Category Archives: statistics

Fundie Probability: Even Worse Math than Swinburne

I recently got a real prize of a link from one of my readers. He’d enjoyed the [Swinburne][swinburne] article, and had encoutered this monstrosity; an alleged [probability of christianity][prob] argument *significantly worse* than Swinburne.
[swinburne]: “My shredding of Swinburne”
[prob]: “Mathematical Probability that Jesus is the Christ”
The difference between Swinburne and this bozo (who’s name I can’t locate on the site) is that at least Swinburne made *some* attempt to use some math to justify his position. It may have been sloppy as hell – but at least he *did* go through the effort of using actual Bayesian methods. I think that he did an *appallingly* bad job of it; but at least there was something there.
Our new friend doesn’t even bother to do that.
Here’s a very typical example of his “argument”:
>The reason why prophecy is an indication of the divine authorship of the Scriptures, and hence a testimony to the trustworthiness of the Message of the Scriptures, is because of the minute probability of fulfillment.
>Anyone can make predictions. Having those prophecies fulfilled is vastly different. In fact, the more statements made about the future, and the more the detail, then the less likely the precise fulfillment will be.
>For example, what’s the likelihood of a person predicting today the exact city in which the birth of a future leader would take place, well into the 21st century? This is indeed what the prophet Micah did 700 years before the Messiah. Further, what is the likelihood of predicting the precise manner of death that a new, unknown religious leader would experience, a thousand years from now – a manner of death presently unknown, and to remain unknown for hundreds of years? Yet, this is what David did in 1000 B.C.
>Again, what is the likelihood of predicting the specific date of the appearance of some great future leader, hundreds of years in advance? This is what Daniel did, 530 years before Christ.
>If one were to conceive 50 specific prophecies about a person in the future, whom one would never meet, just what’s the likelihood that this person will fulfill all 50 of the predictions? How much less would this likelihood be if 25 of these predictions were about what other people would do to him, and were completely beyond his control?
>For example, how does someone “arrange” to be born in a specific family?
>How does one “arrange” to be born in a specified city, in which their parents don’t actually live? How does one “arrange” their own death – and specifically by crucifixion, with two others, and then “arrange” to have their executioners gamble for His clothing (John 16:19; Psalms 22:18)? How does one “arrange” to be betrayed in advance? How does one “arrange” to have the executioners carry out the regular practice of breaking the legs of the two victims on either side, but not their own? Finally, how does one “arrange” to be God? How does one escape from a grave and appear to people after having been killed?
>Indeed, it may be possible for someone to fake one or two of the Messianic prophecies, but it would be impossible for any one person to arrange and fulfill all of these prophecies.
So the basic method is. Assert that there were prophecies that unambiguously identified a specific event. Further, assert that those prophecies were fulfilled. Now, ask, what’s the probability of all of those prophecies coming true?
The arguments that he presents range from the vague to the silly. In the vague cases, he makes a classic mathematical mistake: switching between a priori and a posteori probabilities. In general, probability calculations are done a priori: “I *don’t know* what specific situation I’m going to apply my calculations to, so when I set the probabilities, I do it without any specific knowledge of a desired outcome”. But he does it a posteori: “Since this description of an event *clearly references* this specific incident, I’m going to set the probabilities using my knowledge of the outcome”.
For example, he asserts things like prophecies naming a specific city in which his alleged messiah would be borne. Of course, the specific prophesy that supposedly makes this claim is not specified. And if you go to other places that babble about the various prophecies about the messiah, you find that none of them are actually *specific*. That is, they all talk in very vague and symbolic terms, and *a posteori* interpretations of those can say that they identify a specific place associated with Jesus; but if you were to read them with an open mind, without any idea of a set of events that you were trying to link them to, you almost certainly would not have demanded that they describe a single, specific location. If they could describe 20 locations, then your probability calculations would need to include the probability for each of those possibilities; if you use the a posteori perspective to narrow it down to one, you’re making invalid use of hindsight to skew the numbers.
Even worse than just using the alleged fulfillment of vague prophecies, he makes an even worse kind of a posteori error: numerous citations of prophecies from the *new* testament: a set of books written *after* the events that were supposedly prophesized – as in the citation of the book of John in the quoted section above. We’re supposed to take the fulfillment of a prophecy that wasn’t written down until *after* the event, and act surprised that there’s exactly one supposedly historical event that matches that prophesy.
Ooh, I’m surprised. A bunch of guys who were trying to convince the world that Jesus was the messiah wrote down prophesies *after the fact* in a way that only Jesus could possibly have fulfilled. Adding *that* to an alleged probability calculation to reduce the probability of anyone but Jesus fulfilling all of the prophecies isn’t even bad math. It’s just plain old lying.
In the category of just plain silly, I absolutely *love* the quote where he’s talking about how hard it would be for anyone else to fulfill these alleged prophecies: “how does one “arrange” to be God?”. Yeah, one of the statements that he supposedly calculuates a probability for is “being God”.
What’s the probability of being God? I’d really like to know. Do I have any real chance of fulling it?
Alas, I can’t tell, Because despite insisting that there are 456 different prophesies that Jesus supposedly fulfilled, and that each of those is factored into the calculuation, he doesn’t tell us how any of those individual probabilities were calculated – for example, he says the probability of an alleged messiah being born in Bethlehem was one in 2.8×105. Where’d that number come from? We don’t know.
And for most of the alleged events that were fulfilled prophesies, he doesn’t even give us that much information.
For example, he says that the odds of fulfilling 48 prophesies – he doesn’t say which 48 – is 1 in 10157. He just asserts that. And then goes off into a classic “big numbers” babble about how terribly unimaginably large that number is. He even goes so far as to pull out one of those bullshit “anything less likely than X is impossible”. (I’m actually playing a game of spider solitaire in the background as a write this; which means that I’m doing something absolutely impossible!)
He’s even got a ripoff of the PSICOP challenge:
>But, of course, there are many more than eight prophecies. In another calculation, Stoner used 48 prophecies (Idem, 109) (even though he could have used Edersheim’s 456), and arrived at the extremely conservative estimate that the probability of 48 prophecies being fulfilled in one person is the incredible number 10^157. In fact, if anybody can find someone, living or dead, other than Jesus, who can fulfill only half of the predictions concerning the Messiah given in the book “Messiah in Both Testaments” by Fred J. Meldau, the Christian Victory Publishing Company is ready to give a ONE thousand dollar reward! As apologist Josh McDowell says, “There are a lot of men in the universities that could use some extra cash!” (Josh McDowell, Evidence that Demands a Verdict, California: Campus Crusade for Christ, 175).
The catch of course is that you need to fulfill the prophesies *in exactly the way that these fundies interpret them* – in other words, starting from the assumption that Jesus fulfilled them, and that the prophecies specifically point at exactly the events of the life of Jesus.
I can actually save the authors a lot of trouble. The probability of anyone else fulfilling these prophesies *is zero*. Because they’re interpreted a posteori as the specific events from the life of Jesus, the odds of it being Jesus who fulfilled them is exactly 100%, and the odds of anyone else doing it are exactly 0%.
Course, if you put it that way, suddenly it doesn’t sound so impressive, even to the bunch of idiots who’d accept this argument to begin with.

Election Fraud? Or just bad math?

I’ve gotten an absolutely unprecedented number of requests to write about RFK Jr’s Rolling Stone article about the 2004 election.

RFK Jr’s article tries to argue that the 2004 election was stolen. It does a wretched, sloppy, irresponsible job of making the argument. The shame of it is that I happen to believe, based on the information that I’ve seen, that the 2004 presidential election was stolen. But RFK Jr’s argument is just plain bad: a classic case of how you can use bad math to support any argument you care to make. As a result, I think that the article does just about the worst thing that it could do: to utterly discredit anyone who questions the results of that disastrous election, and make it far more difficult for anyone who wanted to do a responsible job of looking into the question.

Let’s get right into it. He starts his argument by claiming that the exit polls indicated a different result than the official election results:

The first indication that something was gravely amiss on November 2nd, 2004, was the inexplicable discrepancies between exit polls and actual vote counts. Polls in thirty states weren’t just off the mark — they deviated to an extent that cannot be accounted for by their margin of error. In all but four states, the discrepancy favored President Bush.

The key sentence that indicates just how poorly RFK Jr understands the math? “they deviated to an extent that cannot be accounted for by their margin of error”. That is a statement that is, quite simply, nonsensical. The margin of error in a poll is a statistical measure based on the standard deviation. Contrary to popular opinion, a poll with a margin of error of “4%” doesn’t mean that the actual quantity being measured must be within plus or minus 4% of the poll result.

A margin of error is measured to within a level of confidence. Most of the time, the MoE that we see cited is the MoE with 95% confidence. What this means is that 95% of the time, the sampled (polled) result is within that +/- n% range. But there is no case in which a result is impossible: the margin of error is an expression of how confident the poller is in the quality of their measurement: nothing more than that. Like any other measurement based on statistical sampling, the sample can deviate from the population by any quantity: a sample can be arbitrarily bad, even if you’re careful about how you select it.

Elections have consistently shown a bias in the exit polls: a bias in favor of the democratic vote. For some reason, which has not been adequately studied, exit polls almost always err on the side of sampling too many democratic voters. This could be the result of any number of factors: it could be a question of time (when were the polled people asked?); it could be a question of location (where were the pollsters located relative to the polling place?); it could be a social issue (the group of people that consistently votes for the democratic party may be more willing/have more time to answer pollsters questions); it could be something else entirely.

But you can’t conclude that an election was stolen on the basis of a discrepancy between official election results and exit polls. The best you can do is conclude that you need to look at both the election and the exit polling process to try to determine the reason for the discrepancy.

According to Steven F. Freeman, a visiting scholar at the University of Pennsylvania who specializes in research methodology, the odds against all three of those shifts occurring in concert are one in 660,000. ”As much as we can say in sound science that something is impossible,” he says, ”it is impossible that the discrepancies between predicted and actual vote count in the three critical battleground states of the 2004 election could have been due to chance or random error.”

That entire quote is, to put it crudely, utter bullshit. Anyone who would make that statement should be absolutely disqualified from ever commenting on a statistical result.

Now, thanks to careful examination of Mitofsky’s own data by Freeman and a team of eight researchers, we can say conclusively that the theory is dead wrong. In fact it was Democrats, not Republicans, who were more disinclined to answer pollsters’ questions on Election Day. In Bush strongholds, Freeman and the other researchers found that fifty-six percent of voters completed the exit survey — compared to only fifty-three percent in Kerry strongholds.(38) ”The data presented to support the claim not only fails to substantiate it,” observes Freeman, ”but actually contradicts it.”

Again, nonsense. There are two distinct questions in that paragraph, which are being deliberately conflated:

  1. In each given polling place, what percentage of people who voted were willing to participate in exit polls?
  2. In each given polling place, what percentage of the people who were willing to participate in exit polls were voters for each of the major parties?

The fact that a smaller percentage of people in places that tended to vote for the democratic candidate were willing to participate in exit polls is entirely independent of whether or not in a specific polling place a larger percentage of democratic voters than republican voters were willing to participate in the exit polls. This is a deliberate attempt to mislead readers about the meanings of the results – aka, a lie.

What’s more, Freeman found, the greatest disparities between exit polls and the official vote count came in Republican strongholds. In precincts where Bush received at least eighty percent of the vote, the exit polls were off by an average of ten percent. By contrast, in precincts where Kerry dominated by eighty percent or more, the exit polls were accurate to within three tenths of one percent — a pattern that suggests Republican election officials stuffed the ballot box in Bush country.

It could indicate that. It could also indicate that democratic voters were consistently more willing to participate in exit polls than republican voters. And therefore, in polling places that were strongly democratic, the sampling was quite representative; but in polling places that were strongly republican, the sampling was lousy.

Just to give an idea of how this works. Suppose we have two polling places, each of which has 20,000 voters. Suppose in district one, there is a 60%/40% split in favor of democratic voters; and in district two, there’s the opposite; 60% republican, 40% democrat. And let’s just use similar numbers for simplicity; suppose that in both polling places, 60% of democrats were willing to participate in exit polls, and 40% of republicans were willing. What’s the result?

  1. District one will have 12000 votes for the democrat, and 8000 for the republican. The exit polls will get 7200 democratic voters, and 3200 republican voters, or 69% of the vote going to democrats according to exit poll, versus 60% actual.
  2. District two will have the opposite number of votes: 8000 for the democrat, and 12000 for the republican. The exit polls would get 4800 democrats, and 4800 votes for republicans – predicting a 50/50 split.

The democratic margin of victory in the democratic area was increased; the republican margin was decreased by slightly more.

It continues very much in this same vein: giving unreliable samples undue evidence; bait-and-switch of statistics; and claims of measurement errors being impossible. But none of the mathematical arguments are true.

Was there fraud in the election? Almost certainly. Particularly in Ohio, there are some serious flaws that we know about. But this article manages to mix the facts of partisan manipulation of the election with so much gibberish that it discredits the few real facts that it presents.

RFK Jr. should be ashamed of himself. But based on his past record, I rather doubt that he is.