if no one voted for a president or any other political positions, what would happen?
Is there a threshold below which an election is deemed invalid? I honestly don't know. It would be interesting to see what would happen if no candidate got a single vote.
It really is a shame there isn't an option to say "none of the above". Elections seem to be more and more about both sides putting up some extreme nutjob who appeals to the party faithful and offers nothing to even moderates (often even moderates on their own side), and the question might as well be "Choose the form of the destroyer" from Ghostbusters.
An interesting comparison between humans and animals is that animals never choose the least capable to lead them. We seem to do that depressingly frequently. It's not even as if it's a new thing - during the Bush/Gore election much of the chatter was wondering how, in a country of some 250,000,000 people, the US couldn't find two more inspiring candidates for the top job.