https://www.youtube.com/watch?v=w3_0x6oaDmI&feature=youtu.be
An excellent video. He does an exceptional job of explaining in relatively non-geek terms why it isn't possible to have a trustworthy electronic voting system.
That said, I think that there's yet another problem with electronic voting which is a different aspect of the trust problem. From my perspective, one of the key features of a conventional paper ballot system where humans do all the counting is that it is possible for pretty much any concerned citizen to look at the system carefully and convince themselves that it is trustworthy in the sense that nobody will be able to see how they voted or be able to fake the results or any number of possible things that a concerned citizen might be concerned about.
Now let's assume that you have an electronic voting system that actually is perfectly secure (remember, I said "let's assume") and is actually worthy of our trust. The only citizens who are in a position to actually convince themselves that the electronic voting system is trustworthy are a tiny handful of geeks who are in a position to actually inspect the system. The only thing that an arbitrary concerned citizen can do, assuming that they are not one of this tiny handful of geeks, is ask said tiny handful of geeks if the system is trustworthy and then try to trust the answer they get (obviously, if they actually do trust the answer that they get then they are fools since nobody in their right mind would accept an answer along the lines of "trust me, I'm a geek and I happen to know that the system is trustworthy").
The bottom line is that even if their electronic voting system actually is trustworthy (an admirable yet impossible goal as Computerphile explains in this video), only a concerned citizen who is a complete fool would ever trust that their electronic voting system is trustworthy.
As it turns out, this conclusion leads directly to yet another problem with electronic voting - since any concerned citizen with half a brain will realize that they cannot trust the electronic voting system, the fact that the electronic voting system is essentially being forced on them will breed distrust and cynicism in their democratic system as a whole. This is fatal to any democratic system because, quite frankly, even if it is possible for a concerned citizen to truly and properly convince themselves that the system is trustworthy, the vast majority of citizens actually have faith in the system only because they have faith in the system (i.e. their faith is circular and illogical and unfounded but it is all that they have to work with).
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