Monday, February 17, 2014

Weighing Evidence

How good are you at weighing evidence? Here is a simple test:

Suppose random people are tested for a rare (1 in 50,000) disease and one tests positive. The test is 99% accurate, meaning it gives the correct result 99 times out of 100. To be extra sure, he is tested again with the same 99% accurate test. Its result also is positive. Does he have the disease? How sure are you?

If you're thinking “yes” or that it's very likely, you are interpreting the data irrationally. But you're not alone. Psychologists have found that people generally give too much weight to specific, individuating information and not enough weight to general, less-specific information that we perceive as less relevant. The phenomenon is known as the base rate fallacy or base rate neglect. In the above example, there's actually only a 17% chance that he has the disease, but most people are fooled by the 99% accurate tests.

Base rate neglect is common in theology because there is a universe full of data with apparently little relevance, along with religious books that contain very specific individuating data. Though the Bible says God is revealed through nature, evidence from nature is often neglected in theological discussions.

Many theologically conservative Christians focus entirely on the Bible to answer theological questions. They start with their interpretation of the Bible, then interpret the rest of the universe according to what they believe the Bible says. That method is prone to overfitting, which can make it an insidious form of base rate neglect, even if the Bible is 100% true. On the other hand, many theological liberals start with their interpretation of the universe (i.e., worldview), then force the Bible to conform to it and/or reject the parts that don't. That's the extreme opposite of base rate neglect, which is equally irrational. Both use a heavy dose of circular reasoning.

Ironically, many atheists are on the theological conservatives' side here. They start with an interpretation of the Bible (usually a very conservative fundamentalist one that neglects data from outside the Bible), then compare it to their understanding of the universe and conclude that the Bible is morally objectionable and/or contradicted by science. This approach leads to straw man arguments against religion.

My last post discussed the problem of matching beliefs to irrelevant data. This post says we don't give enough weight to data that seems irrelevant. It's not a contradiction, but it's a fine line -- one that's easy to cross in both directions. I cross it all the time. It's a reason why tools like Bayes' rule are so useful. It's also a reason for all of us to be humble about what we believe and don't believe. Our beliefs may seem to perfectly match the most relevant data, but some of them are probably wrong.


  1. The extent to which atheists are "on the side of theological conservatives" is related to the fact that a literal interpretation of the bible (e.g., the KJ translation) is a fixed target. When theists allow themselves the luxury of ignoring the literal words of the bible, the target becomes so fluid, it's impossible to address it. The literal words of the bible used by fundamentalists (e.g., the KJ version) truly are: morally objectionable (condoning slavery, misogeny, homophobia, genocide, etc.), internally inconsistent (e.g., 4 different versions of the gospel story, and contradicted by science. Hence, you've not managed to show how these are straw man arguments.

    1. What you're calling "literal" is only literal if we read it as if it was written to us (in 2014, in English, to answer the questions we ask of it) and ignore the original context, purpose, genre, and language. You wouldn't ignore those things when reading any other book, so why must we ignore those things when reading the Bible?

      I agree about fluid targets, and criticized theological liberalism for similar reasons. Regarding 4 different versions of a story, how is having 4 accounts worse than having only one?

      The straw man is because the Bible, especially in the original context and language, does not advocate slavery, misogyny, homophobia, genocide, etc. It only does if you ignore the historical context (i.e., ignore the distinction between moral teachings of the Bible vs. typical standards of ancient near-east culture). There is signal and there is noise.

  2. Having 4 different versions is OK unless they contradict one another, or fail to mention important parts of a differing account.

    The KJ version I was familiar with wasn't written in 2014 - it was completed in 1611. I grant our context for those words has changed dramatically from when they were originally written and the 1611 context surely differs from the 2014 context. But the words are the only constant in what is a moving target. Could an omniscient deity not write a document that would withstand a changing social context? How can morality be considered absolute if it changes with the times?

    Interesting technique ... consign the dicta regarding women and gays and other tribes and other religions into a bin called "noise", thereby disavowing them neatly. The standards of the era were what they are: immoral. If the holy word of the deity didn't condone those standards, then a denial of them should be prominent. Its absence conveys consent.

    1. Yes, I agree about the 4 different versions. I don't know of any substantive contradiction in them. Do you?

      The KJV is irrelevant. The Bible was written in Hebrew, over 2000 years before the KJV. More/better manuscripts have been discovered since then (e.g., Dead Sea Scrolls), and better translations have been done since then. None are perfect because in many cases there is no exact English equivalent of the Hebrew words. It does withstand the changing social context if people bother to take the time to understand the social context. No, an omniscient deity can't write a book in Hebrew that has an exact equivalent in English. It's a limitation of English, not a limitation of the deity.

      Why is the Bible required to identify and condemn every immoral thing that existed at the time? Who says it was meant to be an exhaustive guide to morality? Also, on what basis are you concluding that the standards of that era were "immoral"? It's difficult to comment on the Bible's morality when I don't know what your standards for morality are.

      Regardless, most of the Bible's moral teachings were very utilitarian, given for the stated purpose of making Israel prosperous in the new land. It wasn't as concerned with a lot of the moral issues that we argue about today. For example, back then they were very concerned about preventing (by whatever means necessary) diseases spread by homosexual acts, but weren't particularly concerned with (and the Bible says nothing about) homosexuality per se.

  3. You've brought up an interesting point about the base rate fallacy and how people tend to give more weight to specific information rather than general data. It's a common cognitive bias we all fall victim to. When it comes to theology, it's important to consider a wide range of evidence, including both specific religious texts and general observations from nature. Speaking of relevant topics, let's not forget the importance of Trash Pickup Schedules in keeping our city clean and environmentally friendly. By adhering to these schedules, we can ensure proper waste management, reduce pollution, and create a healthier living environment for everyone. It's a small but impactful step towards maintaining the cleanliness and sustainability of our city.