Bayes' Theorem and Mr. Obama's Literary AgencyBy Jason Kissner
A mathematical tool is offered to evaluate the likelihood, in light of the Breitbart disclosure, that Mr. Obama was born in the United States.
How ought one evaluate the evidentiary significance of the 1991 literary agency promotional booklet claiming that their client Barack Obama was born in Kenya?
The "birther" issue is clearly one that is very charged. This contribution is directed toward those persons who are willing to reason carefully about it no matter what conclusion they may have reached so far.
It should be acknowledged at the outset that no conclusive answers are offered herein. In fact, the chief result of the following probabilistic analysis is that interesting and potentially important questions are raised that, absent the analysis, might not otherwise have been asked.
It is hoped that the subsequent presentation will help stimulate genuine debate, particularly since persons are encouraged to form their own conclusions. If the presentation ends up contributing to meaningful, genuine debate, it will be because the great Reverend Bayes provided an excellent rational and scientific framework within which to reason about questions like the one at hand. Should reasonable people conclude that the booklet lends any additional credence to the idea that Obama was born in Kenya and not the United States? Unsurprisingly, the answer to that turns out to be: it depends. What it depends on, however, turns out to be quite fascinating, and may end up spurring additional investigation along lines that, it must be admitted, are sometimes paradoxical and therefore very easy to miss.
Those who are unfamiliar with Bayes' theorem may be interested to know that is has wide application in sciences including biology, physics, criminology, and much else besides. With apologies to those already comfortable with the theorem, let us begin considering the impact of the booklet with respect to judgments regarding Mr. Obama's birthplace by considering that aspect of the theorem known as the "prior probability."
What Bayes' theorem does is allow one to calculate the probability of an event by adding new information to the information one begins with. In Bayesian analysis, the information one begins with is called the "prior probability." This prior probability is then "updated" with additional information. In our analysis, the update consists in information contained in the promotional booklet. The prior probability can be specified in several ways; essentially, though, it is the probability that Mr. Obama was born in Kenya irrespective of the booklet.
The prior probability (herein, p(A)) in case you wish to employ Bayes' formula yourself) is important. If it is "strong" enough, which is to say probable enough, then updating might well do little to alter one's initial judgment. Suppose, for example, that a wife has been murdered and that a highly specific and accurate DNA test has been performed that matches the husband's DNA. Suppose also that we knew before the test was conducted that at the time of the murder the husband was incarcerated in a maximum security penitentiary and that after the test was conducted he was still there. In that event, it would be rational to conclude that the test was mistaken. True, the husband could have slipped out under cover of darkness, made his way to his wife's location, done the deed, and returned to his cell but...you get the picture.
What then shall we say about the prior probability p(A) that Mr. Obama was born in Kenya? There are many who take themselves to be certain that he was born in Hawaii. It is reasonable to ask such persons what, if anything, in life is truly certain. It is also reasonable to point out that such persons are also saying that there is no evidence that could possibly come to light that would prompt them to change their minds. Is that a reasonable position to hold?
Probably not, so all else equal, it is rational to exclude such persons from the discussion (and they probably have not read this far anyway). What really is it issue for reasonable people here is just how unlikely it is that Mr. Obama was born in Kenya given all the evidence before the Breitbart disclosure. If if one wants to be as reserved as possible on this issue (and that may well be the best approach on this question) one would form the prior by considering only the evidence that favors Mr. Obama, which entails disregarding the Arpaio material.
Thus, many consider the combination of the long form birth certificate file, the certificate of live birth, statements of Hawaiian officials, and information such as the 1991 Illinois Daily Herald and New Times articles linked by the Breitbart people to amount to compelling evidence that Obama was born in Hawaii. Of course, persons are free to add whatever additional evidence they think is favorable to Mr. Obama on the issue, including their view, if such it is, that Mr. Obama is, generally speaking, highly credible.
At this point, reasonable people will ask themselves just how compelling they think the evidence favorable to Mr. Obama is. Many will find it extremely compelling. If you're one of them, can you, at least approximately, quantify your judgment?
A reference point may prove useful here. The Indianapolis Colts won 2 games and lost 14 last year. How likely do you think it is that they will win next year's Super Bowl?
Vegas odds makers are very good at what they do; they have to be. Vegas.com currently has the odds on the Colts winning Super Bowl XLVII at 100 to 1, which in probability terms is .0099, or just below one percent.
With that in mind, reasonable people might compare their presumptively evidence-based confidence that Obama was born in the United States with their confidence that the Colts will not win the Super Bowl. Personally, and aside from the Breitbart disclosure, I see no reason to believe that the Colts are any more likely to win next year's Super Bowl than Mr. Obama is to have been born in Kenya on the basis of evidence such as that discussed above, and partly for that reason I'm going to go ahead and, having rounded, use .01 as the prior probability that Mr. Obama was born in Kenya.
If readers think, on the basis of evidence other than the Breitbart disclosure, that Obama is far less likely to have been born in Kenya than the Colts are to win Super Bowl XLVII, they can revise their prior downward accordingly. Here, it is worth mentioning that the lower the probability you assign to the prior, the less weight the Breitbart disclosure will have for you, which should fit your intuition as to how things should work with Bayes' theorem.
With the prior in hand, we can look at the rest of the calculation. The rest of the calculation can certainly be framed in different ways which are open to debate. Since generating debate is part of the intent of this contribution, alternative formulations are welcomed. One reasonable way to frame the rest of the calculation is as follows. We want to update our prior probability that Mr. Obama was born in Kenya by taking into account the newly acquired promotional booklet's declaration that he was. That is, we want to assess the probability that Mr. Obama was born in Kenya given that the promotional booklet says he was (p (A/B)) and given our prior probability that he was.
To do this, Bayes' Theorem directs us to compare the probability that the promotional booklet says Mr. Obama was born in Kenya under the supposition that he really was born in Kenya (p (B/A)) with the probability that the promotional booklet says Mr. Obama was born in Kenya given that he was born in the United States (p (B/-A)), and then view this comparison in light of the prior.
An analogy may make this clearer. Suppose we want to assess the probability that someone has used an illicit drug. We might start with a prior probability p (A) that incorporates whatever information bearing on the likelihood of the person's drug use we could find (by analogy, the favorable information in support of the idea that Obama was born in the United States). Then, we might perform a test to update the prior. Suppose the test turns out positive for usage. Then, evaluating the contribution of the positive test update (by analogy, the promotional booklet) to the likelihood of usage would involve consideration of not only the probability of a positive result supposing the person did in fact use (p (B/A), (by analogy, the probability that the booklet says Obama is from Kenya supposing that he really is), but also the probability of positive result supposing that the person did not use (p (B/-A), (by analogy, the probability that the booklet says Obama is from Kenya supposing he was born in the United States).
We can now proceed somewhat more swiftly. Surely it has been the case at least since 1991 (the year of the booklet) that when persons who were born in Kenya (or in pretty much any country for that matter) did an autobiography, their literary agent in the United States correctly stated their country of origin when a country of origin was stated. It therefore seems appropriate to assign a very high probability here, but it is worth pointing out that the lower the probability one assigns here, the more likely the conclusion that Obama was born in the United States even though the booklet says he was born in Kenya will turn out to be (and vice versa). This should again make intuitive sense, especially since we can refer back to the analogy where we are considering the impact of a positive drug test. The less likely the test is to come out positive when the subject of the test really is using, the less likely we are to conclude that the subject really is using.
How high should we set this probability? In thinking about this, we might reflect that one Miss Miriam Goderich says that she was an assistant at Mr. Obama's literary agent in 1991, and that the pamphlet indicates that Mr. Obama was born in Kenya due to her own "fact-checking" error. Maybe so, and we shall have to reflect on that in a moment when we consider the last element of our calculation, which contemplates the probability of Ms. Goderich's having said in the promotional booklet that Mr. Obama was born in Kenya if he was in fact born in the United States.
In assigning a probability to the booklet's stating that Mr. Obama was born in Kenya if he in fact was, we should make doubly sure to notice that there is a big difference between a literary agent's stating of an autobiographical client who really was born in the United States that they were born in Kenya and a literary agent's stating of an autobiographical client that they were born in Kenya if they really were. Clearly, it is the latter probability that concerns us now (once more, we will address the probability that a literary agent would say of someone who was really born in the United States that they were born in Kenya momentarily, which is to say no questions are being begged here).
So, unless we can say Kenya was unusual from a probabilistic standpoint in connection with the representations of literary agents and/or that literary agencies have become less reliable over time, we can frame the immediate inquiry as: how likely is it that an autobiographical client's literary agency will correctly state that they were born in the country they were in fact born in?
I daresay they will be accurate in the above sense 9999 times out of 10000, and even that strikes the present writer as rather, shall we say, "unappreciative" of the accuracy of literary agents. That is, when they choose to specify a place of birth for an autobiographical client, they almost always get it right, do they not?
Let us identify a probability of .9999 as the likelihood that the booklet would say Mr. Obama was born in Kenya under the supposition that he was born in Kenya. As before, just revise it if you don't like it.
Finally, we have the matter of the probability that the booklet would say Mr. Obama was born in Kenya under the supposition that he was born in the United States. This is where things get truly intriguing. With respect to this component of Bayes' theorem, the higher the probability one assigns, the lower the probability of the conclusion that Obama was born in Kenya even though the booklet says he was born there (and vice versa). One last time, this should be intuitive since if drug tests frequently come out positive even if the subject isn't using, we should assign less weight to tests that say they are.
To begin, let's look at the information we currently have about the nature of the error. Was it more or less random?
Mr. Obama's own campaign seems to be say it was more or less random. To be exact, Mr. Obama's campaign says that "the mistake in the pamphlet was 'nothing more than a fact-checking error' by the agent [Ms. Gonderich]."
This echoes quite well Ms. Gonderich's statement that "[t]his was nothing more than a fact checking error by me -- an agency assistant at the time. There was never any information given to us by Obama in any of his correspondence or other communications suggesting in any way that he was born in Kenya and not Hawaii. Mr. Obama never suggested in any way that he was born in Kenya and not Hawaii."
So Ms. Goderich did not receive information that Mr. Obama was born in Kenya from Mr. Obama. Perhaps, then, Ms. Goderich declared that Mr. Obama was born in Kenya as a result of some stray rumor, or perhaps Ms. Goderich for some unknown reason inferred that Mr. Obama was born in Kenya because his father was? What else could account for a literary agent's (and one responsible for an autobiography, at that) mistaken assumption that someone born in the United States was born in Kenya if the agent was not led to the conclusion in one way or another?
How likely is it that a random error like the one asserted by Mr. Obama's campaign and Ms. Goderich explains the mistake of stating that Mr. Obama was born in Kenya if in fact he was born in the United States? A one percent chance, for a probability of .01 (again approximating the probability of the Colts winning the Super Bowl next year) seems a rather reasonable, even kind, estimate. If you use that estimate, and if you also set the prior at .01 (which means the complement of the prior is .99, which you'll need to complete the calculation under the extended version of Bayes' theorem used here), and, lastly, if you once again set the probability that the booklet would say he was from Kenya if he in fact was at .9999, your updated probability that Mr. Obama was born in Kenya is an astonishing .502, or 50.2%, as anyone who consults Bayes' Theorem can confirm for themselves. Thus, the booklet information would prompt you to move from judging that Mr. Obama is about as likely to have been born in Kenya as the Colts are to win the Super Bowl next year to concluding that Mr. Obama is more likely than not to have been born in Kenya.
Paradoxically, if you believe the Obama campaign, and therefore Ms. Goderich's statement that Mr. Obama never suggested in any way that he was born in Kenya and not Hawaii, under Bayes' Theorem it becomes more likely, not less likely, that Mr. Obama was born in Kenya. By way of analogy, if a drug test has only a low probability of indicating that a subject of the test is not using when they really are not, all else equal we are considerably more confident in the test.
In fact, if you keep all the probabilities other than the prior and change that to .5 (which would represent someone who was sitting on the fence before the disclosure of the booklet), you can see that those who were sitting on the fence prior to disclosure should update their judgment and conclude that Mr. Obama was born in Kenya with a whopping probability of .99, or 99%!
However, in spite of what the Mr. Obama's campaign currently says, suppose that you believe that the error was not due to chance. If you believe that then you disagree with Mr. Obama's claim via Attack Watch, and the claim of Ms. Goderich's that the Attack Watch claim is predicated upon, having to do with the idea that the information in the booklet is attributable to a fact-checking error that has yet to be explained and has no clear explanation, which is to say that at the moment it is inexplicable.
Be those things as they may, if you believe that the Obama campaign is not telling the truth on this issue, you might reason as follows. Perhaps Mr. Obama, as many have suggested, was simply trying to appear exotic? Or, perhaps Mr. Obama was simply trying to enhance the marketability of his book? Once again, that's not what the campaign says, but it's possible, so let's look at matters under the assumption of intentional misrepresentation just in case there has been a misunderstanding.
The "intentional misrepresentation" view might be a reasonable view (particularly if one has good reasons to explain the inconsistency with the campaign's current statement), but how many people have considered that if Ms. Gonderich is not telling the truth (meaning that Mr. Obama did contribute to misrepresentation of his place of birth and that Mr. Obama's campaign is currently not telling the truth), one of the following two things must be true:
It follows under the supposition of intentional misrepresentation that if one wishes to make a rational case for the belief that the promotional booklet's declaration that Mr. Obama was born in Kenya has nothing much to do with the likelihood that he really was, one should either provide good reasons for thinking that Mr. Obama had good reasons to misrepresent his place of birth, but only to his literary agency, or make a reasonable attempt to locate another document -- itself obviously not dispositive of the issue and also independent of literary agency processes -- paradoxically indicating that Mr. Obama was born in Kenya.
That is, if Mr. Obama did, contrary to his campaign's current statement, intentionally misrepresent his place of birth to his literary agent but did not have good reasons to restrict his misrepresentation to just his literary agent, do we not have reason to expect that there are other documents, independent of literary agency processes, that indicate a Kenyan birth?
Overall, a few things seems to be clear. First, many people seem to think that it is easy to rationally justify dismissing the promotional booklet's declaration that Mr. Obama was born in Kenya if the issue pertains to "birtherism." It is reasonable to believe that those people are wrong.
Second, the Breitbart people have clearly indicated that they do not think the promotional booklet says anything at all in regard to the birther issue. The above analysis indicates that reasonable people can disagree with their assessment.
In addition, Obama's own campaign does think that the promotional booklet connects with the birther issue. Attack Watch currently has a bold-faced header that states "Latest attack about the President's birthplace ignores the facts on record."
The same page also states of the Breitbart people that "they're citing an errant work to push the false idea about President Obama's public image while drudging up the birther conspiracy."
Clearly, Mr. Obama's campaign thinks that the promotional pamphlet pertains to the birther issue.
As was indicated before, the very same page also attributes the statement in the promotional booklet that Mr. Obama was born in Kenya to what amounts to a random "fact-checking" error that Mr. Obama had nothing to do with.
Since the immediately preceding statements are true, it follows logically from earlier statements in the article that:
If one believes the Obama campaign, then, if one is to avoid the conclusion that Mr. Obama is more likely than not to have been born in Kenya and at the same time be reasonable, one should provide reason for believing at least one of the following three things, and even then things will depend on probabilities assigned to remaining items, if any:
So, all told, is the birther position correct? Maybe.
Is the birther position at present unreasonable? Surely not; in fact, it may well be the most reasonable position to adopt even if you still think you had very good reasons to the contrary in advance of the promotional booklet's release.
I have done so, and I accept responsibility for much of the misunderstanding expressed in regard to the "Bayes' Theorem and Mr. Obama's Literary Agency" article.
I want to express my heartfelt gratitude to Thomas Lifson for giving me the opportunity to more clearly express myself, particularly since I really think the main conclusion of the article is both important and powerful.
Misgivings about the article seem to cluster around three related ideas: (1) uncertainty about the main conclusion drawn; (2) what the point of the article was; and (3) why information unfavorable to Mr. Obama on the birther issue was not included.
The main conclusion of the article was that given the release of the promotional booklet that says Mr. Obama was born in Kenya, it is more reasonable to believe that Mr. Obama was born in Kenya than it is to believe that he was born in the United States (it's a bit more involved than that, but that's the essence of it). Personally, I believe a conclusion stronger than merely "more likely than not" should be reached, but why push the issue before those who disagree with us have engaged the debate?
The conclusion may not sound like much. Please notice, though, that the conclusion was reached on the basis of the promotional booklet's having said that Mr. Obama was born in Kenya, and no one can deny what the promotional booklet says. That is, the promotional booklet is evidence regarding where Obama was born that we can be certain exists. We cannot say we are certain that the birth certificate released by Obama is phony, can we? In making our case, why not begin with something everyone has to agree on?
Debates like that seem to be never-ending, don't they?
What the "Bayes' Theorem" article really does is provide a way around this never-ending debate. Perhaps if you give the article one more chance with the above ideas in mind, you might come to agree that it does, and that it therefore has a point that is worthwhile.
The truth is that the article is not easy reading, but conservatives shouldn't balk at that should they? Also, I'm happy to answer any questions that you have via e-mail.
Finally, the reason why evidence that disfavors Obama was not included in the article is that the case conservatives make is even stronger if it can win even when it makes serious concessions to the other side, right?
Jason Kissner Ph.D., J.D. is associate professor of criminology, California State University, Fresno.
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