Elections must strive for universal verifiability: every aspect of the election is verifiable by the general public.
This means every individual person can personally verify that no aspect of the election can be hidden. A person without the specialized knowledge and skill to validate the election can still plainly see that a skilled individual has all the necessary information to do so.
In other words: we must prove that the kid in the crowd pointing out that the Emperor has no clothes cannot be found, stopped, or silenced.
For ranked voting, the Board of Elections must publish the full set of ballots and the method of computing results. Any person can plainly see this, and knows that any skilled person can use this to recount and verify the election, thus the election results are either true or will be declared false by one of the billions of people who have access to this information.
Universal verifiability must extend to any electronic voting machines. We must prove that the voting machines start and remain running only known, public software, and are in a known state which anyone on the planet can inspect, even in the future.
Universal verifiability must extend to ballots themselves. Whether electronic or paper, ballots must be made traceable to a polling center through mathematical verification, ensuring a corrupt chain of custody cannot tamper with the paper ballots.
With simple plurality voting, we can achieve this by disclosing the simple vote count at the polling center. Anything using ranked ballots—Single Transferable Vote, Instant Runoff Voting, and Tideman’s Alternative Smith—requires the original ballots, and so such protection requires high-complexity mathematics.
Because generating proof for advanced voting systems requires the use of a computer, we focus heavily on methods of verifying electronically-cast ballots without putting the state of the machines at risk.