Ukraine's Election body has recently used NEM's blockchain in a voting trial. A member of Ukraine’s Central Election Commission, Oleksandr Stelmakh, has recently commented on Facebook regarding a voting trial conducted using NEM’s blockchain which lets users create their own assets. According to his post, blockchain’s advantages of allowing decentralized data storage and immutability can help in an electoral voting process.
For Russian readers --
https://www.facebook.com/permalink.php?story_fbid=1824010517666145&id=100001716433858 This post is in Ukrainian, Russian readers won't be able to read it.
Basically, they are saying that they've pushed the data from 2014 elections to NEM's testnet blockchain, but I don't see any transactions on explorer.
They are also planning to do the same with the upcoming elections, but on mainnet.
However, this is by no means any sort of "blockchain voting", they are just taking some data from polling places and putting it on public blockchain. If someone wants to rig elections, they can do it at the polling stations, or simply send malformed data to the blockchain.