Identity is a huge topic itself with lots of projects doing fundamental research and experiments but essentially if it's a traditional physical government then it would work like it does today where you would use your government secured ID to vote. Not much would change. If it's a digital government then it would probably be using an identity based on built up history of actions and financial settlements and connections to other highly verified accounts. Ethereum has a project called POAP (Proof of Attendance Protocol) which is a way of identifying that a real person attended a specific event or performed some important action. These POAP badges can't be faked and are already being used for things like being able to vote on certain dev polls if you've attended a Devcon.