The way around this is to give each person 1 ballot for each of N candidates. 1 ballot goes into an envelope and into the vote box. N-1 ballots go into envelopes and into the discard box. It's trivial to show a photo of your ballot for Dr. Evil, but it would take a video of you going into the voting booth, closely following your hands to prevent three-card-monty, and continuing to follow you into the public lobby containing the vote and discard boxes. If you strictly enforce no recording in the public lobby, then there's no way for you to prove to your boss which box got your ballot for Dr. Evil in the end.
Edit: Perhaps I wasn't clear. Each of the N ballots is already filled out for a different candidate. The envelopes are all identical and sealed by you inside the voting booth. That way an existence proof of a ballot for the given candidate leaks absolutely no information. There are no empty paper ballots, and none of the paper ballots can leave the polling station. Ballots need to be counted both from the "vote" and from the "discard" boxes. Ballots missing from the discard box prove vote tampering.
Well there's no need for an elaborate scheme like this, certainly no need for video. The buyer gives a paper ballot that's already marked for Dr. Evil, and asks the vote seller to bring back the empty paper ballot to get paid. It's that simple :( and being done in the places which still uses paper ballots.
There are no empty paper ballots, and if a ballot is brought back, then it's not in the discard box. Since votes in the discard box are still tallied, if someone leaves the polling station with a ballot, it will be obvious that someone has tampered with the election.
But each ballot is pre-filled out for a different candidate. The vote fixer already knows what's on all of your ballots, they just don't know which goes into which box. Photos showing what's on the ballot don't disclose any information. The attacker already knows that you have one ballot pre-filled for each candidate. The only secret is which ballot goes in which box.
You go into the voting booth, seal the N ballots in the N identical envelopes, being sure to keep track of where the ballot for your desired candidate is. You leave the voting booth and drop the one envelope in the vote box, and the N-1 envelopes in the discard box.
Even if you're forced to videotape inside the voting booth of your sealing the N ballots in the N identical envelopes, you could pull a quick 3-card-monty when leaving the voting booth. Even a quick random shuffle would be sufficient to statistically nullify your vote, or if you're only able to keep track of where the Dr. Evil ballot is, a quick deal from the bottom of the deck would guarantee a vote for a random opposition candidate. As long as there's some spot between the polling both and the ballot boxes that isn't covered by video, there's no way for a third party to know which ballot went where.
You aren't allowed to leave the polling station with any of the envelopes, and a tally of the ballots in the discard box will show what percentage of people have left the polling station with their discarded ballots. Any non-negligible percentage of "discard" ballots leaving the polling station will make the whole vote suspect. (The discard ballot count will also provide circumstantial evidence for which way the tampering is going, although Dr. Evil will always claim it's false flag vote tampering to make him look bad).
If someone is really coerced in sneaking their discard ballots out of the polling station, they could sneak N-1 ballots out and either put the ballot for Dr. Evil in the discard box or burn it right outside the polling station. They then show the jackbooted thugs the other N-1 ballots. They end up not voting, but at least Dr. Evil is denied the vote.
I suspect the envelope with the good ballot is sealed in some way. All they would have to do in that case is force you to take a picture of the sealed ballot with the non-desired ballots next to it.
All of the envelopes are identical. Absolutely the only difference is which envelope goes into which ballot box. Taking a photo of N-1 ballots for non-Dr. Evil next to one sealed envelope only discloses that the Dr. Evil ballot was put into an envelope first. It gives no information as to which box that envelope was placed into later, and therefore leaks no information about how the vote was cast.
Edit: Perhaps I wasn't clear. Each of the N ballots is already filled out for a different candidate. The envelopes are all identical and sealed by you inside the voting booth. That way an existence proof of a ballot for the given candidate leaks absolutely no information. There are no empty paper ballots, and none of the paper ballots can leave the polling station. Ballots need to be counted both from the "vote" and from the "discard" boxes. Ballots missing from the discard box prove vote tampering.