Social pressure can make it scale pretty well. For example, there could be a neighborhood election day party. You vote when you enter, the organizers observe how you vote, and then you leave your devices in a storage locker. The party continues until voting has ended and the results have been announced.
You are over-engineering. You do not need to coerce a voter if you are the administrator and can just add the record into the database directly. Also no need to spend money for a party.