A Simple Mathematical Proof

All right, the system ate my post the first time, so this one might be shorter.

Throughout the feminist blogosphere runs the current of thought that "pro-lifers" are not, in fact, in favor of life, as their name might suggest, but instead variously anti-woman, anti-sex, or pro-fetus. I offer a mathematical proof that this is so.


Take as a given that illegal abortion is more dangerous than legal abortion. We know this is true. If you haven't already, read this article by a doctor who recalls treating complications of illegal abortion before Roe v. Wade.

To be difficult, I will assign a value of 0 to the mother's survival, since no new life is created, a value of -1 to either party dying (assuming, which I do not believe, that they are of equal value), and a value of +1 to a successfully born baby.

LEGAL, SAFE ABORTION
Mother lives 0
Fetus dies -1
Net life -1

ILLEGAL, UNSAFE ABORTION
Mother dies OR Mother lives -1 OR 0
Fetus dies -1
Net life -2 OR -1

(Control: BIRTH
Mother dies OR Mother lives -1 OR 0
Fetus dies OR Fetus lives -1 OR +1
Net life -2 OR -1 OR 0 OR +1)

Conclusion: Illegal abortion is either worse than or equal to legal abortion.

(This proof, of course, ignores non-fatal complications of illegal abortion and does not take into account the socioeconomic status of the woman and child after any birth.)

While it may seem that forcing women to give birth produces the best result, according to game theory, what many people don't seem to realize is that abortion is not like plastic surgery. Women who need abortions - and if they're willing to stick a knitting needle through their cervix then you can be pretty sure they really need not to have that baby - will get them whether they are legal or illegal, and suffer infertility, illness and death.

Oh, and the fetus dies anyway.

Some pro-life.


Other slightly tangential thoughts:

  • I'm not sure if CIANA has actually been signed into law, but wouldn't it be very, very unconstitutional? It would effectively stop pregnant minors from traveling out of state, that's pretty much unquestionably discriminatory.

  • Would pro-choicers please stop using the phrase "aborting a fetus"? It's playing into anti-choice mentality. It's not as bad as "aborting a baby," but the implication is the same. The correct usage is "aborting a pregnancy."
  • Posted by Rebecca - July 24, 2008, at 03:36PM | in Reproductive Rights
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    10 Comments

    [0+|0-] Author Profile Page Alice said:

    This argument assumes that all women who would otherwise get legal abortions will always acquire or perform illegal abortions. This may be true in areas where everyone is a total badass who can always overcome the strong psychological barrier against stabbing oneself, will never be intimidated by possible repercussions of committing a crime, and always either does or does not want an abortion, with absolutely no room in the middle for people who chose one or the other but who could be persuaded otherwise with sufficient changes in the costs involved with either choice.

    Interestingly, if we do accept the assumptions of this argument, it follows that all the stumbling blocks being placed in the way of getting an abortion, such as waiting periods, shame, and long travel times to abortion clinics, will never actually result in preventing a woman who wants one from acquiring one, being at worst inconvenient, since surely the trouble of overcoming those barriers is utterly insignificant compared to untrained self-surgery.

    [0+|0-] Author Profile Page Paul said:

    First of all Rebecca; nice experiment. I wonder what the inspiration for this idea was.

    Second; how do you make the bullet points? I could spend quite some time looking it up my self, or I could be an american and ask some one to do the work for me.

    Third; I would be careful resulting to game theory or mathmatical proofs to regulate morality. I just see all kinds of spurious proofs being designed to counter your arugment based on biased givens.

    Fourt: dont you agree that this point would be way cooler and better organized if it had a square bullet next to it?

    [0+|0-] Author Profile Page JKayOh said:

    Great idea, Rebecca. I have to slightly disagree with Paul on one point and agree on another. The use of game theory is very often used to give mathematical value to areas that typically would have no empirical "values" or data sets (IE: very often used in International relations or on questions of Diplomacy) So, using it in this manner is no different. I agree that it can be massaged towards any belief system (as can anything else.) I, too, can imagine an anti-choicer giving a -1 value for the "psychological damage to the woman" blather, etc, etc, etc.

    On another, but related, note--after the popularity of "Freakonomics," I am still shocked that the data garnered about the right to choose, hasn't been highly publicized in the mainstream. It informs us that the right to choose (granted in the 70's) DIRECTLY and ABSOLUTELY correlates mathematically with the very dramatic drop in the crime rate of the 90's. So, not giving birth to an entire generation of children that would be born into a less that desirable condition (as KNOWN and defined by the woman) actually is a smart CHOICE? Who knew?
    Some may say that this is a highly controversial line of reasoning to use in support of choice. But others see it as WOMEN BEING SMART ENOUGH to MAKE SMART DECISIONS--knowing what is right for them. It turns out that women's choices do end up affecting us all. (Again, surprising--right?)

    And finally on the math subject again, how about those recent mainstream news reports that girls are "as good as boys" in math? They finally picked up on the alternative media's "discovery." Jezebel wrote: "Whoever is shocked, raise your hand!" Love it.

    Not to be a jerk about it, but this isn't a proof, or a very good place to apply game theory. Your setup only looks at the benefit on the margins, not the aggregate benefit. Even if you were to exaggerate the numbers and say that half of all women who want an abortion are still willing to do so when it is illegal\unsafe, and a full half of women who perform illegal abortions die doing so, making abortion illegal would cause a 25% decrease in "lives" (as you've defined them) lost. [Current # of abortions VS (Current # of abortions)(.5) + (Current # of abortions)(.5)(.5)].

    What's more important is your point that the "pro-life" position is really closer to "pro-fetus". It's only beneficial in this model under the assumption of the value of a pregnancy (not even a fetus) being = to the value of the life of a woman, a proposition which is clearly absurd. That's also taking out things like the affect of having a child on the quality of life of the mother, the quality of life of the child, and even the affect on future crime (if you were to include Levitt's work in your model, for instance, it would increase the cost of life for banning abortion, by way of future murders, by a few thousand lives).

    Also, just to point out, you referred to a pregnancy not occurring under "birth control" as a fetus being lost. As you pointed out in your second bullet point, that's playing into the anti-choicer's game. Even the most extreme anti-abortion advocate would be hard-pressed to say birth control is exactly as bad as a late-term abortion (ie: a value of 1 in your model).

    You beat me to the punch on Levitt, I see. Glad you're a fan too. More precisely, the legalization of abortion had a statistically significant affect on the decrease in crime on a regression controlling for other variables (~"directly and absolutely correlated"). If I remember correctly, the rough estimation given was 10 percentage points of the total decrease in crime in the early 90's.

    I also agree with you that game theory, and more broadly, economics, can be incredibly useful in policy making\analysis. The problem with it comes in that it is both difficult, and can make people uncomfortable, to assign numeric values to human life, etc. When it's offered as a tool for analysis, accusations of being too callous about human life from the detractors of whatever the findings support are not far behind. Levitt, for instance, got in some media trouble when his book came out for saying abortion prevents crime.

    Alice, identity: Ja, I know it's not really a proper proof. It was more a slightly lighthearted way of pointing out that the pro-life position is in fact pro-fetus.

    Paul: bullet points are [li] except with angle brackets instead of square.

    JKayOh: That's fascinating, about the drop in crime. I never knew that.

    identity: I'm not sure what you're talking about, I didn't mention birth control at all. I did, however, use birth as a control state in the "experiment." Birth also has a chance of the fetus dying.

    You're right, I misread "control birth", so my 3rd paragraph is completely wrong. My apologies.

    [0+|0-] Author Profile Page Hilary said:

    Instead of simply guessing (or assuming) how women behave to barriers to abortion, commenters, it is really easy to research it.

    Here is a great quote from the Guttmacher institute:

    "Opponents of abortion in the United States and around the world may be expected to continue to insist that the best way to reduce abortion is to restrict it. With the passage of time, however, more and more countries can now demonstrate the facts to be otherwise."

    Woman DO, overwhelmingly, choose illegal abortion when legal, safe abortion is not available. It is a major cause of maternal mortality world wide.

    Uniformed theoretical musing may be entertaining to unaffected commenters on community blog site, but real women are dying worldwide in large numbers, most of them leaving behind their other children who are much more likely to die without their mothers. If you all are really so concerned about women's reproductive health, here is an entire journal issue of the Lancet, one of the world's most renowned medical journals, dedicated to improving women's health. One of their main recommendations is to increase access to safe abortion worldwide.

    [0+|0-] Author Profile Page JKayOh said:

    Hilary,
    First of all, I appreciate your information, truly. However, there are better ways to inform and enlighten individuals than referring to fellow feminists as "unaffected commenters" and suggesting that our discussions on abortion is merely "entertaining," whilst "real women are dying." The use of the term "musing" was particularly condescending. Did you feel that was necessary? Hey, we're on your side! :) Anyone concerned with choice and a woman's right of dominion over her own body has my full attention!

    If we were "unaffected," we wouldn't be here. And how you, personally, can determine our levels of being affected by this issue remains in question as well. Engaging in all types of discussions is highly beneficial and gets everyone thinking. Hence, the existence of this website. (As far as I understand it.)

    It's strange that you would choose to come into a thread of people obviously supporting choice and lob the blog equivalent of a verbal "hand grenade" into the room.

    I'm just saying.

    [0+|0-] Author Profile Page Hilary said:

    It is not a hand grenade to point out that there is research on this issue. Telling someone that they make an improper assumption about life and death is also not a hand grenade. I pointed to research by the two of the most reputable sources on the topic. How am I ruining the discussion?

    I was specifically responding to certain commenters who implied that making abortion illegal will prevent some women from getting them, which would be a net benefit in lives. This was the biased kind of quibbling an earlier poster warned about.

    In reality, making abortion illegal actually dramatically increases the morbidity and mortality from abortion and would not add lives, (see sources above) so it is a flawed (and rather callous) example.

    It also happens to be the third leading cause of maternal mortality in countries where abortion is illegal. Someone who is pro choice and in a discussion about women living or dying from the procedure should look up these things if they want to discuss them and not have people refute their points.

    Also, if anyone who is affected by maternal mortality due to illegal abortion consequences was on this thread and said it was actually a net benefit, life wise, I am sorry if I cast aspersions on your affectedness. (Because that's where the real victims are in this discussion. Good to focus on the important stuff. Right.)

    As an aside, I am really confused as to why someone would resort to using such extreme terms as "hand grenade", you know, a weapon that kills and maims people to describe an argument point, but tell me I am being dramatic when I say women are dying when, well, women are actually dying. In large numbers. No exaggeration.


    Keep musing.

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