At Ruxcon last year there was a very interesting talk by an electoral systems researcher (I can't recall her name). She went through a number of electronic voting systems, and they all suck. Some more than others. The only case where she found a system that was close to acceptable was in a crypto organisation where everyone was highly technically fluent in the system. Certainly not transferable to the general public. She also noted that computerised systems tend to favour right-wing policies even if the algorithm is fair - people who vote for leftist policies are over-represented amongst migrants, people with disabilities, and other non-mainstream demographics.

She did have the opinion though that there was as place for electronic machines in the voting booth, and it was this: register your vote on a machine. It prints out a slip with clear, unambiguous markings against your selected candidate(s). Verify that it has the content you want, then go lodge the slip like any other paper ballot. You now have a clearer, less ambiguous version of the paper ballot, which is more accessible to people with certain kinds of disabilities to boot.

Most of the times that a paper ballot recount differs is not because of inept counters, but because some voters leave ambiguous marks. She said that in Australia, it has about the best system possible (edit: probably 'in current use') in terms of verifying the count: an AEC official does the counting, and the major parties volunteer scrutineers to challenge ambiguous voting slips. As there are mutually opposing witnesses, you get a fairly robust count - the differences come when one set of scrutineers allows one ambiguous mark, but on a recount that same ambiguous mark gets treated differently by another set of scrutineers.

The important thing is the pile of paper though - the evidence that people voted a certain way. In effect, as soon as you don't have the physical evidence, you're at the mercy of "trust us, it's accurate". How do you scrutinise that?