From Symmetry to the Borda Count and Other Procedures

In this chapter I explore how geometric symmetry helps explain voting outcomes and procedures. For instance, the beverage example proves that the pairwise votes can reverse the plurality outcome, but why? The Condorcet profile shows that pairwise votes can create a cycle, but why? Certain profiles, such as a division between voters of types-one and five, create problems with voting procedures, but why? Some w _s procedures seem better than others, but is this true? In the first technical section, I show why some procedures lack certain symmetry properties; the cost is demonstrated with new paradoxes. The remaining sections return to the analysis of particular procedures.