> is coercion really a threat on a large scale in the US
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.
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.