# Schulze STV

Schulze STV is a PR method that reduces to Schulze in the single-winner case. It was designed by Markus Schulze to maximally resist Hylland free riding while still being proportional for Droop solid coalitions. It works by using a combination of a variant of STV and pairwise counting among winner sets, using the concept of a beatpath, to find the winner.[1]

## Notes

Schulze STV's party list case is D'Hondt. This is because between any two winner sets, the winner set that is closer to the D'Hondt result will win, since the party that gains a seat in the winner set closer to D'Hondt can split more votes among its candidates than the opposing party in the other winner set. Because of this, the D'Hondt winner set will have a beatpath to all other winner sets, but the same will not be true in reverse.

Schulze STV can be used to find a Smith set of winner sets, which any Condorcet method can be applied to to find the winner. This Smith set can be found by using the concept of the beat-or-tie path.

Some ideas for adapting non-Schulze cycle resolution methods to this Smith set:

• Condorcet-IRV hybrids: each voter's 1st choices are considered to be the winner set(s) that have the most of their most-preferred candidates in them, their 2nd choices are the winner set(s) with the second-most of their most-preferred candidates, etc.
• Condorcet-cardinal hybrid methods: One can either use a cardinal PR method with constraints applied in order to guaranteeably result in a Smith winner set, or can use a cardinal method to pick the Smith winner set that is overall most satisfying. See Algorithmic Asset Voting#The multi-winner Smith Set and Smith-efficient cycle resolution.

Schulze STV always picks a winner set from the Smith set, according to Schulze's own multi-winner generalization of the Smith criterion.

## References

1. Schulze, Markus (2019-11-16). "The Schulze Method of Voting". arXiv:1804.02973 [cs]: 268.