I am nobody's blockchain expert, but hopefully we can agree that, for all its flaws, bitcoin's integrity is legendary. That is, a bitcoin may be stolen, but when it is spent (transferred to another party) the entire blockchain "knows" about it. (Put differently, for al l bitcoins flaws, I'm not aware of a single case where a bitcoin was successfully counterfeited, nor spent "twice" at the same time).
If we can agree with that, then imagine a system where EVERY voter got ONE "voting coin" for a particular election. Every coin is thus unique and the number of coins in the system is fixed by the number of voters.
A vote "coin" is "spent" by giving a portion of the coin to any party (or issue) the legitimate controller designates. The original controller may choose not to vote at all, or not to vote for a particular office/issue, but in that case they remain the controller of the voting coin.
Else, when the initial controller (voter) votes for someone or something they give up their coin (or relevant portion of the coin).
The system, as a whole, must always be in balance. There are only a fixed number of total initial coins and, once the election is over, the SAME number of total coins must still be somewhere: with the initial voter or with the politician or issue the originally designated voter "spent" their bitcoin on.
Wouldn't that self-evidently work?