AFAIK if you don't trust the server and want to know exactly what code was run by it, there are only two options: a smart contract blockchain, or ZK Proofs (which came out of blockchain research)

It's a social technology. It allows outsiders to validate that the election tally code was run correctly. Elections are run every day on the Ethereum blockchain often that has financial implications for the voters. It doesn't mean they never get hacked, but it certainly gives the users more visibility and trust in their vote than a centralized black box