One of the motivating factors seems to be laziness, another ignorance of dangers.

A paper-ballot count can still be fudged, but since it involves many people the fudging should be harder to achieve at a large scale.

I'm curious about the possibilities that public key crypto open-up for verifiable, anonymous voting.

From what i can tell, it should be possible for people to generate a public/private key, and sign their vote. There would be no central authentification authority. But all signed votes would be published in the individual districts, and any citizens group could verify a random sample of votes by calling a subset of voters and asking them to check (with their key) whether their vote as published online was counted correctly.

I can set up a demo of this if you like. I can't believe i'm the only person to have invented it.