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The aim is to isolate and formalize proof mechanisms behind impossibility theorems in economics, focusing on aggregation and representation issues.

April 7, 2026Open Access

Anchored Controllability and a Three-Sector Obstruction Calculus for Impossibility Theorems in Aggregation and Representation

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The aim is to isolate and formalize proof mechanisms behind impossibility theorems in economics, focusing on aggregation and representation issues.
Isolated core theorem evaluating conditions for mixed 2-cycles.
Utilized differential refinements and transversal kernels for localization.
Identified three canonical obstruction sectors impacting representability.
Applied various mathematical theorems for establishing impossibility and representation dimensions.
Formalized anchored controllability as a mechanism causing impossibility.
Demonstrated the collapse sector leads to observational indistinctness in decision-making.
Established a closed-graph sufficiency theorem linking closed partial orders to scalar representation.
Provided six application verifications of the established obstructions.

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Formal analysis demonstrates impossibility theorems in aggregation and representation, illustrating critical economic implications.

Kevin Fathi (2026) studied this question.

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