people understand economics, the first statement is the important one. It’s the important one first because it’s the one that illustrates a way of thinking that permeates economics, and second because efficiency is more important than disease reduction (since efficiency accounts for disease reduction AND other things we care about). But the best evidence we’ve got is that the second statement is also true.

As far as spelling it out more carefully, everything I’ve just said above is in fact spelled out in considerable detail in my book “More Sex is Safer Sex” and in multiple blog posts and magazine articles that I’ve written on this subject.

PS— As far as your “Stop sleeping around” strategy — sure, if we abolished sex we’d eliminate (most) HIV transmission — but that wasn’t the question being addressed. The question was: TAKING AS GIVEN the behavior of the promiscuous, do we reduce transmission by increasing or by decreasing the activity of the prudes? Again, the answer is a) model dependent but b) based on all the evidence I’ve seen, more likely to be “increasing”.

PPS—I have not reread the response you linked to, but will tomorrow. I realize it’s possible you’ve already
responded to some of the above.

• bobmurphy says:

Steve wrote:

As I’ve said many times, the second externality is empirically the more important one. It’s this: The prude who gets infected might go home and die with the disease, in which case the virus dies with him.

Whoops if you indeed have said that many times, then you’re right I missed it and my bad.

2. Steven E Landsburg says:

Let me add one more thing to the above: One reason I think this example is so instructive is that the case for subsidizing sex-by-prudes is formally identical to the case for taxing polluters. (In one case we subsidize a positive externality, in the other we tax a negative, but that’s just the same argument with a sign change). People who think it’s crystal clear we should tax polluter often balk at subsidizing casual sex. i think it’s good for people to confront their own discomfort and ask what that tells them about the case for taxing polluters.

Any time you can make people uncomfrotable by taking an argument they accept in one context and showing them that it implies something they’re reluctant to accept in some other context, I think you’ve done a productive thing. Intellectual discomfort is the source of intellectual progress.

• Major_Freedom says:

Steve,

The second is that more sex leads to a lower rate of disease transmission, which is a model-dependent statement, but turns out to be true in the most detailed and careful models we’ve got (i.e. Michael Kremer’s). Kremer finds you can slow down HIV transmission substantially if you can bring everyone with fewer than 2.25 partners a year up to 2.25.

Assuming you are referring to this paper from Kremer:

http://homepage.ntu.edu.tw/~luohm/kremer.pdf

I just read it and I understand and accept the intuition he puts forth, however I don’t see how the statement “more sex lessens the transmission of HIV” requires us to assume that those who originally had no sex, and then increased their partners to say one partner per year, are required via assumption to have sex with “random” people, such that those in the high activity minority start to be partnered with around 5 active people and 5 non-active people per year.

Is it not a more accurate assumption to say that those who are originally non-active who then increase their partners to say one per year, are going to be extremely “picky” when it comes to choosing sexual partners, for example the type of people who are “prudes” and wait until he or she is 25 and/or married before they have sex, I would argue are not going to, on average, select a member of the high activity group with the same frequency as they select a member of the low activity group. If we consider the “prudes” who wait until they are older or married say, then wouldn’t the probability of them becoming partnered with another former “prude” partner be much higher than the probability of them becoming partnered with a highly active partner from the promiscuous group?

The people who are prudes but who then select one partner a year are the types of people who “care” about things such as HIV, and other factors that are more prevalent with highly active people.

So if we assume then that with the originally non-active group who then choose one partner a year, the probability of them selecting a sexual partner from “their own” group I would say should be greater than 50%, not 50% as assumed in the paper. Hence, if we take for example the assumption that those who were already active and we consider the paper’s assumptions of active people having 10 highly active partners per year, and then changing to 5 highly active and 5 lowly active partners per year, we should instead assume that the new ratio were, say, 9 highly active partners and 1 lowly active partner per year.

The specific numbers are not important, but the intuition I am getting at is that it is possible, if not likely, that the new ratio of “highly active / lowly active” partners for the highly active group could be such that HIV is maintained. For example, suppose that we continue to assume that 9 partners per year are required to keep HIV endemic. But let’s change the frequency of partners for the “highly active” minority from 10 to say 20 partners per year. If this highly active minority starts having more sex with the prudes, such that the 20 partners per year include more lowly active people, then the highly active group could have sex with up to 11 lowly active people per year (and hence 9 highly active people per year), and HIV will not only be maintained and endemic, but now HIV has been spread out into the lowly active population as well. In other words, the prevalence of HIV in general has increased, precisely because “more people are having more sex” and it just so happens that the number of partners per year required to keep HIV endemic is far fewer than what the highly active people have now.

Does this make sense, or did I make a huge error somewhere?

My impetus for all this is of course the initial “common sense” intuition that it is extremely counter-intuitive to argue that more sex leads to less HIV, when it is precisely sex that is (one of) the largest mechanisms for HIV transfer/infection. I can imagine everyone increasing their sexual partners to say 50 partners a year, and HIV spreading like gangbusters.

• Major_Freedom says:

Oops,

When I said

“So if we assume then that with the originally non-active group who then choose one partner a year, the probability of them selecting a sexual partner from “their own” group I would say should be greater than 50%, not 50% as assumed in the paper.”

I incorrectly attributed the 50% to the lowly active group instead of the highly active group. Please disregard that comment.

3. Alex Tabarrok says:

Not only is Steve correct in theory there is empirical evidence! See here

http://marginalrevolution.com/marginalrevolution/2008/06/more-sex-is-saf.html

4. stickman says:

FWIW, I think that Landberg’s basic idea here – i.e. casting a critical eye over your own posts – is very cool. I’m constantly dismayed at the tendency towards dirty, irrelevant ad hominen tactics in the (economic) blogosphere: Instead of debating someone on current matter X, simply dismiss them on the basis that they were incorrect on matter Y ten years ago. (Or even less.)

PS – Bob, any candidates from your own posts?

• stickman says:

* Landsburg
Sorry. Blame my South African schooling.