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.
- 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).