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Smith set: The Smith criterion, Properties & Relation to other tournament sets

The Smith set, sometimes called the top-cycle generalizes the idea of a Condorcet winner to cases where no such winner exists. It does so by allowing cycles of candidates to be treated jointly, as if they were a single Condorcet winner. Voting systems that always elect a candidate from the Smith set pass the Smith criterion. The Smith set and Smith…

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Smith set topic overview

The analysis highlights The Smith criterion, Properties and Relation to other tournament sets as prominent areas in the source structure around Smith set.

Related topics
25
Source areas
6
Connected nodes
31
Extracted relationships
111
Concept neighborhoods
23
Bridge connections
31

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

The Smith criterion · 11 topics
Properties · 5 topics
Overview · 4 topics
Computing the Smith set · 2 topics
Relation to other tournament sets · 2 topics
Definition · 1 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

Definition

Properties

The Smith criterion

Relation to other tournament sets

Computing the Smith set

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

How Smith set connects Entity context

The extracted context around Smith set shows recurring relationship patterns in the source. For example, Smith set → Aggregation, Allocation, Applied Mathematics, Benjamin, BF00132454, But Smith, Collective Choice, Columbia University Press, Condorcet Criterion, Condorcet Social Choice Functions, Conflict Resolution, Deb, Decision, Discusses, Econometrica, Economic Theory, Fishburn, Four Condorcet-Hare Hybrid Methods, GETCHA, Gives Another extracted example is Smith set → Another, Condorcet, For, Minimax, Moreover, Nanson's, Schulze's, Smith, Smith//Minimax, The Smith, Tideman. Use these groups to spot repeated connection types before inspecting the individual relationships.

Smith set

Top relations

related to Further reading · 59
Smith set → Aggregation, Allocation, Applied Mathematics, Benjamin, BF00132454, But Smith, Collective Choice, Columbia University Press, Condorcet Criterion, Condorcet Social Choice Functions, Conflict Resolution, Deb, Decision, Discusses, Econometrica, Economic Theory, Fishburn, Four Condorcet-Hare Hybrid Methods, GETCHA, Gives
has method · 11
Smith set → Another, Condorcet, For, Minimax, Moreover, Nanson's, Schulze's, Smith, Smith//Minimax, The Smith, Tideman
related to Other criteria · 7
Smith set → Any, Condorcet, Conversely, It, MMC, Mutual, Smith
related to Properties · 7
Smith set → Condorcet, Condorcet's, If, It, Smith, The Condorcet, The Smith
related to Relation to other tournament sets · 7
Smith set → Banks, Bipartisan, Copeland, It, Landau, Smith, The Smith
related to Strict top-cycle (Schwartz set) · 5
Smith set → Formally, Schwartz, Smith, The Schwartz, The Smith
related to The Smith criterion · 5
Smith set → Condorcet, Smith, Smith-efficient, The Smith, Though
related to Computing the Smith set · 4
Smith set → Floyd, Kosaraju's, The Smith, Warshall
is a · 2
Smith set → smallest non-empty dominating set, subset of the MMC set
related to Definition · 2
Smith set → Alternatively, The Smith

Important terminology

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

set smith candidates criterion candidate condorcet schwartz dominating also copeland choice winner score doi methods smallest defeats majority method cells

Smith set relationships Subject–Predicate–Object triples

TTTA extracted 111 structured relationships around Smith set. Examples in this analysis include Smith set → is a → smallest non-empty dominating set and Smith set → is a → subset of the MMC set. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Smith setis asmallest non-empty dominating set0.90text
Smith setis asubset of the MMC set0.90text
Smith sethas methodThe Smith0.60section
Smith sethas methodSchulze's0.60section
Smith sethas methodNanson's0.60section
Smith sethas methodMoreover0.60section
Smith sethas methodSmith0.60section
Smith sethas methodFor0.60section
Smith sethas methodSmith//Minimax0.60section
Smith sethas methodMinimax0.60section
Smith sethas methodAnother0.60section
Smith sethas methodTideman0.60section

Related concept clusters Concept neighborhoods

The concept neighborhoods around Smith set bring nearby vocabulary together. In this analysis, examples include Smith, Criterion and Also. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Smith set
    • Smith
    • Criterion
    • Also
    • Candidate
    • Method
    • Condorcet
    • Candidates
    • Voting
    • Methods
    • Smallest
    • Defeats
    • Outside
  • smith set
    • Smith
    • Criterion
    • Candidate
    • Candidates
    • Also
    • Schwartz
    • Method
    • Condorcet
    • Dominating
    • Voting
    • Smallest
    • Methods
  • john h. smith
    • Criterion
    • Also
    • Candidate
    • Method
    • Candidates
    • Voting
    • Methods
    • Smallest
    • Outside
    • Majority
    • Winner
    • Schwartz
  • landau set
    • Smith
    • Candidate
    • Criterion
    • Candidates
    • Schwartz
    • Condorcet
    • Dominating
    • Smallest
    • Also
    • Defeats
    • Defined
    • Pairwise
  • voting system criterion
    • Also
    • Smith
    • Method
    • Methods
    • Always
    • Criterion
    • Voting
    • Set
    • Majority
    • Outside
    • Candidate
    • Dominating
  • condorcet criterion
    • Winner
    • Criterion
    • Also
    • Smith
    • Method
    • Methods
    • Voting
    • Set
    • Majority
    • Outside
    • Candidate
    • Dominating
  • condorcet loser criterion
    • Winner
    • Criterion
    • Also
    • Smith
    • Method
    • Methods
    • Voting
    • Set
    • Majority
    • Outside
    • Candidate
    • Dominating
  • copeland set
    • Smith
    • Score
    • Candidate
    • Criterion
    • Candidates
    • First
    • Schwartz
    • Condorcet
    • Defeats
    • Dominating
    • Smallest
    • Also

Connections between topic areas Semantic bridges

For Smith set, one of the stronger structural bridges in this analysis connects Smith set with The Smith criterion. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
Smith setThe Smith criterion · splits 20 ⟂ 12
Smith setProperties · splits 26 ⟂ 6
Smith setOverview · splits 27 ⟂ 5
Smith setRelation to other tournament sets · splits 29 ⟂ 3
Smith setComputing the Smith set · splits 29 ⟂ 3

Map overview Semantic statistics

Smith set

Nodes32
Edges31
Triples111
Avg. degree1.94
Density0.0625
Components1

Source & methodology

TTTA analyzes the structure around Smith set to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as The Smith criterion, Properties & Relation to other tournament sets, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Smith set · EN edition · Analysis: TopicsToTalkAbout

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