there is no way for anyone to prove how they voted, so there can be no possible retaliation

think about like… a mafia wanting to control a city government

if there’s no possible way to validate how you voted, they can tell a huge group of people how to vote and you can vote however you like and just say you voted like they wanted: they have no way of knowing either way (same goes for paid votes: they have no way of knowing how you voted so you can vote however you like)

if there’s a way to validate your vote, they can demand your voting slip (or number, or that you show them your validation record) and say they’ll break your legs if you don’t show it… so you vote and say the printer was broken, they’ll probably break your legs regardless (also they’d likely have a way of checking these things… in the case of an abusive relationship, they’d probably accompany you to vote so they’d likely know the status of any hardware like a printer - this isn’t something you can just lie about)

truly nasty organisations and individuals using violence as coercion aren’t likely to just “aw shucks guess i’ll let it go then”. they’re not particularly trusting

now in the current system with no way to validate directly, it doesn’t matter who it is: even the poll workers don’t see your ballot paper… nobody except you sees it. there are no cameras, no people watching over your shoulder, no proof either way after you drop your ballot into the box: you can say whatever you want, and because that’s the standard and known for everyone there no point to anyone saying “prove it”… there’s simply no way, thus there is no way of coercing someone