I was interested to hear Peter Banks theory that women tend to be Bayesian thinkers who regularly update priors, while men are more axiomatic in their thinking. I have never heard anyone put it that way, but it struck me as immediately and intuitively true.

Like living in Utah, I have watched a lot of people change/lose their religious faith, and about half of the men come swinging sort of violently from hard-core true-blue belief into the opposite in a very short period (often with utterly chaotic and devastating impact on their life), while I have never seen a woman do that, they change their mind about it gradually as they update their priors based on new information, seemingly. Also, men seem to often be rigidly axiomatic about their economic beliefs, treating them as almost religious in nature, and fairly impervious to either new information or doubts.

This would also explain the common perception of men that women are flaky or unreliable…perhaps they just actually update their beliefs based on new information more frequently, and/or are more likely to be correctly calibrate for uncertainty.

Anyway, after hearing his theory, I tried to look up whether women were better at forecasting, given that if they think in a more Bayesian manner, that should be the case. However, men are so overwhelmingly more likely to both enter and expend a ton of effort on superforecasting tournaments, that I could not find any data on this.

But I did find that massive studies of millions of Fidelity accounts finds that women’s investment returns are better overall…anywhere from 0.5% to 1.8% annually depending on the study, which would add up to a huge amount when compounding over years. More striking is that women who do sports gambling have average net returns of 20%…compared to negative 5% for men!! That is a huge difference! And yet women are way, way, way less interested in both investing or online betting.

Then this weekend, like a gift handed down, this crazy study got published: journals.uchicago.edu/d…

And it is really long and I know probably none of you will read it, but it takes the Raven Advanced Progressive Matrices - a commonly used IQ test for fluid intelligence, and introduces salient rewards (paying per correct answer rather than just for participating in the study and completing the test without regard to performance, like is usually done). Then it introduces risk and confidence aspects that make the test more closely resemble most real-world problem solving situations, where outcomes are uncertain. Basically they allow the subjects to allocate tokens among answers based on their percentage confidence assigned to each possible answer, by applying a penalty for being confidently wrong, paying the most money for being confidently right, and interim amounts for hedging risk among a few answers or small amounts for just guessing randomly. This makes it resemble forecasting or investing a lot more and they can calculate precise accuracy and “earnings efficiency” by dollars won based on probability allocations.

The baseline in the chart below is them running the test as normal, to test against baselines established previously with huge sample sizes. Women in their sample do 8% worse on average, than men. In condition B they pay per correct answer, rather than paying for completion. Just paying per correct answer causes women to do on average 10% better. In condition C they allow allocating tokens with probability assigned to response and variable winnings for accuracy, and can add up who earns the most, and that is the condition where women really outperform, by almost 20%. Because guys are just so much more likely to be confidently wrong.

Anyway, this basically tells me that in areas where there is one specific and certain correct answer, i.e. math, men will overperform. But with things where there is NOT because outcomes are uncertain, such as…basically anything to do with people, weather, biology, finances, etc, women as a group will overperform, mostly because men are much more confident about being wrong. That’s not really surprising at all.

But the authors propose that this type of risk and penalty-applied probabilistic test is closer to most real-world problem-solving than standard IQ tests, and conclude in their abstract that “Contrary to received literature, women are more intelligent than men, compete when they should in risky settings, and are more literate,” so it is kind of fun watching people whose personal worldviews and identity are heavily premised upon being good at IQ tests freak out about it.

Also, it is hilarious that atheists show such giant overperformance when not given incentives to get a good score on the test, but actually do worse when they pay by correct answers. Really confirms a stereotype that certain people are just a lot more “intrinsically motivated” to score high for its own sake.

The sample size here is tiny, but the methods have good theoretical grounding, and it’s a little shocking that incentivizing performance is not typically factored in to intelligence tests, if it can change results so much.

In sum: Peter Banks theory seems to be correct, and also, way more women should apparently be doing online betting. Or alternatively, allowing men to gamble online, when they’re so bad at it, is probably going to screw them over.

FWIW, I am more male-pattern overly confident when it comes to investing, and get more involved than I should. I would have a lot more money than I do, if I just did it passively instead of thinking I can beat the market. Which I know rationally no one can, not even top level managers with tons of NAV, but my overconfident brain still does it anyway, so I guess I’m not as rational as I like to think.