It's of course possible. In fact electronic voting could be safer. The issue is that voting has nothing to do with technical details of safety and everything to do with trust. If your electorate doesn't understand modular arithmetic, then there's no point to electronic voting.
"trust" is a fuzzy concept - people use iMessage and have no concept of how it's architected or how it works. But they trust it. Why? because trust is something that is transferable. If you trust me, and I tell you iMessage is safe then you have a high likelihood of trusting iMessage. If this is reinforced by other people you trust, even better. There would be ways to create a voting system in the open, and have it validated by third parties. If you've ever bought stock it's because underlying the transaction, and auditor has certified their financials...
