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Da Silva, S.; Bonini, P. Revealed Preference and Order Representation. Encyclopedia. Available online: https://encyclopedia.pub/entry/59868 (accessed on 24 July 2026).
Da Silva S, Bonini P. Revealed Preference and Order Representation. Encyclopedia. Available at: https://encyclopedia.pub/entry/59868. Accessed July 24, 2026.
Da Silva, Sergio, Patricia Bonini. "Revealed Preference and Order Representation" Encyclopedia, https://encyclopedia.pub/entry/59868 (accessed July 24, 2026).
Da Silva, S., & Bonini, P. (2026, July 22). Revealed Preference and Order Representation. In Encyclopedia. https://encyclopedia.pub/entry/59868
Da Silva, Sergio and Patricia Bonini. "Revealed Preference and Order Representation." Encyclopedia. Web. 22 July, 2026.
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Revealed preference is an approach in consumer theory that infers preferences from observed choices rather than treating preferences or utility as directly given. If a consumer chooses one bundle when another bundle is also affordable, the chosen bundle is said to be revealed preferred to the alternative. The theory asks under what conditions such observed choices can be rationalized by a preference relation or a utility function. Observed choices may satisfy local consistency by avoiding direct reversals while still failing to support a single complete and transitive ordering. Stronger acyclicity conditions can restore rationalizability, although finite choice data may still leave the underlying preference ordering underdetermined rather than uniquely identified.
revealed preference
rationalizability
WARP
SARP
GARP
Afriat’s theorem
integrability
underdetermination
Revealed preference theory examines the conditions under which observed choices can be rationalized by a preference relation or a utility function. Central concepts include the weak, strong, and generalized axioms of revealed preference; rationalizability; integrability; recoverability; and the finite-data results associated with Afriat’s theorem and its extensions.
Consumer theory may be developed either from primitive preferences or from observed choice behavior. In the preference-first approach, one begins with a complete and transitive preference relation and then studies utility representation and demand [1][2]. In the revealed-preference approach, one begins with observed choices and derives behavioral consistency conditions from them [3][4][5][6]. This entry surveys the main concepts, historical developments, and applications of revealed preference theory, with particular attention to the distinctions between local consistency, global acyclicity, finite-data rationalization, and underdetermination.
A useful distinction in the literature is among three cases. First, there is local consistency, where direct reversals are absent. Second, there is global coherence, where all revealed comparisons fit a single transitive ordering. Third, there is underdetermination, where such an ordering exists but is not uniquely pinned down by the data. Weak consistency addresses only the first case. Rationalizability requires the second. Finite-data results often deliver the third.
Figure 1 summarizes the main conceptual distinctions discussed in this entry. It shows why weak revealed-preference consistency is insufficient for global coherence, why the issue becomes more salient with three or more goods, and how stronger acyclicity conditions and finite-data results clarify the distinction between rationalizability and underdetermination.
Figure 1. Main conceptual distinctions in revealed preference theory: the preference-first and revealed-preference routes into consumer theory.
References
- Jehle, G.A.; Reny, P.J. Advanced Microeconomic Theory, 3rd ed.; Pearson: Harlow, UK, 2011.
- Samuelson, P.A. A note on the pure theory of consumer’s behaviour. Economica 1938, 5, 61–71.
- Samuelson, P.A. Consumption theory in terms of revealed preference. Economica 1948, 15, 243–253.
- Samuelson, P.A. The problem of integrability in utility theory. Economica 1950, 17, 355–385.
- Houthakker, H.S. Revealed preference and the utility function. Economica 1950, 17, 159–174.
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