Even open source will have issues. Machines work in levels from components through drivers and operating systems to apps and databases. We have seen how Supermicro had some Chinese-made motherboards "infected" with rogue bugs. Some of us will remember how Intel had a bug in their Pentium processors.

Even if the software you know about is open source it is difficult to prove that that is the code that actually ran. Although paper systems have issues adding something else on top just increases the opportunity for cheating.

All that is before you add the situation where users can insert USB sticks into the machines. Extra code could be written into hidden sectors, for instance.

Then there is the possibility of invisible wireless links like wifi or Bluetooth.

Here is a voting machine demo