Beware of base rate fallacy
Published: 2024-07-03 11:45:23

Let's say some scholars have done a research on the relationship between career advancement and overconfidence/underconfidence(with respect to the [Dunning-Kruger effect](https://en.wikipedia.org/wiki/Dunning%E2%80%93Kruger_effect) in this setup) in country A, and the result is as follows:

**Out of all those being promoted in the workplace to some extents in country A, 80% and 20% of them are mostly overconfident and underconfident respectively.**

Then, some media across the globe uses this result to claim the following:

**Of every other aspect being supposedly equal, being mostly overconfident is generally more advantageous to our career than being mostly underconfident in country A.**

Assuming that the test is indeed fair and reproducible in country A with good sampling, and career advancement, overconfident as well as underconfident are all well-defined and carefully examined(maybe even using a double-blinded study), will you just believe in what those media suggested?


At the very least, if you're already aware of the [base rate fallacy](https://en.wikipedia.org/wiki/Base_rate_fallacy), you probably won't jump to conclusions so easily, because you'll want to know the following 2 ratios as well:

1. The ratio between the mostly overconfident and underconfident people in country A

2. The ratio between those advancing well in their careers and those who don't in country A

(Strictly speaking, the 2nd ratio doesn't matter much in this fallacy, but knowing this ratio can make the numbers even clearer)

For example, if the ratio between the overconfident and underconfident people in country A is 9:1, and that between those advancing well in their careers and those who don't is 19:1, then the whole experiment actually points to the opposite result - **Being underconfident is indeed better for the career of those in country A.**

It's because in the overconfident group, only (1 / 19)[8 / (8 + 2)] / [9 / (9 + 1)] = 0.05(0.8 / 0.9) = 4.444...% are advancing well in their careers, while that in the underconfident group is (1 / 19)[2 / (8 + 2)] / [1 / (9 + 1)] = 0.05(0.2 / 0.1) = 10%, which is 10% / 4.444...% = 2.25 times of the former.


Although I don't think any of you will fall into the base rate fallacy so easily, time and again I've seen some media citing some psychological research results without much contexts, and then just use those results to make some likely dubious claims.

While I don't think those psychologists themselves will ever fall into such fallacies, at least not unknowingly, I just sense an urge to write this article, perhaps because I start to grow tired of reading how those media habitually cite more and more of such psychological researches this way.

Actually, the example in this article is already much better than what I've read countless times, because the majority of what what I've read won't even specify that the result is only known to generally apply to career advancement in country A(even if it might do have wider applications) with all other aspects being equal, since they'll instead make claims like this:

**Being overconfident will definitely make you more successful then being underconfident.**

However, if you can spot the base rate fallacy right away, you should be able to figure the rest without much trouble, like "success isn't just about career advancement", "career advancement isn't just about confidence", "what applies to country A doesn't necessarily apply to the rest of the world", "what generally applies to the majority can have exceptions as the non-negligible minority", so if more and more of the targeting audience are aware of all this over time, maybe the media will gradually change their habits of taking psychological research results out of contexts :)