“B-but open software!” Can you prove that the software in some public repo is the same one that they installed on the machine? Did they compile it in front of you? On a completely new, empty machine?
“Open hardware, then!” No. That's even more stupid.
Forget about it! You can't prove the security of electronic voting. Just use paper ballots and transparent boxes, and let regular people chosen at random direct the process and count the results in front of a representative of each party.