Problems with majority voting over pairs as represented by Arrow's Theoremand those of finding the lengths of closed paths as captured by the Traveling Salesperson Problem (TSP) appear to have nothing in common. In fact, they are connected. As shown, pairwise voting and a version of the TSP share the same domain where each system can be simplified by restricting it to complementary regions to eliminate extraneous terms. Central for doing so is the Borda Count, where it is shown that its outcome most accurately refects the voter preferences.