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Smith set

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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The Smith criterion, Properties & Relation to other tournament sets

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Overview

Definition

Properties

The Smith criterion

Relation to other tournament sets

Computing the Smith set

Advanced semantic analysis

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Map overview Semantic statistics

Number of nodes, edges, triples, density and central hubs. Use it to gauge the size and connectivity of the map.

Smith set

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

How this topic connects Entity context

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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 Word statistics

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Important terminology

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

Entity relationships Subject–Predicate–Object triples

Extracted RDF-like relationships with confidence and source. The table includes structured facts and lower-confidence contextual relations.
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

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