I do not think many, if any, ATMs in my country accept cards with only the magnetic strip anymore. It was over 10 years ago my ATM card was replaced by debit ca

I do not think many, if any, ATMs in my country accept cards with only the magnetic strip anymore. It was over 10 years ago my ATM card was replaced by debit card when the banks phased out ATM cards. And anonymity of votes has more aspects than just protecting against the guy by the machine. You also need to protect against to guy issuing the numbers (which you don't for ATMs, it is ok if the bank knows how much money you withdrew :)) and also the anonymity should make it hard to sell votes which disqualifies some cryptographic solutions suggested by other commentors (those where you get a cryptographic receipt which can use to look up afterwards to see what you voted). And some voting machines work exactlty like you describe, and they are not regarded as secure.