Hold a popular vote and then select from among the candidates randomly, weighted by their popular vote percentages.
In a two candidate race that both get 50% of the vote, the electorate has essentially said "We don't clearly know who's better." So flip a coin and go with that one. In a three way race where the 'spoiler' candidate receives 20% of the vote, select him as the winner with a 20% probability.
* The majority doesn't completely drown out the rest.
* Less susceptible to small counting errors. (i.e. the OP).
No chance of this being perceived fair. The conspiracy theorists are going to go apeshit the first time a 20% winner gets elected.
Perhaps use a non-uniform distribution to push the percentages further towards the extreme--e.g. a winner of 80% of the electorate should probably be chosen 95% of the time.
It has just been discovered that research causes cancer in rats.