And then you need to explain how hash functions work to a bunch of people who dropped out of high school to work on the farm so that they don't feel cheated by the new electoral system.
In the long run, though, it shouldn't be so hard to get people to accept these kind of solutions.
We could use sealed envelopes made of heavy paper instead of the first hash function usage, and then have a guy in a lab coat point at a colourful picture of a fractal to demonstrate the randomness of the second hashing step.
Except that you've got people like Beck or Breitbart running around. Your election system has to be simple and transparent in order to make it as hard as possible to delegitimize in the eyes of the electorate. It's bad enough we've got a serious fraction of Americans who think Obama's not a legitimate president and/or who think that ACORN rigged the election, based on extremely spurious evidence. We can't give these factions (on either side) more ammunition.
The goal "impossible to delegitimize" is incompatible with almost all sophisticated election modes, and hard to measure.
I'd settle for "impossible to delegitimize rationally once you analyse how many people who normally distrust each other would have to cooperate". Crackpot-safety is just too much of a requirement.
In the long run, though, it shouldn't be so hard to get people to accept these kind of solutions.