Beatpath example 12

This is an example of a beatpath order with 12 candidates. It has been constructed to illustrate a variety of situations that can occur in terms of beatpaths, the beatpath order, and pair-wise wins, losses, and ties. The example purposely has a lot of pair-wise ties and illustrates what is possible, not necessarily what might be typical.

This example could occur with the following ranked ballots involving 12 candidates A - L:
 * 6: A>B
 * 1: A>C>H>D>B>G>F>E>L>I>K>J
 * 6: C>D
 * 3: E>A>C>H>D>B
 * 3: E>B>D>C>A
 * 2: E>F>G>H>A>B
 * 2: E>G>F>H>B>C
 * 4: F>D>G>H>A
 * 1: F>G>E>H>B>D>C>A>L
 * 4: G>B>F>H>C
 * 1: H>G>F>E>D>C>B>J>I>K>L>A
 * 9: H>G>F>E>D>C>B>L>I>J>K>A
 * 10: K>J>I>L>A>B>C>D>E>F>G>H

These ballots are evaluated in pair-wise contests using a typical procedure. For example, the first line says there are 6 votes for A in each contest involving A, there are six votes for B in each contest involving B except for the one against A, and there are no votes for either candidate in any other pair-wise contest.

Note that the cycle equivalence class for A is {A,B,C,D} and the cycle equivalence class for I is {I,J,K}.


 * Beat Path Order:


 * The weak Condorcet winner is E.
 * The Schwartz set = {A,B,C,D,E}.
 * The Smith set = the set of all candidates.

Winner under different methods of ambiguity resolution

 * Copeland: B
 * Schulze: B
 * Ranked Pairs: B
 * Borda/Black: B
 * Approval voting/Llull, assuming every ranked candidate is approved: B
 * Minimax(winning votes): H
 * MMPO: E
 * IRV: E
 * Raynaud (Gross Looser): E and G tie
 * Plurality: E, H and K tie