In a previous posting, I referred to paper ballots as part of a recipe for election procedures that provide provide integrity and assurance by not relying solely on either computers or people to operate perfectly. As promised, here is some more info, especially important because there seems to be an increasing trend towards a "hybrid" style of election operations with both paper ballots and a variant of computerized voting.
But for starters, I hope it doesn't bear much discussion about how you fundamentally can't 100% trust computers for, well, for almost anything! and certainly not as the sole source and repository for ballots. But even leaving fundamental trust issues aside, recent history has shown us that it's not wise to assume that any combination of people and computers to really "get it right" a high percentage of the time, for any complex business process that's partly automated with software.
Also fairly obvious, at least to students of U.S. election history, is that many people have and will continue to think that it's very unwise to rely solely on people to correctly perform election operations in the paper-ballot, hand-count (PBHC) methods typical of the 19th century. You yourself might not share this view, but take it from me, it is a strongly held believe by many people. Enough people that, like or not, no matter how much a fan of PBHC you are, going back to pure PBHC is not going to increase confidence in the electoral system, but rather decrease it for a substantial number of people.
Fortunately, we also don't have to rely solely on people in a PBHC scheme, nor on flawless operation of computers.
The hybrid scheme is one in which paper ballots are both hand counted and also machine-counted by optical scanning and tabulation. Voters can certainly hand-mark paper ballots, and in addition, there are also electronic ballot-marking (EBM) devices that provide the legally-required enhanced access and produce a paper ballot to handled just like hand marked ballots. (For more on EBMs, see OSDV's wiki: Voting Method: Paper Ballots Optically Scanned). Using both counting techniques means that you don't have to trust and rely solely on either one. However, to use both, you also need some real clarity in defining procedures for tabulation, as well as for audit, and for re-count too, and of course for canvassing, which is the process of finalizing and blessing the final counts for an election. (That creates some flies in the ointment, but never mind for the moment.)
Hopefully it doesn't come as a surprise that at OSDV our technical activities certainly support this hybrid scheme (our development activities include an improved type of optical scanner device), but are not necessarily limited to this one scheme.