Zero-knowledge proofs can prove that binary code conforms to a specification (e.g. source code) without revealing the process used to turn specification into binary code.

In the analogy, the specification is the information provided to government officials and binary code is planned governmental actions.

If both are known and the specification process for governmental action is proven it doesn't matter what biases the officials exhibit in the decision process - then the governmental action is proven-good according to the specs (e.g. system of laws) and the information provided (in which it would be relatively easy for citizens to have a say, e.g. "you MAY NOT ignore facts X, Y and Z").