Issuing threats to voters to coerce them to vote a certain way is “reciprocity”. Offering substantial monetary rewards to buy votes is “reciprocity”. Both are criminal behavior. We do not need reciprocity in voting. Voters should be encouraged, as much as possible, to be honest in their vote.
If you want voters to cooperate, the problem is our choose-one voting system, which naturally divides the public into two camps that do not benefit from negotiating with each other. Approval Voting is an example of a simple change we could make to the existing system which would open the door for general cooperation among the public. There is no need to publicize people’s votes. There is no security gained by doing so.