Schulze method
Condorcet methods Positional voting Cardinal voting Quota-remainder methods Approval-based committees Fractional social choice Semi-proportional representation By ballot type Pathological response Strategic voting Paradoxes of majority rule Positive results The Schulze method (/ˈʃʊltsə/), also known as the beatpath method, is a single winner ranked-choice voting rule developed by Markus Schulze.
Schulze's method breaks cyclic ties by using indirect victories.
Schulze's method uses ranked ballots with equal ratings allowed.
To help visualize the strongest paths, the set of pairwise preferences is depicted in the diagram on the right in the form of a directed graph.
To avoid cluttering the diagram, an arrow has only been drawn from X to Y when d[X, Y] > d[Y, X] (i.e. the table cells with light green background), omitting the one in the opposite direction (the table cells with light red background).
The only difficult step in implementing the Schulze method is computing the strongest path strengths.
The following pseudocode illustrates the algorithm.This algorithm is efficient and has running time O(C3) where C is the number of candidates.
Schulze's original paper recommended breaking ties by random ballot.
This method is equivalent to the others described here, but the presentation is optimized for the significance of steps being visually apparent as a human goes through it, not for computation.
So we get straight to the second drop (E's loss to C by 3 votes), and that shows us the winner, E, with its clear row.
The Schulze method satisfies the following criteria: Since the Schulze method satisfies the Condorcet criterion, it automatically fails the following criteria: Likewise, since the Schulze method is not a dictatorship and is a ranked voting system (not rated), Arrow's Theorem implies it fails independence of irrelevant alternatives, meaning it can be vulnerable to the spoiler effect in some rare circumstances.
The Schulze method also fails Peyton Young's criterion of Local Independence of Irrelevant Alternatives.
Ranked pairs is another Condorcet method which is very similar to Schulze's rule, and typically produces the same outcome.
The main difference between the beatpath method and ranked pairs is that Schulze retains behavior closer to minimax.
Then the Schulze method, but not ranked pairs, guarantees the winner is always a candidate of the set with minimum minimax score.
[2]: §4.8 This is the sense in which the Schulze method minimizes the largest majority that has to be reversed when determining the winner.
On the other hand, Ranked Pairs minimizes the largest majority that has to be reversed to determine the order of finish.
[7] In 2011, Schulze published the method in the academic journal Social Choice and Welfare.
[2] The Schulze method is used by the city of Silla, Spain for all referendums.
[8][9][10][11] It is also used by the cities of Turin and San Donà di Piave in Italy and by the London Borough of Southwark through their use of the WeGovNow platform, which in turn uses the LiquidFeedback decision tool.
[15] The Boise, Idaho chapter of the Democratic Socialists of America in February chose this method for their first special election held in March 2018.
[16] It is used by the Institute of Electrical and Electronics Engineers, by the Association for Computing Machinery, and by USENIX[citation needed] through their use of the HotCRP decision tool.
