An Informational Basis for Voting Rules

This paper presents a novel combinatorial approach for voting rule analysis. Applying reversal symmetry, we introduce a new class of preference profiles and a new representation (bracelet representation). By applying an impartial, anonymous, and neutral culture model for the case of three alternatives, we obtain precise theoretical values for the number of voting situations for the plurality rule, the run-off rule, the Kemeny rule, the Borda rule, and the scoring rules in the extreme case. From enumerative combinatorics, we obtain an information utilization index for these rules. The main results are obtained for the case of three alternatives