Representation of a preference ordering by a numerical function¶
Debreu, G. (1954). Representation of a preference ordering by a numerical function. Decision Processes.
Cited by¶
3 citations across 3 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Indifference Curves
- T5 — Topological Smooth-Convexity Assumption: Standard indifference curves assume continuous, differentiable preferences with convex level sets (diminishing MRS), but the axiomatic foundations (Debreu 1954)
This sourceFoundational representation theorem: a complete, transitive, continuous preference relation on a suitable space admits a continuous real-valued utility representation; establishes that utility is one (non-unique) representation of an underlying ordering, not the primitive itself.
- T5 — Topological Smooth-Convexity Assumption: Standard indifference curves assume continuous, differentiable preferences with convex level sets (diminishing MRS), but the axiomatic foundations (Debreu 1954)
- Order
- utility representation theorems (when can an order be represented by a real-valued function — Debreu's (1954) conditions of continuity and separability give the canonical answer)
This sourceFoundational representation theorem: a complete, transitive, continuous preference relation on a suitable space admits a continuous real-valued utility representation; establishes that utility is one (non-unique) representation of an underlying ordering, not the primitive itself.
- utility representation theorems (when can an order be represented by a real-valued function — Debreu's (1954) conditions of continuity and separability give the canonical answer)
- Preference
- Utility functions, rankings, revealed choices, policy priorities, qualitative value orderings, and learned reward signals are all implementations of the same ordering relation; the relation is the prime, the implementation is local technology — a substrate range that runs from Debreu's (1954) representation theorem for continuous preference orderings to Christiano et al.'s (2017) deep-RL reward models fit from pairwise human comparisons.
This sourceFoundational representation theorem: a complete, transitive, continuous preference relation on a suitable space admits a continuous real-valued utility representation; establishes that utility is one (non-unique) representation of an underlying ordering, not the primitive itself.
Supported in partVerified against the work's full text
Debreu (1954) is the representation-theorem endpoint the sentence names: its title states a preference ordering is represented by a numerical function, but only a table-of-contents page was fetched.
“Completing a RightsLink (open access) transaction > Representation of a preference ordering by a numerical function Mathematical Economics Twenty Papers of Gerard Debreu”
- Utility functions, rankings, revealed choices, policy priorities, qualitative value orderings, and learned reward signals are all implementations of the same ordering relation; the relation is the prime, the implementation is local technology — a substrate range that runs from Debreu's (1954) representation theorem for continuous preference orderings to Christiano et al.'s (2017) deep-RL reward models fit from pairwise human comparisons.
Verification¶
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