##
Probabilistic Voting with 3 Ballots

You want to vote for party A with probability *p* and
party B with probability *q* = 1 - *p*.
You are alone in the voting booth, where there are paper ballots
marked A and B, exactly one of which you must put
in the given voting envelope.
You want to do this with *zero knowledge* about your actual vote,
i.e., such that you will only know that you have voted with
probabilites *p*, *q* and nothing else (formally,
the posterior probabilities must always be *p*, *q*).
Finally, you are not allowed to deform the ballots or
mark them in any way (as it will disqualify the vote).

For *p* = 2/3, you can easily do it with two A-ballots and one B-ballot:
turn them upside down, mix them, choose one at random (i.e., uniformly)
and put it in the envelope, and finally dispose of the other two
(in such a way that you won't see what they are).