What question did this study set out to answer?

The aim is to explore the maximum cardinality of Condorcet domains and the properties of their extensions and deletions.

August 12, 2026Open Access

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

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Authors

KFK. FathiIslamic Azad University North Tehran Branch

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Implication

This research demonstrates the extension number's behavior in Condorcet domains and explores structural bounds, suggesting implications for theoretical understanding.

Key Points

The aim is to explore the maximum cardinality of Condorcet domains and the properties of their extensions and deletions.
Exact searches to determine the extension number for eight and nine alternatives.
Enumeration of assigned rules to analyze maximum neighborhood behaviors.
Development of a complete nine-coordinate deletion-capacity integer program.
The extension number of the eight-alternative maximum is confirmed as 492.
Counterexamples challenge existing bounds, showing deletions below expected values.
A new average inequality is established, reinforcing conjectures about deletion behavior.

Cite This Study

K. Fathi (2026) studied this question.

synapsesocial.com/papers/6a7c209506a85aed514b7653 https://doi.org/10.5281/zenodo.21879466

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Implication

This research demonstrates the extension number's behavior in Condorcet domains and explores structural bounds, suggesting implications for theoretical understanding.

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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