I don't think the judges are "randomly selected", though some were poorly selected.
Again, this does not require any judges, it does not require a plebiscite, either.
Just the recognition that everyone, EVEN WOMEN , own their own bodies and that not government, nor masses of people, nor laws, should deny them this.
If you DID have a plebiscite, I would say let only the women decide, since this is only about women.