Keep a record that I voted. Don't attach it to my vote.

Ok, and how do you verify that your vote was cast for X candidate (i.e. that the machine didn't count your vote for Y candidate)?

There's no way to do that without tying the voter to the vote somehow. Why not hash the voter ID + a secret of your choosing and store that with the vote? Then, even if counting by hand, you can verify your vote was indeed cast for X candidate.

Such verification would enable a market for selling votes.

Just make vote selling illegal then? Or just make verification onerous, so that you can only do it during a recount, not on-demand via the internet.

I would rather be able to verify that my vote was cast to the desired candidate than to have a strictly anonymous (but unverifiable) voting system.

Paper.

That's a trivial problem, long solved. In order to vote, one must be registered. Registrations are printed on a paper book for that precinct. When you show up to vote, you have to sign your name in the registration book. Then they give you a ballot.

Easily gamed without strong (physical presense) voter ID requirements.

EDIT: Mail in voting is skimmed with little to no risk. Oops, lost 1% of that zip code...

https://www.youtube.com/watch?v=yW2LpFkVfYk

Not really. The odd vote here and there might be gamed, but enough votes to statistically affect most elections is extremely difficult. Think about it. You need a voter, physically present at the precinct, matched up to a registration. What does that mean?

Assume a million votes are cast in an election. To move the needle 1%, you need 10,000 votes. And let's assume a single fake voter can realistically cast ten votes in different precincts, considering vote time and travel time (they can't just keep coming to the same precinct, for fear of recognition).

So you need 10,000 fake registrations, that must match real addresses, and you need 1000 people working all day at fake voting. One voter out of every thousand would be working for this conspiracy.

Now, you need to do this in complete secrecy. Nobody can talk. Nobody can gather evidence. They can't go to the police, or the media. Even one leak is enough to not only ruin the scheme, but create a nationally known scandal. And if it can be connected in any way to a particular political party, that party's name would be dragged through the mud across the country.

It's insanity. No one could safely pull it off.

You know what can be pulled off, though? Voter suppression. Make it much more difficult for certain categories of voters to actually vote. Such as poor people who might not have ID (or might hesitate to use it). Then, convince a large swath of the public - people like you - that this is about security, not suppression. That form of election manipulation is now seen as patriotism, not corruption.

Seems difficult to do. You'd need to know the name and address of the voter, and be sure that that haven't voted yet, and won't try to vote after you.

I can see that happening maybe a few times, but it seems ineffective on a large scale.

Most of that isn't true. When I lived in California, you simply asserted that your name was X, where X is someone on the list, and you got X's ballot. No need to know their address.

If they already voted? "Oops, I forgot."

If they haven't voted and come in later, so what? You're long gone.

In Milwaukee, Wisconsin, we have two people cross checking each other to consult 3-ring binders of registered voters for the particular district they are assigned to vote in. Your name is check-marked as part of handing you a paper ballot.

This may sound laborious and slow but it should be enough to block repeat voting, IMHO.

I think lots of countries will stamp your wrist and check for a stamp before allowing a vote to happen. I could be mistaken, but something akin to this is possible.

Just mark it down on a list. Whether someone has voted is not a secret.

In Russia you need to show an ID (internal passport) to receive a ballot and put a signature into the voters registry. So duplicate voting is possible only with the help of election staff (usually in such case a person has something in their passport, or says a code word that gives a hint that he should receive a ballot without checking his name against the registry).

Then you could wash off the stamp and vote again