This is is the nature of the debate that I'm having, and you'll probably find out soon who raises it most. But we know that statistically, empirically, there's no gainsaying that there's a higher proportion of women elected in countries that use proportional representation. But then you also get academics who say, which is true, “Well, we don't know there's any causality, it might be a coincidence”.
I always think the example of Australia is very helpful, because if it's cultural and societal that PR countries elect more women, then you look at Australia where for the house in Australia, which uses a majoritarian system of ranked ballots, they have 26.7% women. But in the same country, where they elect their senate using a single transferrable vote PR, they have 38% women.
How would you explain this? We don't have academic literature that says there's causality between moving to PR and electing more women. But what does your analysis tell you about these differences?