Discrimination axiom

Discrimination. If a particular profile P0 gives rise to a tie, then it should be possible to find a profile P that does not give rise to a tie and in which the proportion of ballots of each type differs from its value in P0 by an arbitrarily small amount. This rules out, for example, the following method of electing one candidate from three: elect the candidate who beats both of the others in pairwise comparisons, if there is such a candidate, and otherwise declare the result a three-way tie. For in that case, not only would the profile in Election 3 below give rise to a tie, but anything at all close to it would also give a tie, contrary to the axiom of discrimination.