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the claim
Mathematical conditions exist that are both necessary and sufficient for the existence of a utility function
the verdict
SUPPORTED
the evidence backs this
confidence 84/100

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.

Evidence for · 3
On continuous multi-utility representations of semi-closed and closed preorders
2016 · cited by 24
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
2020 · cited by 13
Paper 1 establishes axiomatic necessary and sufficient conditions for choice functions yielding utility representations in decision making.
Testing theories of financial decision making.
2016 · cited by 3
Paper 8 characterizes specific utility models by identifying revealed preference axioms that are necessary and sufficient for their representation.
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first checked01 Aug 2026
judged → SUPPORTED · 8401 Aug 2026
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