Vote Counting as Mathematical Proof

Trust in the correctness of an election outcome requires
proof of the correctness of vote counting. By formalising
particular voting protocols as rules, correctness of vote counting
amounts to
verifying that all rules have been applied correctly. A proof
of the outcome of any particular election then consists of a
sequence (or tree) of rule applications and provides an
independently checkable certificate of the validity of the result.
This reduces
the need to trust, or otherwise verify, the
correctness of the vote counting software once the certificate has
been validated. Using a rule-based formalisation of voting
protocols inside a theorem prover, we synthesise vote counting
programs that are not only provably correct, but also produce
independently verifiable certificates. These programs are
generated from a (formal) proof that every initial set of ballots
allows to decide the election winner according to
a set of given rules.