Hi !
Here in Brazil, all elections use electronic voting machines. In fact they are PCs with a single keyboard (numbers, enter, cancel, blank and null buttons), a display screen where you can see the candidate´s number you have typed and his/her picture and name. The keyboard is enabled by the fiscalization that checks our id and via network communicates with the voting machine. After the end of typing you enter the number and a sound is heard indicating the end. In the end of the day, a file from this voting machine is recorded in a floppy disk and sent to the electoral justice. I don´t have any idea about the inside circuit or software used.
I think you can use a microcontroller to do a very simple voting machine, with a keyboard and a LCD display to show the numbers or names. After, you can communicate with a PC via serial to receive the data about voting.