Mathematical conditions exist that are both necessary and sufficient for the existence of a utility function

the verdict

SUPPORTED

the evidence backs this

Recorded sources

3 sources for · 0 against

Counts group repeated records of the same source within each side. They do not measure evidence strength or source independence.

Mathematical conditions, such as specific axioms of revealed preference or topological properties, exist and are well-documented as both necessary and sufficient for the existence of utility functions.

The analysis

The retrieved literature includes multiple theoretical papers in mathematical economics and decision theory (e.g., Papers 0, 1, and 8) that explicitly derive and prove necessary and sufficient conditions for various utility representations.

Evidence for · 3

On continuous multi-utility representations of semi-closed and closed preorders

Recorded source metadata

G. Bosi, G. Herden. On continuous multi-utility representations of semi-closed and closed preorders. 2016. https://doi.org/10.1016/j.mathsocsci.2015.10.006

Paper 0 provides topological necessary and sufficient conditions for continuous multi-utility representations.

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More for · 2

Archimedean Choice Functions: an Axiomatic Foundation for Imprecise Decision Making

Recorded source metadata

Jasper De Bock. Archimedean Choice Functions: an Axiomatic Foundation for Imprecise Decision Making. 2020. https://doi.org/10.1007/978-3-030-50143-3_15

Paper 1 establishes axiomatic necessary and sufficient conditions for choice functions yielding utility representations in decision making.

Source citation format

Testing theories of financial decision making.

Recorded source metadata

Chambers CP, Echenique F, Saito K. Testing theories of financial decision making.. 2016. https://doi.org/10.1073/pnas.1517760113

Paper 8 characterizes specific utility models by identifying revealed preference axioms that are necessary and sufficient for their representation.

Source citation format

The paper trail · every fact has a biography

first checked01 Aug 2026

judged → SUPPORTED · 8401 Aug 2026

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