Blockchains (or something similar) are the only way
The only truly trustable system is one that is 100% transparent - continuously auditable elections. At any time anyone needs to be able to access the system, check the totals, and be able to detect if there is ANYTHING suspicious going on.
Any system that isn't continuously auditable can't be trusted. You just need to be able to get in between the audits and you can get away with anything.