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This research investigates the maximum cardinality of Condorcet domains and their extension numbers, focusing on exact values and bounds.

August 12, 2026Open Access

Deletion Shadows, Kemeny Edges, and One-Alternative Extensions of Condorcet Domains

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KFK. FathiIslamic Azad University North Tehran Branch

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Implication

Exact searches and structural analysis reveal bounds on deletion and extension numbers in Condorcet domains, suggesting new implications for parent constraints.

Key Points

This research investigates the maximum cardinality of Condorcet domains and their extension numbers, focusing on exact values and bounds.
Conducted exact searches for alternative extension numbers and classified equality cases.
Utilized complete assigned-rule enumerations to analyze extensions and shells of parents.
Developed a full nine-coordinate deletion-capacity integer program and verified its rational dual.
Extended the maximum record of alternatives from eight to nine with specific counts of orders.
Established that a proposed bound on extension number is false, indicating larger parent sizes may be necessary.
Proved that deletion shadows and average rates have contradicting bounds, with a new direction-focused conjecture on deletion.

Cite This Study

K. Fathi (2026) studied this question.

synapsesocial.com/papers/6a7c3d1906a85aed514b7c73 https://doi.org/10.5281/zenodo.21879935

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Implication

Exact searches and structural analysis reveal bounds on deletion and extension numbers in Condorcet domains, suggesting new implications for parent constraints.

Deletion Shadows, Kemeny Edges, and One-Alternative Extensions of Condorcet Domains

Discussion

Member takes

Implication

Key Points

Cite This Study

Deletion Shadows, Kemeny Edges, and One-Alternative Extensions of Condorcet Domains

Discussion

Member takes

Implication

Key Points

Cite This Study

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