Combining Voting Rules Together

We propose a simple method for combining together voting rules that performs a run-off between the different winners of each voting rule. We prove that this combinator has several good properties. For instance, even if just one of the base voting rules has a desirable property like Condorcet consistency, the combination inherits this property. On the other hand, some important properties can be lost by the introduction of a run-off, including monotonicity and consistency. In addition, we prove that combining voting rules together in this way can make finding a manipulation more computationally difficult.