Applied Statistics

Stephen Dubner quotes Gary Becker as saying:

According to the economic approach, therefore, most (if not all!) deaths are to some extent “suicides” in the sense that they could have been postponed if more resources had been invested in prolonging life.

Dubner describes this as making “perfect sense” and as being “so unusual and so valuable.”

When I first saw this I was irritated and whipped off a quick entry on the sister blog. But then I had some more systematic thoughts of how Becker’s silly-clever statement, and Dubner’s reaction to it, demonstrate several logical fallacies that I haven’t seen isolated before.

No, it’s not true that most deaths are suicides

I’ll get to the fallacies in a moment but first I’ll explain in some detail why I disagree with Becker’s statement. The claim that most deaths are suicides seemed evidently ridiculous to me (not just bold, counterintuitive, taboo-shattering, etc., but actually false), and my inclination in such settings is to mock rather than explicate–but Becker and Dubner are smart guys, and if they can get confused on this topic, I’m sure others can too.

To start with, the statement “all deaths are suicides” is hard to criticize because it is obviously wrong and must, like the Bible and much of the work of A. J. Liebling, be taken metaphorically. if somebody tells me that the temperature in Paris yesterday was 20 degrees C, I can argue, both from personal experience and the weather report, that it wasn’t. But if I tell Gary Becker that, no, I know his statement is wrong–both of my grandmothers died and neither of them committed suicide–that wouldn’t cut much ice with him. After all, he probably has a couple of grandmothers who died without committing suicide too.

Suicide is “the intentional taking of one’s own life.” Or, if we want to put a statistical spin on it, choosing an action that increases the probability that you’ll die sooner. I interpret Becker as saying that most (if not all) deaths arise from such a choice.

It’s not so simple, though. Consider the following example. A couple and their two children are driving on the interstate to Grandma’s house for Thanksgiving, a few hundred miles away, when all of a sudden a tractor-trailer jackknifes right in front of them, resulting in a crash that kills them instantly.

Ha! Becker might say, in response to this hypothetical example. Everyone knows that flying is safer than driving. If this family had really cared about safety, they would’ve flown. Instead, they drove, which reveals their hidden preference: they really care more about saving money, or convenience, or having the kids watch DVD’s in the back seat, or whatever.

I don’t buy this argument. Even setting aside the kids’ deaths here–were they committing suicide too? Are four-year-olds with leukemia committing suicide? etc?–and setting aside the possibility that maybe Mom and Dad didn’t happen to be aware of the stats on flying and driving, there’s a bigger problem here, which is that people die all the time, even while making statistically correct decisions.

For example, suppose this particular family had flown to Grandma’s instead of driving, but then the plane crashed. It wouldn’t make much sense to say that they’d made the suicidal decision not to drive! OK, maybe you want to push this back one more step and say that the suicidal decision was to visit Grandma at all. But what if they’d stayed home and Junior had cracked his head open falling out of his treehouse. Or maybe the solution is to stay inside? Certainly not! The suicidal result could be that Junior and Missy get no exercise and die young of heart attacks. Also, being stuck in the house all day, they don’t learn how to make friends; as a result, they don’t succeed in the business world, they can’t get a job with health insurance, and so on.

Another line of reasoning is that, if only their car had been a Sherman Tank, the family could’ve withstood the tractor-trailer impact–thus, the death really represents the Smith family’s unwillingness to pay more for safety. But this line of reasoning is wrong too, both on an individual and a societal level. A tank isn’t cheap, either to buy or to drive, and the resources spent maintaining the tank (thus reducing the risk of death on the highway) are resources that can’t be used to make one’s life safer in other ways.

Just to nail that down one last time, no, I don’t see the evidence that “most (if not all) deaths . . . could have been postponed if more resources had been invested in prolonging life.” Transferring resources to avoid death from cause A could very well increase the probability of dying sooner from cause B.

A bouquet of fallacies

Now for the fallacies. The “puzzle” (as we say in the social sciences) is the “stylized fact” (ditto) that a scholar as intelligent and accomplished as Becker, and a pundit as intelligent as accomplished as Dubner, could get something so wrong. I will consider some fallacies that may have led them astray. As usual with this sort of thing, I hope that the exposure of these fallacies will allow people to better avoid them in the future.

The smart people fallacy. Lots of important issues have smart people on both sides, so it’s clearly a fallacy to think someone’s correct just because he or she is “smart.” Remember, Isaac Newton believed in leprechauns! Well, not really, but you get my point. Gary Becker is smart, but he can make mistakes–and the “smart people fallacy” can lead him to compound his mistakes, if people who know him just assume he must be correct and don’t call him on it.

The transitivity fallacy. We all know that a friend of a friend is not necessarily a friend. But we tend to forget that this lack of transitivity also holds with knowledge. Dubner knows and trusts Levitt; Levitt knows and trusts Becker. So Dubner should trust Becker, right? Wrong. The problem here is that knowledge and trust are contextual. Dubner knows Levitt enough to know when to take Levitt seriously and when to ask him some tough questions. Similarly, Levitt knows Becker well enough to trust him and also to evaluate his arguments critically. But when Dubner cuts out the middleman and reads Becker directly, he also bypasses two stages of critical filtering. That’s the transitivity fallacy.

The fallacy of qualitative counting We can imagine ways in which individual deaths could’ve been avoided–more money spent on safety here, more preventive screening there–so it’s natural to think that these possibilities cover everything. But, as Zeno taught us, you can add up lots and lots of little things and still not get so far. (Bill James once made a similar point about all the different unlikely ways you can get to first base without a hit, but I can’t remember where or what exactly he said. His point was that sometimes people list all these possibilities without recognizing that some of them are extremely rare.)

The fallacy of forgotten tradeoffs I mentioned this one above, and it’s a funny error for an economist and an economic journalist to make. At some level, I think they were aware of opportunity cost–Becker’s idea is that people are trading off safety for convenience, or, more generally, for quality of life–but they didn’t see their argument through to the end and realize that, no, you can’t just trade everything else in life off for safety. To draw an analogy, if you make a car bigger (without changing its engine), it will go slower, but that doesn’t mean you can strip down a Ford Fiesta and make it go 250 mph.

The illusion of control

Let me conclude by bringing up something that affects many of us in our professional lives: the tendency to focus on aspects of our lives where we feel we can make progress. I think the illusion of control is what leads Becker to write about suicide using mathematical expressions of optimality followed by phrases such as “That is, where a ray from the origin is tangent to the utility function (see Figure 1).” In another era, we might dig up some rocks and build a burial mound with our bare hands; in this white-collar era, we express our frustrations with the world with our words and equations. (I’m not saying that Becker thinks that he can control suicides by writing his article; what I think is that, when faced with difficult items beyond our control, we keep ourselves busy doing what we can control.) I’m surely involved in my own illusion of control by writing about these fallacies, but just maybe they will lead to a better understanding of the role of mathematical models in the social sciences. Dubner and Becker have made a contribution by putting there ideas out there where they can be criticized and refined.

Comments

  1. #1 Markk
    December 21, 2009

    I don’t know if it is a fallacy but isn’t this idea also an example of the “infinite knowledge” problem. Suicide implies intention. Even if one grants everything to their argument it still assumes individuals could intentionally make appropriate decisions, in this case on lesser risk alternatives, if they wanted to.

    That is not true, we’ve all only got so many minutes of life, we have to make decisions and so we cannot process all data and make optimal decisions no matter what. So we all make some distribution, if you will, of decisions on a correctness dimension. By correctness here I mean whether or not a decision as measured by our own personal moral and life rules is correct or wrong simply because of lack of knowledge or a reasoning error. Not along some objective measure. I would guess that we are doing well in general – not stepping in front of cars or off roofs for example, but we make many of these all the time whether we want to or not.

    It would be interesting if one could project backwards somehow, and get some clue as to the distribution over “correctness”.

  2. #2 John
    December 21, 2009

    This type of post really irks me. Becker’s point adds a lot to the debate. It is a point that hasn’t received enough attention. It forces us to think about what really are choices. Sure, the use of suicide is a strong word but that’s the point. The world would be a far poorer place without Becker’s comment and saying he is making a mistake is somewhat insulting. To me, it seems that Andrew is the one falling for the fallacy that just because you are smart, other people are the ones always making mistakes. The idea that if you made different choices with the express intention of reducing your death rate, you’d actually mistakenly increase it seems highly, highly dubious. Yet that’s Andrew’s entire argument!

    Can you really honestly disagree with “most (if not all) deaths . . . could have been postponed if more resources had been invested in prolonging life.”? Exercise and healthy eating would easily lead to “most” deaths being postponed slightly. Cardiovascular diseases alone accounts for 30% of deaths. So, yes, the majority of deaths are suicides in the sense that they could be postponed slightly by better choices earlier in life. And even if you disagree, that’s your opinion not some fundamental fact.

    What really, really irks me is the condescending tone and assumption that because you might have a different view, everybody else is making silly mistakes. They aren’t! Becker’s perspective is perfectly reasonable. The same can be said about your “I’m smarter than you” take on Levitt’s drunk driving example. You seem to be irked by Becker and Levitt thinking their clever stories make them smart, but at least they aren’t explicitly claiming that everybody else is stupid like you are. They’re just trying to bring up ideas they find interesting and counterintuitive so that other people can think about them.

  3. #3 Jeremy Miles
    December 21, 2009

    What if the word used wasn’t suicide? That seems to me like a term that is designed to attract attention, rather than to be accurate.

    It’s not so simple, though. Consider the following example. A couple and their two children are driving on the interstate to Grandma’s house for Thanksgiving, a few hundred miles away, when all of a sudden a tractor-trailer jackknifes right in front of them, resulting in a crash that kills them instantly.

    I don’t think the point is about flying, the point is that the more you drive, the higher your probability of being killed in a car crash. Those people didn’t have to make that trip, and if they hadn’t they’d still be alive. That’s a price that most people are prepared to pay – but one reason I don’t want to live a long way from where I work is that it will increase the chances of having an accident of some sort on the way to work.

    Are four-year-olds with leukemia committing suicide? etc?

    No, four year olds with leukaemia are not avoidable deaths, but four year olds dying of leukaemia are a pretty small proportion of deaths (although they have a pretty big impact).

    I’m not sure what etc is – it seems that all this is so obvious to you that it doesn’t need explaining, but it’s not obvious to me.

    Or maybe the solution is to stay inside? Certainly not! The suicidal result could be that Junior and Missy get no exercise and die young of heart attacks. Also, being stuck in the house all day, they don’t learn how to make friends; as a result, they don’t succeed in the business world, they can’t get a job with health insurance, and so on.

    That’s a pretty big leap from not driving to Grandma’s house to not getting a job, if you don’t mind my saying. In addition, you can never eliminate the chances of dying, but you can change the probability of dying through your actions. Not making a car journey (the necessity of which could be argued about) is not the same as refusing to leave the house.

    Of course, but if my probability of dying from A is reduced from 0.1 to zero, and my probability of dying from B is increased from 0 to 0.05, my life expectancy increases. That’s like the argument for not wearing a seatbelt – your car might be engulfed in flames, in which case having been thrown through the windscreen increases your chance of survival, so by wearing a seatbelt, I increase my chances of dying from A (being engulfed in flames) and decrease my chances of B (injuries sustained by being thrown through windscreen). I’ll take B, thanks.

    We can imagine ways in which individual deaths could’ve been avoided–more money spent on safety here, more preventive screening there–so it’s natural to think that these possibilities cover everything. But, as Zeno taught us, you can add up lots and lots of little things and still not get so far.

    But these aren’t little things. Some of them are pretty big things – much like wearing a seatbelt, or not smoking.

    I wonder if people’s reactions to this are in some way determined by your beliefs about causal influences on health. When I was young, my father put a sticker on the mirror in the bathroom which said: “the person you are looking at is responsible for your health”. I had a girlfriend who was incensed with rage by this, she hated it, she was NOT responsible for her health. To me, it seems obvious that (a) I’m responsible for my health, and (b) that many deaths could have been avoided or postponed had the person who died made different choices. (I would say that that was true for at least 3 of my 4 grandparents).

  4. #4 Andrew Gelman
    December 21, 2009

    Thanks for the comments. To respond briefly:

    Markk: I agree with you. I’d also point out that, even if we did know the “correct” life-extending decision, people would still be taking that decision and dying.

    John: I was of course aware that I might be making these same fallacies. But I don’t think I am! You write that my entire argument is: “The idea that if you made different choices with the express intention of reducing your death rate, you’d actually mistakenly increase it seems highly, highly dubious.” My point is that no matter what you do, you’re going to die. Becker’s the one who wrote “most (if not all!) deaths.” My grandmothers tried to live healthy lives, and they were lucky enough to live into their eighties. In what sense did they commit suicide? Did my grandmother who had cancer commit suicide because she didn’t live her life inside a lead-lined box? This just makes no sense to me.

    If Becker wants to say that lifestyle changes could save lives, they could say that. He went further, though, and likened most if not all deaths to suicide. I think that claim goes way too far.

    As I wrote at the very end of my blog entry, I agree with you that Becker and Dubner are making a contribution by putting these ideas out there to be discussed (leading to the comments on this blog, among other things). You say that I am “explicitly claiming that everybody else is stupid,” but I’m not. In fact, I explicitly characterized both Becker and Dubner as “intelligent”–not a controversial assessment in either case, I’d say! I feel that I am showing them the deepest respect by stating clearly where I disagree with them and how I think they went wrong.

    Jeremy: I agree with you completely that had Becker and Dubner made their points using a more accurate term such as “preventable death” rather than “suicide,” this would’ve helped. I still think they’re overstating it. Seatbelts and smoking save lives, but I don’t think “most if not all deaths” could be avoided using this or similar preventive measures. Again, my grandmothers come to mind.

  5. #5 John
    December 21, 2009

    I completely agree with Jeremy. Sadly, according to Andrew that means I’m falling for some obvious fallacy.

    I’d be interested in a clearly stated position from Andrew: Does he really believe that if people made different choices, taking into account all the constraints and tradeoffs they face, that there is no way they could postpone over 50% of deaths by an additional day? And does that not suggest that “in some sense” the majority of deaths are suicides? Becker’s carefully stated argument seems like a reasonable and interesting position, and one that hardly deserves public ridicule as being silly.

  6. #6 John
    December 21, 2009

    I just saw Andrew’s response. Thanks!

    I don’t think just because we’re all going to die that nothing can be “in some sense” suicide. Becker used the term suicide, which he qualified, since it brings in stark relief how important our choices are. That’s not a cheap trick or fallacy, that’s good writing. Anybody who reads what Becker writes, knows exactly how he is using the term. It’s also a classic style in philosophy. For instance, by not contributing more to various causes, am I not, in some sense, murdering those who need my help. That is, is there really a difference between action and inaction if the outcome is the same? Throughout my own life, questions framed in this fashion have had the most profound impact on me, even if I don’t find them that persuasive in the end.

    We also disagree with how many deaths can be slightly postponed. That’s fine. But saying that Becker and Duber are giving us a “bouquet of fallacies” is, in my view, just totally wrong.

  7. #7 Alex
    December 21, 2009

    The world would be a far poorer place without Becker’s comment

    Really? Far poorer??

    Get a room.

    and saying he is making a mistake is somewhat insulting.

    Becker’s a big boy, I’m sure he can take someone telling him he’s made a mistake (seriously, if you think calling someone out on a mistake is an insult, then perhaps scienceblogs isn’t the blog network for you).

  8. #8 Andrew Gelman
    December 22, 2009

    John:

    You ask how I fell about the statement that “if people made different choices, taking into account all the constraints and tradeoffs they face, that there is no way they could postpone over 50% of deaths by an additional day.”

    If Becker had said that, I’d have no problem. But that’s not what he said. He said “most (if not all!) deaths.” This includes my grandmothers, it includes four-year-olds dying of leukemia, people who get run over on the street, and all the rest. “If not all” implies that Becker thinks that it’s at least plausible to liken these deaths to suicide.

    Here’s my point. Becker could’ve said something true but commonplace–that, in many cases, resources could be used to decrease the chances of death are instead used elsewhere. Instead, he said something provocative and false. Arguably, it was a good thing that he did this–the very provocativeness (and falseness) of the statement got people’s attention. But the statement is still false as he said it, and I think it does illustrate some fallacies that Becker and Dubner were making. (And, no, I don’t think these fallacies are necessarily “obvious.” It’s the nature of common fallacies that we fall into them when we’re not careful.)

  9. #9 Brian de Alwis
    December 24, 2009

    John wrote:

    That is, is there really a difference between action and inaction if the outcome is the same?

    The difference lies in the intent behind the action. The intent is important, as reflected in the law’s differentiating between unpremeditated manslaughter vs premeditated murder.

  10. #10 osmanlı iksiri
    December 29, 2009

    I’d be interested in a clearly stated position from Andrew: Does he really believe that if people made different choices, taking into account all the constraints and tradeoffs they face, that there is no way they could postpone over 50% of deaths by an additional day? And does that not suggest that “in some sense” the majority of deaths are suicides? Becker’s carefully stated argument seems like a reasonable and interesting position, and one that hardly deserves public ridicule as being silly.

  11. #11 Andrew Gelman
    December 29, 2009

    Osmanlı:

    Becker wrote “most (if not all!),” which suggeest to me that he thought that it was at least a reasonable possibility that all deaths could’ve been postponed etc. Maybe you’re right that 50% of deaths could’ve been delayed but I don’t think it’s close to 100%. For example, I don’t see how the constraints and tradeoffs in my grandmother’s life had anything to do with her dying of cancer at the age of 82. I also don’t think that it makes sense to talk about the people dying in the World Trade Center plane crashes as “suicides” (except, of course, for the actual suicide terrorists). How were they supposed to make tradeoffs to extend their life? Were they supposed to follow the known principle of not going into the office on a Tuesday in September?

    The bit about resources that could be used to prolong life–I agree there’s something to that. It’s a pretty obvious point, but that’s fine. But, no, I don’t think it’s possibly all deaths, and I don’t see what’s gained by calling these “suicides.”

    If Becker had written, “Many (possibly most) deaths could’ve been delayed, sometimes by a nontrivial amount, through a reallocation of resources,” I’d have no problem with that. He chose to make a more dramatic statement and he got some attention with it, which is fine, but I think it’s also fine for me to point out that he’s twisting and exaggerating (or, should I say, he’s speaking with poetic license).

  12. #12 jodyaberdein
    January 3, 2010

    Having read this I was motivated to find out just how many deaths there are thought to be in the world, and the age distribution of said deaths. I had the suspicion that there are a large number of infant and child deaths.

    According to WHO life tables from 2000:

    http://tinyurl.com/yahqdrs

    There are a total of 56X10^6 deaths annually, of which about 12X10^6 are in under fourteens, and of these 11X10^6 are under 4.

    Most of these will be from avoidable causes such as infection or violence, but I’d have trouble ascribing the word suicide, even an odd sort of economists notion of suicide.

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