Reading some neglected mail from 2007, I happen to see a quotation from Prof Paz’s speech in The Moon Is a Harsh Mistress:
“You might even consider installing the candidates who receive the least number of votes; unpopular men may be just the sort to save you from a new tyranny. Don’t reject the idea merely because it seems preposterous–think about it! In past history popularly elected governments have been no better and sometimes far worse than overt tyrannies.”
Of course, if everyone knows this is the rule, the candidate elected will not be the least popular but the least unpopular, the one who inspires the fewest voters to say “anyone else!”.
But this gives an inappropriate advantage to unknowns. There ought to be a qualifying round of positive voting before the negative vote.
Approval voting takes care of both phases at once, meseems.