I just don't know if what you're saying about Monero is true, regardless of convenience. I would think proving it would require math skills and stuff, aside from just running a node.
As far as vote counting, yes, blockchains would definitely make for more legitimate elections.
Of course, at the Presidential level, US elections aren't legitimate at all anyway. They don't even pretend to let everyone have equal votes - most states openly have unfair restrictions, and some states just don't allow votes to be counted at all, their court systems have declared that election officials should simply pick the candidates for voters in those states. No matter what state you're in, your vote for President doesn't count because the electoral college will still have you outweighed by states like Iowa that just give their electoral votes to whoever the officials decide without counting Presidential votes. Your vote for governor or congressman might count if you're in a state that counts the votes, but Presidential elections would need to happen at the national level to happen at all.
With these states openly saying they don't count votes, and people rarely talking about it, there probably wouldn't be much difficulty in keeping it a secret in other states. So there are probably lots of states where they also don't count the votes, but they at least pretend to. This invalidates all the elections in those states, not just the Presidential elections. This is what you're talking about when you bring up closed-source voting machines.
But we don't need voting machines at all. It would be much more simple to modernize the voting process than anything blockchain-related:
1. Don't modernize the part where officials count the votes, just have them keep counting stuff on pieces of paper on an actual physical table with their actual physical hands and eyes and brains like the old days
2. Make it a nationwide voting right that every paper ballot has unused whitespace where voters are allowed to mark their ballots in any way they want
3. Put high-resolution camera coverage above the vote-counting tables and make live feeds available to the public via multiple different sources (internet, low-wattage local TV broadcast, maybe actual screens outside the building, maybe cable TV broadcast)
4. When you cast your ballot, the ballot box you're leaving the ballot in tells you when and where to watch the video feed for the ballots being counted from that box at that time
5. Votes from each ballot box are shuffled before counting so that someone can keep their vote private from others they traveled to the polling place with (not able to check how person before you voted by seeing which piece of paper comes out before yours)
You can literally sum up every single block reward since the creation of Monero. It's very simple math for that part.
For bulletproofs and commitment, yes, it does take a higher level of math, but it's still verifiable.
You can't say the same thing for the current state of voting at all regardless of your level of math (that's assuming you think voting is morally legititmate to begin with i.e. a group of rapists or theives could just out vote their victim)
People like to throw around blockchains as the solution for everything, but it definitely could improve this area. Make it open source, throw in ZK proofs to hide who you are and who you voted for, while still making it verifiable that your vote was counted in the final result, and total number of votes cast for each candidate. It would have to require KYC/ID and would still have problems. But it could definitely be much better.
Its reliance on electronics would make it less durable. With my system, the assumption is that if technology goes away such that the video feeds fail, then the old system still just works as it did before.
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