Voting schemes based on candidate-orderings or discrete choices considered harmful Warren D. Smith, NECI December 2001 Abstract: We give a family of scenarios in which \emph{any} voting system in which each voter's vote is based purely on his perceived ordering of the 3 candidates, is entirely helpless -- must regard the election as a 3-way tie -- and will necessarily elect a random candidate. (By slight tie-breaking perturbations we could instead make them elect any particular candidate, in particular a bad one.) These scenarios are based on a new construction of ``intransitive dice'' having independent interest. I further argue that any voting system involving discrete vote choices must often elect bad candidates in my scenarios. Meanwhile, voting systems in which votes are permitted to continuously vary, need not regard the election as tied nor experience any difficulty. A specific case of my scenarios is given that is a ``universal counterexample'' causing every voting system so far proposed to misbehave (simultaneously). Keywords: Range voting, nontransitive dice, universal counterexample. not patentable. 5 pages.