i.e. we generally say election fraud is not a huge problem because its too easy to get caught.
if that's the case, one would think any vote buying scheme would be even easier to get caught.
i.e. I feel we can both have total anonymity if a person desires, while also having verifiability.
as an example: a random uuid is assigned to me and my votes are printed out on a slip of paper with the uuid (and with a cryptographic signature to verify that it was produced by a voting machine). I can choose to burn the paper and no one can know how I voted or I can keep the paper and anonymously verify that my vote was recorded correctly (i.e. download the whole set of uuid -> vote mappings).
if the number of uuids submitted at each polling place is recorded reliably (i.e. observers from multiple sides having agreed upon counts), you have a good belief that no votes were added or removed.
if every voter who chose to keep their slip is able to verify their vote is recorded correctly you have a good belief that the votes weren't manipulated (assuming enough people verify their votes).
yes, there are issues, vote buying / coercion, but I'm just not convinced that those issues are severe enough or probable enough (at least in the USA) to want to avoid simple steps that will make people more comfortable with the election outcomes.
i.e. make the punishments harsh enough for anyone caught coercing / paying others for their votes to make it unlikely to happen at a scale that will negatively impact things.
but perhaps I'm naive about this.
No, largely because of the secret vote and the fact that there is no way anyone can verify how "you" voted after the fact. So you can lie to the thug threatening you with a wrench that you voted for "candidate A" and the thug has no way to know otherwise.
> But if the onl way to know my vote is to have my random identifier, if I dispose of my random identifier, they can't know my vote.
If the thug with the wrench who has /suggested/ you vote for candidate A lest he break your kneecaps also knows you can verify your vote by using your random identifier, then if after the election you have disposed of your random identifier, the thug breaks your kneecaps because you disposed of your random identifier. Therefore you are still coerced to reveal your vote, because you are also coerced not to dispose of your random identifier until after the thug has verified you voted "the proper way". I.e. the thug changes tactics from "vote for A lest I break your kneecaps" to "vote for A and do not dispose of your identifier until I verify you voted my way lest I break your kneecaps".
> I feel we can both have total anonymity if a person desires, while also having verifiability.
If there is any form of ability to verify your actual individual vote, in any way, then there is no anonymity.
Anonymity is only available if there is no ability to verify an individual voted a particular way after the fact. Any opening of verification destroys all anonymity.
edit: or perhaps better, a random sampling were permitted to print out a proof of vote slip, but didn't have to. But if not chosen, you didn't get a proof of vote slip.
Now, in thinking it through, it might not help much. if someone can manipulate the voting machines, they can know who printed out their slips and manipulate the other votes. With that said, if done correctly, with a paper trail, I think it be difficult.
i.e. users are giving 1 or 2 outputs. piece 1 is a paper print out with a uuid and their votes that gets deposited in big box and counted as deposited. piece 2 that not everyone even has an option to get, can be kept. there has to be no way to distinguish the different piece 1s of those who get a piece 2 or not. If so, if everyone who got a piece 2 sees that their vote was recorded per the record they have, they can be confident that their vote was recorded correctly.
if their vote is not recorded correctly, they should have an anonymous mechanism to deposit their slips to make known that their vote was not recorded correctly. (hand waving at that, as unsure how to do that).
Sadly, the thug also knows this. But what the thug (=ruling party) does know is whether an entire voting district votes for the opposition.
Then they come down hard on the entire district. In all sorts of creative ways.
It's not so much about the ruling party - if they want to steal the vote, they can just just send an officer into the booth with you that makes sure you're not cheating.
It's more about those that don't have that ability, e.g. religious groups, families, social circles. That's why ballot selfies are sometimes outlawed and generally strongly discouraged: if it's illegal and punishable to prove to third parties how you voted, you have plausible deniability for why you can't produce proof.