References#

Academic papers underlying PrefGraph’s implementation, organized by the methods they enable. Chapter numbers throughout the documentation refer to Chambers & Echenique (2016).

  • Chambers, C. P., & Echenique, F. (2016). Revealed Preference Theory. Cambridge University Press.

Consistency Testing#

GARP and HARP test whether budget choices are rationalizable: GARP via SCC + Floyd-Warshall on the expenditure graph (Varian 1982); HARP for homothetic preferences via log-space Floyd-Warshall (Varian 1983); Production GARP on profit graphs (Varian 1984). On discrete menus, SARP and Congruence use Floyd-Warshall on the item graph (Richter 1966).

  • Varian, H. R. (1982). The nonparametric approach to demand analysis. Econometrica, 50(4), 945–973. [DOI]

  • Varian, H. R. (1983). Non-parametric tests of consumer behaviour. Review of Economic Studies, 50(1), 99–110. [DOI]

  • Varian, H. R. (1984). The nonparametric approach to production analysis. Econometrica, 52(3), 579–597. [DOI]

  • Richter, M. K. (1966). Revealed preference theory. Econometrica, 34(3), 635–645. [DOI]

Efficiency Measures#

CCEI and utility recovery use Afriat’s LP (Afriat 1967). VEI solves a per-observation LP (Varian 1990). MPI uses Karp’s max-mean-weight cycle algorithm (Echenique, Lee & Shum 2011). The Houtman-Maks index finds the maximum consistent subset via greedy FVS (Houtman & Maks 1985). The Swaps Index uses a greedy Feedback Arc Set (Apesteguia & Ballester 2015).

  • Afriat, S. N. (1967). The construction of utility functions from expenditure data. International Economic Review, 8(1), 67–77. [DOI]

  • Varian, H. R. (1990). Goodness-of-fit in optimizing models. Journal of Econometrics, 46(1–2), 125–140. [DOI]

  • Echenique, F., Lee, S., & Shum, M. (2011). The money pump as a measure of revealed preference violations. Journal of Political Economy, 119(6), 1201–1223. [DOI]

  • Houtman, M., & Maks, J. A. H. (1985). Determining all maximal data subsets consistent with revealed preference. Kwantitatieve Methoden, 19, 89–104.

  • Apesteguia, J., & Ballester, M. A. (2015). A measure of rationality and welfare. Journal of Political Economy, 123(6), 1278–1310. [DOI]

Stochastic & Attention#

The RUM LP tests whether choice frequencies are consistent with any random utility model via an LP over K! orderings (Block & Marschak 1960; Kitamura & Stoye 2018). WARP-LA models limited attention via consideration sets: WARP violations are explained by consumers not seeing all options (Masatlioglu, Nakajima & Ozbay 2012). Regularity and IIA testing follows Debreu (1960).

  • Block, H. D., & Marschak, J. (1960). Random orderings and stochastic theories of responses. In I. Olkin et al. (Eds.), Contributions to Probability and Statistics (pp. 97–132). Stanford University Press.

  • Kitamura, Y., & Stoye, J. (2018). Nonparametric analysis of random utility models. Econometrica, 86(6), 1883–1909. [DOI]

  • Masatlioglu, Y., Nakajima, D., & Ozbay, E. Y. (2012). Revealed attention. American Economic Review, 102(5), 2183–2205. [DOI]

  • Debreu, G. (1960). Review of R. D. Luce, Individual Choice Behavior. American Economic Review, 50, 186–188.

Welfare & Extensions#

CV/EV welfare measures use expenditure function duality (Vartia 1983). GAPP tests consistency of preferences over price vectors rather than bundles (Deb, Kitamura, Quah & Stoye 2023). Intertemporal analysis recovers discount factor bounds via interval propagation (Echenique, Imai & Saito 2020).

  • Vartia, Y. O. (1983). Efficient methods of measuring welfare change and compensated income in terms of ordinary demand functions. Econometrica, 51(1), 79–98. [DOI]

  • Deb, R., Kitamura, Y., Quah, J. K. H., & Stoye, J. (2023). Revealed price preference: Theory and empirical analysis. Review of Economic Studies, 90(2), 707–743. [DOI]

  • Echenique, F., Imai, T., & Saito, K. (2020). Testable implications of models of intertemporal choice. American Economic Journal: Microeconomics, 12(4), 114–143. [DOI]

Algorithmic Methods#

The complexity and greedy algorithms for HM and VEI come from Smeulders et al. (2014). Exact HM computation via MILP runs in Rust using HiGHS (Demuynck & Rehbeck 2023). The GARP SCC decomposition follows Talla Nobibon et al. (2015). VEI exact computation follows Mononen (2023). Utility recovery via Bellman-Ford follows Shiozawa (2016).

  • Smeulders, B., Cherchye, L., De Rock, B., & Spieksma, F. C. R. (2014). Goodness-of-fit measures for revealed preference tests: Complexity results and algorithms. ACM Transactions on Economics and Computation, 2(1), Art. 3. [DOI]

  • Demuynck, T., & Rehbeck, J. (2023). Computing revealed preference goodness-of-fit measures with integer programming. Economic Theory, 75, 1101–1130. [DOI]

  • Talla Nobibon, F., Smeulders, B., & Spieksma, F. C. R. (2015). A note on GARP testing in one pass. Journal of Optimization Theory and Applications, 166(3), 1080–1093. [DOI]

  • Mononen, L. (2023). Computing and comparing measures of rationality. Working paper.

  • Shiozawa, K. (2016). Revealed preference test and shortest path problem. Journal of Mathematical Economics, 67, 1–14. [DOI]

AI & Alignment Applications#

Revealed preference methods applied to LLM decision-making and AI alignment. Chen et al. (2023) tested GPT on GARP/CCEI budget tasks (PNAS). Wen et al. (2025) found that specialization increases GARP violations. Ge, Procaccia, Halpern et al. (2024) axiomatize alignment from human feedback using welfare economics. Zhi-Xuan & Carroll (2024) challenge the preference-maximization framing. Gu & Han (2025) measure divergence between stated and revealed preferences in LLMs. GARP-EFM (2026) uses revealed preference structure to improve foundation models.

  • Chen, Y., Liu, T.-X., Shan, Y., & Zhong, S. (2023). The emergence of economic rationality of GPT. Proceedings of the National Academy of Sciences, 120(51), e2316205120. [DOI]

  • Wen, S. (2025). Economic rationality under specialization: Evidence of decision bias in AI agents. Working paper.

  • Ge, L., Procaccia, A. D., Vorobeychik, Y., Halpern, D., & Micha, E. (2024). Axioms for AI alignment from human feedback. arXiv:2405.12164. [arXiv]

  • Zhi-Xuan, T., Carroll, M., Franklin, M., & Ashton, H. (2024). Beyond preferences in AI alignment. Philosophical Studies. [DOI]

  • Gu, Z., & Han, S. (2025). Alignment revisited: Are large language models consistent in stated and revealed preferences? Working paper.

  • GARP-EFM (2026). GARP-EFM: Improving foundation models with revealed preference structure. arXiv.