> This is clearly wrong - I demonstrated a stupidly simple alternate theory which disagrees with the consensus, but still lacks constant power shifts.
Your theory didn't even explain the data (in the software industry), and had nothing to say about power. Basically, it can comfortably exist beside the consensus theory as a second-order effect (and the data actually looks like that is probably the case, explaining representation differences of up to 2:1).
> So why cling to that theory, rather than, say, my theory of p=A - B x math_content + second_order_corrections?
Two reasons: 1. your theory doesn't explain the anomalous software industry (neither the very low participation nor the sudden change) while the consensus theory does, and 2. your theory doesn't explain the lack of representation (and possible correction after well-documented struggles) in fields of high prestige and little math (such as law, medicine and politics). In all those fields: law, medicine, politics and software, women participation was (or is) far lower than 30%. It was/is lower than 20%.
You might think that singling out software is uninteresting from a statistical perspective, as in Scott Alexander's regression it was just a single (outlier) data point, but in fact, the software industry is larger than all "heavy math content" professions combined, and holds more power in today's society.
> My theory predicts more things (e.g., it predicts % women in academia, % women in finance, % women in tech vs non-tech roles) and is vastly simpler. How is that not a win?
Because it predicts fewer things, and not even what you claim it does. At best, it predicts fewer women than men in certain subjects, but that's it. However, we see that while the binary relation "fewer" may remain, how much fewer decreases over time. Second, it only holds (even as a binary prediction) when you look at the past few decades -- far too short to look at social change -- which means it does not explain the exclusion of women from law, medicine and politics. Third, it does not explain the way-too-low representation in CS, nor the drop in participation. The consensus theory explains all of it, for any time duration. It even explains interesting shifts we see in, say, education (more women as prestige drops, while in CS fewer women as prestige rises). Yes, it's more complicated, but fits reality better, plus it's supported by lots and lots of data.