Making it secret doesn’t help. A woman living in fear and or oppression in a Muslim marriage will not vote anyway other than how she is told to.
That is one of premises of battered woman syndrome.
The same can be said for a son or daughter in such a family.
It is kind of group voting.
Some dominant figure (father) brings in, sometimes by force, all kind of people, family or not, and supervises their voting.
Basically voter multiplication.
It happens in the US too.