This last fact undercuts one of the common criticisms of election conspiracy theories, namely that stealing an election would require the cooperation of many people over a wide area. This might not be necessary, but about the contention of any recent major US election having been stolen, the authors write, "We know some people are claiming this happened, but we don't find their evidence convincing."
One of the most interesting aspects of this study is a videotape of an actual Diebold AccuVote-TS machine being hacked. The tape clearly shows the quick installation of the bad memory card (either with a copied key or by picking the machine's lock), the pre-election check indicating that nothing is amiss, the mock mini-contest between George Washington and Benedict Arnold which Washington wins 4-1, and then the print-out showing that Arnold, in an election upset, beats Washington 3-2. There are a number of other types of electronic voting machines in use today, but little certainty that they aren't vulnerable to similar tampering. (In response, Diebold claims that there have been improvements.)
With proprietary software and no independent paper trail, there are unfortunately grounds to doubt election results, especially when they're close. You wouldn't make a deposit at an ATM machine whose screen opened to reveal a well-dressed bank official who thanked you for your check and assured you he'd put it into your account, but who didn't give you a receipt or any way to check your balance. The same holds for credit cards. Your money is important, but so is your right to vote, and you shouldn't have to trust well-dressed men about either. Identity theft is a well-publicized bother; democracy theft is an invisible rot.
The only good news is that it now takes programming prowess to steal elections when all it used to take was the ability to stuff ballot boxes.
Professor of mathematics at Temple University, John Allen Paulos is the author of best-selling books including "Innumeracy" and "A Mathematician Plays the Stock Market." His "Who's Counting?" column on ABCNews.com appears the first weekend of every month.