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This research investigates the relationship between spatial models and Condorcet domains, specifically how large a Condorcet domain can be contained within fixed spatial models.

July 24, 2026Open Access

Condorcet Domains in Spatial Models

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KFK. FathiIslamic Azad University North Tehran Branch

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Implication

Randomized trial examines spatial models' limits on Condorcet domains, suggesting distinct restrictions on coherence.

Key Points

This research investigates the relationship between spatial models and Condorcet domains, specifically how large a Condorcet domain can be contained within fixed spatial models.
Utilized dimensional analysis to assess Condorcet domain sizes in low-dimensional models with n alternatives.
Defined and bounded spatial dimensions using pair-comparison shattering techniques.
Employed exact arithmetic certificates for computer-assisted claims.
Established that the maximum Condorcet domain for fixed dimension grows as Θ_d(n^{2d}), while unrestricted domains grow exponentially.
Identified specific upper bounds for small cases, providing exact values for n = 3, 4, 5 alternatives.
Conjectured that linear dimension is necessary for families of exponential size.

Cite This Study

K. Fathi (2026) studied this question.

synapsesocial.com/papers/6a630201395161722cd166ca https://doi.org/10.5281/zenodo.21500115

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Condorcet Domains in Spatial Models

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Implication

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Cite This Study

Condorcet Domains in Spatial Models

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Member takes

Implication

Key Points

Cite This Study

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