Schwartz set

SchwartzSchwartz sets
In voting systems, the Schwartz set is the union of all Schwartz set components.wikipedia
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Condorcet method

Condorcet votingCondorcet methodsCondorcet

Smith set

Smith criterionTop cycle
The Schwartz set, known as the Generalized Optimal-Choice Axiom or GOCHA, is closely related to and is always a subset of the Smith set.

Schulze method

SchulzeCloneproof Schwartz Sequential Droppingmodified minimax
The Schulze method always chooses a winner from the Schwartz set.

Electoral system

multi-membervoting systemvoting systems

Union (set theory)

unionset unionunions

Political science

political scientistPolitical Sciencespolitical analyst
The Schwartz set is named for political scientist Thomas Schwartz.

Disjoint sets

disjointpairwise disjointdisjoint set

Condorcet criterion

Condorcet winnerCondorcetCondorcet "beats-all" winner

Subset

supersetproper subsetsubsets

Floyd–Warshall algorithm

Warshall's algorithmFloyd algorithmFloyd-Warshall
The Schwartz set can be calculated with the Floyd–Warshall algorithm in time Θ(n 3 ) or with a version of Kosaraju's algorithm in time Θ(n 2 ).

Big O notation

Obig-O notationlittle-o notation
The Schwartz set can be calculated with the Floyd–Warshall algorithm in time Θ(n 3 ) or with a version of Kosaraju's algorithm in time Θ(n 2 ).

Kosaraju's algorithm

The Schwartz set can be calculated with the Floyd–Warshall algorithm in time Θ(n 3 ) or with a version of Kosaraju's algorithm in time Θ(n 2 ).

Preorder

preordered setpreordered setsquasiorder

Partially ordered set

partial orderposetpartially ordered

Tideman alternative method

These methods are Smith- and Schwartz-efficient, respectively, and thus are Condorcet methods.

Instant-runoff voting

alternative votepreferential votinginstant run-off voting
The Tideman alternative method avoids this by first eliminating all candidates not in the Smith set or Schwartz set, then performing exactly one round of IRV, repeating this process until a Condorcet candidate appears.

Participatory budgeting algorithm

The algorithm uses Schwartz sets.

Kemeny–Young method

Kemeny-Young methodKemeny-YoungCondorcet–Kemeny

Smith criterion

Smith
The Smith set and Schwartz set are sometimes confused in the literature.