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First, let me say that I believe the most ideal voting system of all may very well be a touchscreen computer with a well designed and implemented VVPT. Touchscreens allow large text, different languages, etc, that can help more people vote independently. You combine that with the security of VVPT (basically, the computer just acts as a very consistent, neat bubble-fill-in tool so you don't have the ambiguously marked bubble or the hanging chad), and you have as good a system as you're ever likely to find.
However, the existing VVPT systems absolutely do not meet the criteria of well designed and implemented.
First of all, there is the policy issue. There is a very significant legal difference between a "paper trail" and a "paper ballot." Supposing an elections official suspects fraud in the electronic tally, and does a recount from the VVPT, and indeed, the VVPT record shows a different tally, there is nothing the offical can do about it! The paper trail does not have legal standing as a ballot of record, so that tally cannot simply be substituted for the electronic tally in case of mismatch.
Secondly, there are the technical and design issues. The paper printout is extremely tiny and not in a very friendly format. I've heard that some machines come equipped with a magnifying glass, just so people can do the VV of VVPT. Whether that's true or not, unquestionably, one would be useful.
In addition to the unreadableness of the VVPT, there is the issue that it completely ruins the privacy of your vote. When ballots get dropped into a ballot box, they are mixed up enough that you can't tell whose is whose (apart from maybe telling which are from early morning vs late evening by which are towards the top of the pile). But with the single long, continuous tape of paper used in VVPT systems, votes recorded in flawless order. The GOP polling place observers, who are there to challenge people's registrations and whatnot (and equally other observers), simply need to note the name of each voter that uses the machine. Then, when those same observers go observe the counting or auditing of the paper trail, they can reconstruct the match between every single vote and the voter, including the voter's full name, home address, and everything. A disaster for privacy. Be extra careful who you vote for on an electronic machine, if you ever plan on running for office later in life!
Finally, the current VVPT systems I've seen could still sneakily steal votes. When a voter examines the paper trail, and if they see an error, they can tell the computer. The computer prints out additional lines of information, basically saying, "disregard the above; here is the corrected vote." Unfortunately, with the continuous tape, there is nothing to prevent the machine from "correcting" your vote, after you have walked away by printing the additional information. This could be fixed by, for example, having the machine cut the paper and let it drop into a box after each voter votes. The voter would know that their voting was fully complete and their vote unchangeable.