Election Systems - how to audit them?

Here is the logic problem I'm working on at the moment.

I need to build an election system. An electronic election system.

How do I build an electronic voting system that the users can audit? I can't tie a vote to a person's ID or name due to privacy. I can't print out a copy of a paper ballot.

The only idea I have is to count the number of voters against the number of votes.

interesting problem....