https://archive.org/details/yes-prime-minister-power-to-the-...
- You publish a public list of randomly generated numbers/IDs (the number of IDs corresponding to the number of eligible voters, guess you need a reasonably accurate census data for this)
- Divide up into subsets and distribute these IDs to each voting booth.
- When you go to vote you draw on of those numbers and attach it to your vote.
- Election results are published as "ID X voted for Y".
Now everyone can check that their vote was counted, and everyone can check that the original list of of IDs matches the final results (or in reality, count(final list) < count(original list) since not everyone votes).
Here very recently the Federal Road Administration was caught stopping buses in regions where the left leaning presidential candidate had the strongest support. We also had a few tens of cases where business owners were discussing strategies on how to get their employees to vote for the right-wing candidate, and some strategies depended on breaking the law by taking you smartphone to the voting booths and taking a picture (breaking the law in the process).
Seriously. We are talking about people who would claim rain is not wet, while it pours down their face if it was somehow helping them "owning" the other side. No clever system is going to fix people not wanting democracy anymore.
This is an issue of decades of uncontrolled "news" media and a lack of education and the US is going to harvest the fruit of that neglect for the next decades at least.
It might be my education about the roots of fascism that I got by growing up within the borders of former Nazi Germany, but US democracy is in an extremely dangerous spot right now. The specific mixture of economic pressures, media bubbles, lack of education, corrupt political actors and processes and split culture is a volatile explosive mix.
The media has covered this with varying effect but we hardly conjured it into existence. In fact the media can barely keep the lights on, let alone fund the lawsuits, "grassroots" redistricting efforts, organized disinfo campaigns, etc that have shaped politics at the state level — including anti-media campaigns that paint the elite mainstream media as the authors of the present electoral crisis.
Except for the past half-a-decade the media is increasingly pitting people against each other. Each side considers their rivals evil or crazy and is not ready to respect their opinion, listen or compromise. This creates incentives to cheat and legitimate reasons to suspect cheating. No matter what algorithmical or organizational approach you take, there will be always human factor, and hence reason for doubt. And the only way to resolve it is to make sure that you can always recheck the results in a way that satisfies the losing party, rather than screaming "blasphemy" to shut them up.