Blockchains may be theoretically secure. But almost nobody is in a position to understand this thoroughly. The debacle around the DAO and frequent hacks of online wallets, even if those events are only tangentially related to blockchain technology, also undermine any potential trust.
It's also unnecessary: I just witnessed the federal election in Germany. In large cities, there's a polling place on every second block or so, each serving maybe 500 voters. The polling place is open to the public. Meaning you can see that the ballot box is empty in the morning, you can watch all day, and after polls close, you are free to watch the poll workers sort and count the ballots, as close as you want. You can then compare the count you witnessed to the official numbers posted online.
The whole process is end-to-end verifiable by anybody, and it requires no special skills other than counting.
https://en.wikipedia.org/wiki/GeenPeil#First_initiative_2014
Paper ballots work really well too, and though they can go missing just like files get deleted, it's pretty easy to see that.
That sounds like a terrible idea. What happens when somebody tries to hold the election process hostage by not casting a vote?
Honest question, I'm all ears if there's a good rebuttal.