# 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.