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.