Why break Condorcet cycles when we can make them disappear?

Abstract

A Condorcet analysis shows that preferential ballots produce cycles in certain elections. Arrow’s impossibility theorem demonstrates that we cannot avoid this issue while maintaining some measure of basic democratic criteria, such as the Independence of Irrelevant Alternatives Criterion (IIAC). In fact, some groups can be incoherent when the individual preferences of its members are considered. However, using rated ballots to evaluate the different options or candidates in an election, we propose a way to make Condorcet’s cycles disappear and guarantee a single winner, with the exception of pure ties obviously. The general idea is to redefine the criteria used to apply pair-wise comparisons between two options. Instead of margins (or relative margins or winning votes), we use a criterion named median of differences. Starting with a median of rank one or two, we try to resolve the pair-wise comparisons. If a cycle appears, we raise the rank and try again until the pair-wise comparisons produce no cycle and no tie. In the worst case, the process will produce a coherent sorted list that represents the arithmetic average of all rates produced by each option. Because a coherent result is guaranteed, the choice between the different cycle-breaking Condorcet methods (Schulze, Tideman, Minimax, Nanson, Kemeny-Young, Dodgson, Copeland, etc…) becomes obsolete. The result can be extended to produce grades for every option or candidate.