Linda vs. the serial killer

There's a logic problem that's often nicknamed "The Linda Problem," and I hasten to state that by calling it that I don't mean any general criticism of people named Linda.  It goes like this:

Linda is a 30-year-old woman who lives in a big city in the United States.  She is single, has a master's degree in sociology, and is deeply interested in issues of discrimination, social justice, and addressing poverty and homelessness. 

Which of the following is more likely?

1. Linda is a bank teller. 
2. Linda is a bank teller who voted for Hillary Clinton.

The whole thing rests on what is known as the conjunction fallacy, and it's amazing how many smart people this one trips up.  The answer is that the first statement has to be more likely; the more qualifiers you add to a list, the fewer people will meet the whole list at the same time.  To give an illustration that is less likely to elicit a wrong answer, consider the following.

You see a dog.  Which is more likely?

1. It's a golden lab.
2. It's a golden lab wearing a red collar.
3. It's a golden lab on a pink leash wearing a red collar.
4. It's a golden lab sitting on a sidewalk while on a pink leash and wearing a red collar.

For this one, it's clear that each additional qualifier makes the pool of (in this case) dogs that fit the description smaller and smaller.

[image courtesy of photographer Eric Armitage and the Wikimedia Commons]

So why does the Linda Problem trip people up?  It's because in statement #2, the second qualifier -- that she voted Democrat in the last election -- is actually quite probable, given what we know about her.  Once people see that, they tend to grab on to it and ignore the bank teller part, thinking, "Well, I have no idea how likely it is she's a bank teller; but it's really likely she voted for Clinton.  So the second one must be the most likely overall."

Which is why I found the results of a paper that appeared last week in Nature: Human Behavior simultaneously so funny and so appalling.  The study, conducted by a team led by Will Gervais of the University of Kentucky, investigated biases against people based on their religious adherence (or lack thereof).  Test subjects were asked one of two versions of a question designed to see if people connected atheism with sociopathy.  They were given the following scenario:

A 45-year-old man, who tortured animals when he was young, later moved on to hurting people.  He has killed five homeless people that he abducted from poor neighborhoods in his home city.  Their dismembered bodies are currently buried in his basement.

Half of the test subjects were then asked the following:

Which of the following is more probable?

1. The man is a teacher.
2. The man is a teacher who does not believe in any gods.

The other half got a different question:

Which of the following is more probable?

1. The man is a teacher.
2. The man is a teacher who is a religious believer. 

Well, you can see that this is just the Linda Problem in a different guise, and that in each case statement #1 is more probable, regardless of the qualifier (or what the additional qualifier was in statement #2).  But Gervais found a surprising result -- a full 60% said that in the first case, the second statement was more likely, and only 30% said the same for the second scenario.  (For comparison purposes, one study found that the average number of people who miss ordinary conjunction-fallacy problems is around 48%.)

So that means that people's innate biases against atheists make them more likely to fall for the conjunction fallacy.  Unsurprisingly, when this test was carried out in highly religious countries -- like the United Arab Emirates -- the percentage who miss it was even higher.  In less religious countries, such as New Zealand, the percentage was lower, but the bias still exists, in that the percentage who got the question wrong was still higher than the average of 48%.

Most interesting of all, people who were themselves non-believers were less biased -- but not by much.  (52% of self-described atheists got the first question wrong, as compared to 60% average for the entire group of test subjects.)

As fascinating as this is, it's also pretty disheartening.  I know there's prejudice against atheists, but really... a serial killer?  And even my fellow atheists have that perception?  I do run into this kind of thing, usually in the guise questions like, "If you don't believe in god, how do you have any moral compass?  Why don't you go around committing immoral acts?"  My response usually is something like, "If your fear of punishment in the afterlife is the only thing that's keeping you from lying, stealing, and hurting others, then you're the one whose moral compass needs examination, not mine."

But I didn't realize how deep the bias goes.  Gervais et al. write:

The results contrast with recent polls that do not find self-reported moral prejudice against atheists in highly secular countries, and imply that the recent rise in secularism in Western countries has not overwritten intuitive anti-atheist prejudice.  Entrenched moral suspicion of atheists suggests that religion’s powerful influence on moral judgements persists, even among non-believers in secular societies.

Which is kind of terrible, really.  Any kind of unfounded prejudice is a bad thing, but judgments like this lead people to make some pretty hideous assumptions.  It'd be nice if the Gervais et al. paper might get people to reconsider their biases, but given the words the authors use -- "intuitive" and "entrenched moral suspicion" -- that's probably a forlorn hope.

In any case, I hasten to reassure readers of Skeptophilia that I have no dismembered bodies buried in my basement.

For one thing, my basement has a cement floor, which would make it kind of difficult.

Poll avoidance

I'm lucky, being an outspoken atheist, that I live where I do.  The people in my area of upstate New York are generally pretty accepting of folks who are outside of the mainstream (although even we've got significant room for improvement).  The amount of harassment I've gotten over my lack of religion has, really, been pretty minimal, and mostly centered around my teaching of evolution in school and not my unbelief per se.

It's not like that everywhere.  In a lot of parts of the United States, religiosity in general, and Christianity in particular, are so ubiquitous that it's taken for granted.  In my home town of Lafayette, Louisiana, the question never was "do you go to church?", it was "what church go you go to?"  The couple of times I answered that with "I don't," I was met with a combination of bafflement and an immediate distancing, a cooling of the emotional temperature, a sense of "Oh -- you're not one of us."

So no wonder that so many atheists are "still in the closet."  The reactions by friends, family, and community are simply not worth it, even though the other alternative is having a deeply important part of yourself hidden from the people in your life.  As a result, of course, this results in a more general problem -- the consistent undercounting of how many people actually are atheists, and the result that those of us who are feel even more isolated and alone than we did.

[image courtesy of creator Jack Ryan and the Wikimedia Commons]

Current estimates from polls are that 3% of Americans self-identify as atheists, but there's reason to believe that this is a significant underestimate -- in other words, people are being untruthful to the pollsters about their own disbelief.  You might wonder why an anonymous poll conducted by a total stranger would still result in people lying about who they are, but it does.  Jesse Singal, over at The Science of Us, writes:

So if you’re an atheist and don’t live in one of America’s atheist-friendly enclaves, it might not be something you want to talk about — in fact you may have trained yourself to avoid those sorts of conversations altogether.  Now imagine a stranger calls you up out of the blue, says they’re from a polling organization, and asks about your religious beliefs.  Would you tell them you don’t have any?  There’s a lot of research suggesting you might not.  The so-called social-desirability bias, for example, is an idea that suggests that in polling contexts, people might not reveal things — racist beliefs are the one of the more commonly studied examples — that might make them look bad in the eyes of others, even if others refers to only a single random person on the other end of the phone line.

As Singal points out, however, a new study by Will Gervais and Maxine B. Najle of the University of Kentucky might have come up with a way around that.  Gervais and Najle came up with an interesting protocol for estimating the number of atheists without having to ask the specific question directly.  They gave one of two different questionnaires to 2,000 people.  Each had a list of statements that could be answered "true" or "false" -- all the respondents had to do was to tell the researcher how many true statements there were, not which specific ones were true, thus (one would presume) removing a lot of the anxiety over admitting outright something that could be perceived negatively.  The first questionnaire was the control, and had statements like "I own a dog" and "I am a vegetarian."  The second had the same statements, with one additional one: "I believe in God."  Since one would presume that in any sufficiently large random sample of people, the same proportion of people would answer "yes" to any given statement, then any increase in the number of (in this case) "false" replies would have to be due to the additional statement about belief.

And there was a difference.  A significant one.  The authors write:

Widely-cited telephone polls (e.g., Gallup, Pew) suggest USA atheist prevalence of only 3-11%.  In contrast, our most credible indirect estimate is 26% (albeit with considerable estimate and method uncertainty).  Our data and model predict that atheist prevalence exceeds 11% with greater than .99 probability, and exceeds 20% with roughly .8 probability.  Prevalence estimates of 11% were even less credible than estimates of 40%, and all intermediate estimates were more credible.

So it looks like there are a lot more of us out there than anyone would have thought.  I, for one, find that simultaneously comforting and distressing.  Isn't it sad that we still live in a world where belonging to a stigmatized group -- being LGBT, being a minority, being atheist -- is still looked upon so negatively that there are that many people who feel like they need to hide?  I'm not in any way criticizing the decision to stay in the closet; were I still living in the town where I was raised, I might well have made the same choice, and I realize every day how lucky I am to live in a place where people (for the most part) accept who I am.

But perhaps this study will be a first step toward atheists feeling more empowered to speak up.  There's something to the "safety in numbers" principle.  It'd be nice if people would just be kind and non-judgmental regardless, even to people who are different, but when I look at the news I realize how idealistic that is.  Better, I suppose, to convince people of the truth that we're more numerous than you'd think -- and not willing to pretend any more to a belief system we don't share.

Contradicting the narrative

In her marvelous TED Talk "On Being Wrong," writer and journalist Kathryn Schulz describes a "series of unfortunate assumptions" that we tend to make when we find out that there are people who disagree with us.

First, we tend to assume that the dissenters are simply ignorant -- that they don't have access to the same facts as we do, and that if we graciously enlighten them, they'll say, "Oh, of course!" and join our side.  If that doesn't work, if the people who disagree with us turn out to have access to (and understand) the same facts as we have, then we turn to a second assumption -- that they're stupid.  They're taking all of the evidence, putting it together, and are too dumb to do it right.

If that doesn't work -- if our intellectual opponents have the same facts as we do, and turn out to be smart enough, but they still disagree with us -- we move on to a third, and worse, assumption; that they're actually malevolent.  They have the facts, know how to put them together, and are suppressing the right conclusion (i.e. ours) for their own evil purposes.

This, Schulz says, is a catastrophe.  "This attachment to our own sense of rightness keeps us from preventing mistakes when we absolutely need to," she says, "and it causes us to treat each other terribly."

I got a nice, and scientific, object lesson in support of Schulz's claim yesterday, when I stumbled across a paper in PLoS One by Clinton Sanchez, Brian Sundermeier, Kenneth Gray, and Robert J. Calin-Jagemann called "Direct Replication of Gervais & Norenzayan (2012): No Evidence That Analytic Thinking Decreases Religious Belief."  Apparently five years ago, a pair of psychological researchers, Will Gervais of the University of Kentucky and Ara Norenzayan of the University of British Columbia, had published a study showing that there was an inverse correlation between religious belief and analytical thinking, and further, stimulating analytical thinking in the religious has the effect of weakening their beliefs.

[image courtesy of Lucien leGray and the Wikimedia Commons]

Well, all of that fits nicely into the narrative we atheists would like to believe, doesn't it?  Oh, those religious folks -- if we could just teach 'em how to think, the scales would fall from their eyes, and (in Schulz's words) they'd "come on over to our team."  The problem is, when Sanchez et al. tried to replicate Gervais and Norenzayan's findings, they were unable to do so -- despite (or perhaps because of) the fact that Sanchez et al. used a much larger sample size and tighter controls.  The authors write:

What might explain the notable difference between our results and those reported by G&N?  We can rule out substantive differences in materials and procedures, as these were essentially identical.  We can also rule out idiosyncrasies in participant pools, as we collected diverse samples and used extensive quality controls.  Finally, we can also rule out researcher incompetence, as we were able to detect an expected effect of similar size using a positive control. 

One possibility is that Study 2 of G&N substantially over-estimated the effect of the manipulation on religious belief.  This seems likely, not only because of the data presented here but also because evidence published while this project was in progress suggests that the experimental manipulation may not actually influence analytic thinking...

Based on our results and the notable issues of construct validity that have emerged we conclude that the experiments reported by G&N do not provide strong evidence that analytic thinking causes a reduction in religious belief.  This conclusion is further supported by results from an independent set of conceptual replications that was recently published which also found little to no effect of analytic thinking manipulations on religious belief.

To their credit, Gervais and Norenzayan not only cooperated with the research of Sanchez et al., they admitted afterwards that their original experiments had led to a faulty conclusion.  In fact, in his blog, Gervais gives a wryly humorous take on their comeuppance, by presenting the criticisms of Sanchez et al. and only at the end revealing that it was his own paper that had been, more or less, cut to ribbons.  He says of Sanchez's team, "I congratulate them on their fine work."

He also included the following in his postscript:

FFFFFFFFFFUUUUUUUUUUUUUCCCCCCCCCKKKKKKKKKKKK!!!!

Understandably.  As Schulz points out, it's often devastating and embarrassing to find out that we screwed up.  Doubly so when you're a scientist, since your reputation and your livelihood depend on getting things right.  So kudos to Gervais and Norenzayan for admitting their paper hadn't shown what they said it did.

So not only is this a great example of science done right, in the larger analysis, it tells us atheists that we can't get away with dismissing religious folks as simply not being as smart and analytical as we are.  Which, honestly, is just as well, because it would leave me trying to explain friends of mine who are honest, smart, well-read, logical... and highly religious.  It supports the kinder (and more accurate) conclusion that we're all trying to figure things out as best we can with what information we have at hand, and the fact that we come to radically different answers is testimony to the difficulty of understanding a complex and fascinatingly weird universe with our limited perceptions and fallible minds.

Or, as Schulz concludes, "I want to convince you that it is possible to step outside [the feeling of being right about everything], and that if you do so it is the greatest moral, intellectual, and creative leap you can take...  If you really want to rediscover wonder, you need to step out of that tiny, terrified space of rightness, and look around at each other, and look out at the vastness and complexity and mystery of the universe, and be able to say, 'Wow.  I don't know.  Maybe I'm wrong.'"