I lived in Canada until I was 39. the system there is as described on this thread. Nigels, point is similar to mine and a very good one. It doesn't have to have to be absolutely secret. Just secret enough so that people can vote with confidence and not be bribed.

In the past, political operatives sometimes used to hang around polling stations, offer a bribe and pay off the people who voted their way. The current UK/Canada system does not allow that. It does not allow for any kind of abuse I can think of.

There are to major differences with the present US system that are very significant. The debacle in Florida, hanging chads, Bush v Gore, could not have happened. The US "voter id" laws causing so much controversy would not be necessary.