[postflopclarity]

I don't know if I'd call this an "unfortunate" result or not. it's neither good nor bad, just a thing.

Arpino & Mogi are different authors that wrote a different paper that I didn't read. _This_ paper does not appear to have controlled for much at all in its primary contribution of analysis of US GSS data, and all the conclusions reached appear to me to be purely observational.

Another nuance is that since their analysis consists of filtering to people already over 40, and then asking about political leaning, there is no way to infer anything about causal association of left - vs - right ideology and fertility. For example, "having children makes you more right wing" is an equally plausible explanation for this data as "being right wing causes you to have more children" (or maybe neither of these statements are true at all, and it's caused by a variety of other confounding factors).