Yes, there are several processes.
But first let us look at the basics of statistics…
Let us divide the world into people with an odd number of letters in their names and those with an even number, call them @'s and #'s
I shall assume that there is no correlation between having an even number of letters in your name and ability.
So if we have two @s and two #'s and we choose the the best of the @'s they will be on average the same as the best #
But what if we have three @'s ?
There is a non zero chance that the extra @ is better and so the chances of the best person being a @ goes up.
Adding more people makes this ever more likely that the best @ is better than the best # and of course this logic applies in both directions.
Here’s where you need to set your prejudices aside, this applies to groups of men and women as well, the labels don’t matter, you can have a set of men whose best is better than a set of women.
This is of course why big countries win more Olympic medals than small ones. They have more to choose between.
So back to judges…
In the UK, unlike the USA judges aren’t chosen by any sort of political process, Butler Sloss wasn’t chosen to be a judge by a politician, she was chosen from amongst senior retired judges to run this enquiry.
Given that nearly as many women as men enter the legal profession, but that at each level of the judiciary you find fewer women, it is reasonable to suspect sexism. But given that it literally takes decades to get to the highest levels, part of this reflects the world of the 1970s and 1980s more than today. However there is still imbalance at the lower levels.
Her rise as you can see from the article I referenced was marked by an indifference to sex crimes, dodgy judgements and covering up of sex crimes when they were committed by fellow Christians.
The question is how did someone like that rise so high ?
One factor is of course nepotism, she is related to some powerful people, who it won’t shock you to learn also helped Christian priests escape punishment, leaving them free to rape again.
But also, one has to allow for the possibility that her grievous shortcomings were ignored at each stage of promotion in order to bump up the number of women, since once you have a mid-level judiciary that is mostly men, the only way to get a bigger number of women at the next level up, you have to lower your standards. Again before your prejudices cut in at the idea that a set of women could be inferior to men, go back and read what I said about odds and evens. The top 10% of women may be exactly as good as the top 10% of men, but if you take the top 20% of women it will on average be less good than the top 10% of men.