River

River is a cloneproof monotonic Condorcet ambiguity resolution method with similarities to both Ranked Pairs and Schulze, but when cycles exist, can in rare cases find a different winner than either of the other two methods.

Quick summary of method, which is identical to Ranked Pairs except where emphasized:

• Rank defeats in descending order of winning vote strength.
• Starting with the strongest defeat, affirm defeats unless a cycle is created or a candidate is defeated twice.

The result is that only sufficient defeat information to determine the winner is included.

Because not all defeats are processed, the social ordering is not linear -- in general it is a tree (or river) diagram, with the victor at the base of the river.

It was first proposed by Jobst Heitzig on the Election-methods mailing list:

• First proposal
• slight refinement
• More concise definition. In this last version, River is defined very similarly to ranked pairs.
• Example using 2004 baseball scores. This shows how a 14-candidate election winner can be determined much more quickly using River than with RP or Beatpath.
• Early criticism of the River method. This shows that the River method violates mono-add-top and mono-remove-bottom