In his talk he likens the e-voting machines of today to cars built without any roof. Paper trails he likens to an umbrella for owners of such roofless cars when, he argues, owners would be better off waiting for new designs resistant to rain. New car designs in his analogy are like the new ideas for e-voting systems centred on cryptography (as opposed to those that just use crypto to secure communications). Such new systems, as proposed by David Chaum and Andy Neff, are based on some very clever mathematics. This maths theoretically proves elections to be accurate and secure.
Rivest is a technologist and cryptographer and so it's not surprising that he's seduced by these proposed systems. But he forgets human nature… candidates, election agents and voters want to be able to trust votes that they can see and not fancy mathematics or cryptography. This isn't an anti-science perspective… I'm not arguing that voters are ignorant and so we can't use technology. I'm arguing that democracy is precious and complex technical systems create too many opportunities for abuse to be worth it.
In the final analysis Rivest is with the majority who fail to even stop and ask… why do we need electronic voting systems?
Thanks to Ian Brown for pointing me to Ron Rivest's notes