Mathematical view of a ballot

Mathematicians sometimes study practical things like elections. Even mathematicians who don't study elections can't help but be problem solvers. I was pondering my punch-card ballot today.

Say you were in the position of voting a nearly straight ticket. In Missouri, that is easy. You punch a hole for your straight ticket vote, but you can go on to punch holes for selected candidates where you wish to deviate. Of course, you can skip the whole straight ticket thing and just vote for everyone individually.

If you didn't trust your ballot to be handled honestly, should you vote individually or should you use the straight ticket method and vote for select individuals? If you think this is a silly question, perhaps you should review our noble American history of elections.

Just as a simple modern example. Did you know that the maker of shiny new Bank Midwest ATM machines, is also a maker of no-paper-trail voting equipment? Did you know that the head of this company is reported to have said that he is "committed to helping Ohio deliver its electoral votes" for George W. Bush? I don't know about you, but I trust my punch card a lot more than I would a touch-screen that comes with that kind of warranty.

If we have touch-screen voting in our next election, I think I'll be voting by absentee.

So. Have you figured out how you should punch your punch card? The answer is: you should vote individually. It minimizes the damage that a dishonest person can do by tampering with your ballot. If you voted straight Democrat, including for president, a dishonest person with access to your ballot could punch the Republican candidate for president. This would effectively deduct one vote from your candidate of choice and deliver it to the opponent. If you voted individually, the most a dishonest person could do is invalidate your ballot by turning it into an overvote (punching extra holes).

If every voter avoided straight ticket voting, the dishonest person would have to tamper with twice as many ballots to achieve the same effect, requiring access to twice as many ballots and increasing the risk of being caught.