Some people have suggested, that in Rivests's 3ballot scheme, it would be better if the voting machine were to choose the 3 ballots randomly, (as opposed to the voter choosing them) and then the machine were to spit out a copy one of them for the voter to take home (as usual). There are two variants here: either 1 the voter chooses which of the three to copy and get, or 2 the machine makes that choice also at random.
The point of these suggestions was supposed to be that the voter has an annoying job filling in 3 ballots (or in BOFFO, five ballots) instead of just one. This way the machine saves that voter the labor. The machine just asks the voter for his one (actual-summed) ballot and creates three that have the desired suma nd meet all the constraints. Saving labor.
But this is a very bad idea. Aside from the fact such a machine would probably have to be computerized (bad!) and we'd have to trust its "randomness" really was random, there are more severe problems.
Variant 2, of the scheme is simply vulnerable to vote-buying and coercing. E.g, the coercer says to the voter: "if you show me a receipt saying 'voted for Clinton' then I will pay you a dollar." The voter then has a 2/3 chance of getting the dollar if she voted for Clinton, and only a 1/3 chance if not. In other words, this "harmless" addition of randomness broke the security properties of the 3ballot scheme.
Variant 1, of the scheme is also vulnerable to vote-buying and coercing if it is used with plurality voting. E.g, suppose the vote-buyer supports Clinton and Nader but is opposed to Bush. Buyer tells voter: "if you show me a receipt saying 'voted for Clinton and Nader' then I will pay you a dollar." The voter then has a 2/3 chance of being able to get the dollar if she voted for Clinton, and only a 1/3 chance if not.