SYMMETRY EXTENSIONS OF NEUTRALITY .2. PARTIAL ORDERING OF DICTIONARIES

For n greater-than-or-equal-to 3 candidates, a system voting vector W( n) specifies the positional voting method assigned to each of the 2n - (n + 1) subsets of two or more candidates. While most system voting v ectors need not admit any relationships among the election rankings; t he ones that do are characterized here. The characterization is based on a particular geometric structure (an algebraic variety) that is des cribed in detail and then used to define a partial ordering ''<--'' am ong system voting vectors. The impact of the partial ordering is that if W1n<--W2n, then W2n admits more kinds of (single profile) voting pa radoxes than W1n. Therefore the partial ordering provides a powerful, computationally feasible way to compare system voting vectors. The bas ic ideas are illustrated with examples that completely describe the pa rtial ordering for n = 3 and n = 4 candidates.