1. A method for conducting an election including the steps of: (a) making public cryptographic commitments to plural codes to form committed codes; (b) producing physical ballots including the committed codes in a hidden form, each code associated with a ballot position, the physical ballots allowing at least one voter to select at least one position on the voter's ballot such that the hidden codes corresponding only to the selected positions are revealed to the voter; and (c) making public, after the election, the hidden codes corresponding to positions selected by voters; (d) providing voters an opportunity to provide purported codes that were revealed on ballots; and (e) opening at least some commitments at least corresponding to corresponding contests in at least a case of voters providing codes purported to have been revealed on ballots that were not made public after the election as codes corresponding to positions selected by voters; wherein the codes are chosen so that voters are unable with substantial probability to guess codes not revealed and so that the revealing of codes provided by voters provides statistical evidence of the published codes being incorrect.