If we want them to be uniquely identifiable, then we don’t need to hide the identifier. If we don’t want them to be uniquely identifiable, then hiding the identifiable ID becomes a violation of the voters privacy.
Also IANAL but I feel like there must be some law about deception of this kind. Selling a product that does something you don't expect it to, were never told about, and would not reasonably even observe feels somehow like fraud.
Or you can register as an independent if you prefer. The rules vary by state, but the worst that happens is you can't participate in the primaries (but can absolutely vote in the final election). Who you, as an individual, voted for is still not traceable back to you.
In other words, it's your right, thanks to the secret ballot, to vote completely differently from the party you registered under or even differently from how everyone in your life perceives you, and nobody will ever know.
There are people who changed their mind years ago about what party they support and have been voting that way ever since, but just haven't gotten around to (or don't care enough to) update the party they listed on their voter registration.
Ballots typically do have unique IDs usually on some part that is removed by the voter. The problem is that isn't linked to anything because we don't want it linked to anything. This form of auditing isn't compatible with ballot secrecy. US elections do undergo rigorous process audits but the electorial process presents challenges to results audits.
1. That each paper ballot was only counted once by the tabulating machine.
2. No extra ballots were returned with an id that was not generated.
3. Easily spot copied ballots.
You could probably audit more things. If for example the id corresponded to a county, and so on.
If the government mails me a ballot with ID #1234 on it at my home address, then they have a way of knowing that Ballot #1234 belongs to me in particular when they're tabulating the votes, which means they can find out exactly how I voted. Now we don't have a secret ballot anymore, and the secret ballot is a fundamental part of our democratic voting system; a secret ballot prevents the government from rewarding people or doling out punishment based on how they voted. It's a safeguard against authoritarianism.
(I think some US states put identifying info on the outer envelope or sleeve that the ballot is returned in, but there's a strict system to keep the envelope-opening step separate from the ballot-tabulation step, so people's votes cannot be personally linked to them as long as the system is followed. And these days there are usually cameras watching to make sure it is followed, and the footage is public.)
If you do get rid of the secret ballot then there's not much of a reason to hide the ballot ID via yellow dots. Just put "Ballot #1234" all over it and/or print a unique barcode. But regardless of whether the ballot ID is displayed or hidden, if you happen to get a dictatorial maniac into power (whatever you personally envision that person to look like) then you would be one step closer to letting that leader use personally-identifiable voting records to punish the people who voted the way he (probably a he) didn't like and/or give the people who voted the way he did like rewards or unfair advantages.
If you want to audit mailed out ballots, use two envelopes instead. The outer one will carry a unique id, the inner one will be completely anonymous and contain the actual ballot. All the auditing can be done on the outer, unopened envelopes. Then they are stripped off, all the inner envelopes are thrown on a heap and only then opened and counted.
Of course, even then, the paper ballots contain traces of the voter's DNA, so the truly paranoid will not be happy either.
> popularity contest driven by peer pressure
No, it's so people can't sell their votes, or be told by their parents/employer/local gangs that if they don't verify they voted correctly, they will be hurt. It's not cancel culture or popularity contests or whatever. Voting is definitely supposed to be a popularity contest based on peer pressure.
The completed ballot goes into an opaque sleeve devoid of identifying information, which then goes inside of an envelope. The envelope has an extra "flap" where you put your information and signature, and then it seals onto the envelope.
When processed, the flaps have perforations that can be physically separated from the rest of the envelope and validated and retained for audit purposes, and later on the collection of sealed envelopes can be opened and the ballots counted without having any attached personal information.
More generally, for ballots you don't need to hide this, you could just have a number on them.
The process should be well known since all it takes to find out is go sit in an election committee.