Schulze STV

Schulze STV is a draft ranked voting system designed to achieve proportional representation. It is a single transferable vote (STV) voting system. It was invented by Markus Schulze who developed the Schulze method for resolving ties under the Condorcet method. It is similar to CPO-STV in that it compares possible winning sets of candidate outcomes pairwise and selects the Condorcet winner. However, unlike CPO-STV, it only compares outcomes that differ by a single candidate. Comparing outcomes that differ by more than one candidate is accomplished by finding the strongest path.

The method is based on Schulze's investigations into vote management and free riding. When a voter prefers a very popular candidate, there is a strategic advantage to the voter if he gives his first choice to a candidate who is unlikely to win (Woodall free riding) or if he doesn't include his preferred candidate in his rankings at all (Hylland free riding). Schulze showed that vote management is merely party coordination of these free rider effects.

Schulze STV is resistant to both types of free riding. However, Hylland free riding is impossible to completely defend against. Schulze creates a criterion called "weak invulnerability to Hylland free riding". A method meets this criterion if it is invulnerable to Hylland free riding, except in cases where the Droop proportionality criterion would have to be violated. Schulze STV meets this criterion.

Each voter ranks the candidates in order of preference. For example:

Schulze STV performs comparisons on every possible outcome of the election in order to find the set of winners it considers the best. However, it only compares outcomes that differ by one winner directly. Outcomes that differ by more than one winner are compared by finding the strongest path between the two outcomes. The outcome, if one exists, that beats all other outcomes pairwise is declared the winning outcome. Otherwise, a Condorcet completion method is required to break the tie.

When two outcomes are compared one against another a special method is used to give each a score and so determine which of the two is the winner.

Assuming that there are S seats to be filled, the two outcomes are considered to be (A₁,A₂,...,A_S) and (A₂,...,A_S,B).

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