The Power of None

Abstract

Borda with None (BwN) adds the binding option of “None of these candidates,” N, to the Borda Count (BC), differing from a method of Dodgson in the scoring of ties. The method incorporates the benefits of approval voting, which allows a simple yes/no vote on each candidate and avoids the disadvantages of adding N as a binding outcome to plurality voting. We prove that BwN uniquely satisfies five rational properties which can be viewed as potential axioms that provide a theoretical basis for the method. It allows individual voters to express a personal veto over all or part of the slate which could, with sufficient numbers, become a veto by the electorate. The power of none, then, is offering a voice to otherwise disaffected voters. We introduce a metric similar to one used in the Bak–Sneppen Evolutionary model, candidate fitness, a number between 0 and 1, which measures a candidate’s ranking relative to N. We illustrate its evolution with a hypothetical example. We examine courses of action if N is ranked in the first place. Using BwN to accommodate partial voting is proposed. We explore the general applicability of BwN. Finally, we address the practical considerations for introducing BwN.