And when I step into the booth, I can say "last time I voted, I got fired for voting" and it'll be on the record, too.
I mean, this is all a theoretical, but lets play it out.
Given that, you're left with needing to argue that the societal benefits of non-secret voting would outweigh the harms of voting-based discrimination. To me, that doesn't seem like a close call, but I'm open to the counter-argument.
Because actually a lot of people might argue that not having this, in the first place, is why our societies are so easily corruptible.
The open society dogma, and I admit this is just a thought experiment, might very much include the fact that, when someones rights are abused, it doesn't just get lost in the noise.
Being able to vote - and address grievances for which I require government support - seems to me to be a way to complete the vote as a proper transaction, between the individual and the state.
Right now, you vote and get nothing back - well, you get the assumption that your government is still going to be, relative to the last one, livable (or else you'd be a refugee and potentially pursuing statelessness..) - but when you use your Vote Statement as a way of communicating something public - per your own free will and agency (and thus right) - this is also a responsibility that must be addressed by the next administration .. giving your vote even more relevance to the incumbents and challengers, alike ..
I'll have to bow out of this convo at this point I think as we seem to be talking past each other, or at any rate you seem to be talking about something different than what I thought we were discussing.
With this function, a vote not only becomes a static erg towards ones favoured party - but a way for the future government to a) be sure it was voted in without corruption, and b) address any corruption occuring during that process, based on open, public, verifiable data.
Yes, this is just theoretical, and thanks for the time anyway .. it was just a thought experiment.