I'm not a libertarian or anything near it, but I like this idea.
Don't reinvent the wheel however. With respect to voting, you want to be able to verify that those voting are legitimate individuals authorized to do so, but at the same time we need to preserve the sense of anonymity with respect to an individuals vote.
This is where Zero Knowledge Proof systems comes into play. Look into something called ZK-STARKS, which is the next iteration on the ZK-SNARKS system used for ZCash.
The paper is located here: https://eprint.iacr.org/2018/046
Also referenced in this CoinDesk article for verification that this is a safe link: https://www.coindesk.com/white-paper-trustless-privacy-tech-zk-starks-published/
It's a long paper and I'm still making my way through it. Also, I'm not an expert by any means, so I can't help beyond providing a heads up to this info.