Pretty sure this would be a good application for blockchain technology, which would work better than pen and paper and open to the public!
Let's say your parks department were headed by a libertarian guy who vehemently opposes using public funds to fill a landfill and turn it into a park and he finds out his deputy voted for the ordinance to spend the money on said park. He could retaliate.
Another hypothetical could involve your local councilman finding out which members of his district voted for him and which didn't, and using that knowledge to influence who's streets get priority when plowing snow this winter and which don't.
Any voting system, including those based on blockchain, should be designed in such a way that disclosure of someone's vote is entirely up to them.