Pith. sign in

REVIEW 2 major objections 6 minor 1 cited by

Ever since Ellsberg

T0 review · 2 major / 6 minor · reviewed 2026-07-13 · grok-4.5

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Choices under uncertainty match risk in consistency with utility and expected utility, yet leave more room for ambiguity models that risk does not.

desk verdict Clean nonparametric risk-vs-uncertainty comparison of the full axiom hierarchy; the multiple-prior FOSD layer is the real addition and the evidence for greater non-EUT scope under uncertainty holds up. read the letter →

arxiv 2607.09355 v1 pith:Q74NM5KK submitted 2026-07-10 econ.GN econ.THq-fin.EC

Aluma Dembo , Shachar Kariv , Matthew Polisson , John K.-H. Quah This is my paper · ORCID
classification econ.GNecon.THq-fin.EC
keywords revealedpreferencerationalityriskuncertaintyambiguitymultiplepriorssubjectiveexpectedutilityexperiment
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper asks whether people choose as consistently under uncertainty (unknown probabilities) as they do under risk (known probabilities), and where any extra inconsistency comes from. Using rich individual portfolio data with three states of nature—one with a known probability and two with unknown probabilities that sum to a known total—it applies a nested battery of revealed-preference tests. Basic utility maximization, first-order stochastic dominance under multiple priors, dominance under a single uniform prior, and subjective expected utility form a chain of increasingly strict requirements. The central finding is that the distributions of consistency scores for utility maximization and for expected-utility maximization are statistically indistinguishable between uncertainty and an otherwise identical risk experiment. What differs is a middle layer: under uncertainty, allowing multiple priors for the unknown states substantially raises consistency relative to forcing a single uniform prior. That wedge is the empirical space for canonical ambiguity models (rank-dependent and recursive expected utility). The size and source of the wedge vary sharply across individuals, so no single model fits everyone.

What carries the argument

A nested chain of critical cost-efficiency (CCEI-type) scores: e* (basic rationalizability via GARP), ãe** (FOSD-rationalizability under multiple priors, accommodating ambiguity), e** (FOSD under the uniform prior), and e*** (subjective EUT). Consecutive gaps locate, for each subject, whether departures from EUT stem from ordering failures, FOSD failures even multiple priors cannot absorb, or genuine ambiguity-sensitive behavior.

What would settle it

An otherwise identical experiment that pays every round (or uses a non-random incentive that blocks hedging) and checks whether the multiple-prior versus uniform-prior wedge shrinks or disappears; if the wedge vanishes under full payment, the ambiguity reading is compromised by the incentive protocol.

Watch

Extended reading notes

Core claim

Individual choices under uncertainty are as consistent with utility maximization and with expected-utility maximization as the same subjects’ choices under risk. The decisive difference is that FOSD-rationalizability under multiple priors substantially outperforms FOSD-rationalizability under the uniform prior under uncertainty, opening first-order empirical scope for non-EUT ambiguity models that have little scope under risk; absolute and relative consistency of EUT versus non-EUT models vary widely across subjects.

Load-bearing premise

That paying only one randomly selected round does not let subjects hedge ambiguity across the fifty sequential, heterogeneous budgets in a way that would artificially shrink measured ambiguity aversion.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 6 minor

Summary. The paper provides a comprehensive, nonparametric revealed-preference test of the full axiom hierarchy for subjective expected utility (EUT) under uncertainty, using the Ahn et al. (2014) three-state portfolio-choice data (N=154), and compares it to an otherwise identical risk experiment (Dembo et al. 2026, N=168). Nested CCEI-type scores—e* (GARP/rationalizability), ˜e** (FOSD under multiple priors), e** (FOSD under the uniform prior), and e*** (EUT under the uniform prior)—decompose departures from subjective EUT. The main claims are that the distributions of e* and e*** under uncertainty are statistically indistinguishable from those under risk, while the ˜e**–e** wedge under uncertainty creates greater empirical scope for multiple-prior non-EUT models (RDU/REU class) than exists under risk; absolute and relative consistency vary substantially across subjects. Supporting analyses include KS tests, subject-level difference-in-differences on half-sample draws, a check that the uniform prior approximately maximizes single-prior rationalizability, and a Bronars-style power simulation against unstructured error.

Significance. If the results hold, the paper supplies the first individual-level, nonparametric, full-axiom test of subjective EUT versus multiple-prior alternatives in a rich portfolio environment, and a clean risk–uncertainty comparison under matched designs. The nested CCEI hierarchy, the individual DiD procedure (1,000 half-samples of 25 observations), and the power simulation against simulated subjects with controlled e†† are genuine methodological strengths: they separate failures of ordering/monotonicity from residual room for ambiguity-sensitive models without fitting free parameters. The finding that basic rationalizability and EUT-rationalizability do not deteriorate under uncertainty, while multiple-prior FOSD opens a measurable wedge that risk does not, is of direct interest to theorists of ambiguity and to experimentalists designing tests of such models. The work is a natural companion to Dembo et al. (2026) and is well positioned for a top field or general-interest journal.

major comments (2)
  1. [Section 7.1, Table 1, Figure 3] The central claim that choices under uncertainty are “as consistent” with utility maximization and EUT as choices under risk rests on a between-subject comparison of two independent pools (Ahn et al. 2014 vs. Dembo et al. 2026). Section 7.1 reports KS non-rejection for e*, e**, and e*** (p ≈ 0.43/0.64/0.23) and nearly identical WARP/GARP patterns in Table 1, which is reassuring. However, the manuscript does not report or discuss demographic or recruitment comparability of the two pools (labs, years, subject composition). Because the “as consistent as” claim is load-bearing for the paper’s contribution relative to the risk companion, a short subsection or appendix table documenting pool similarity (or acknowledging residual confounds) would strengthen the inference. Without that, a skeptical reader can still attribute distributional equality partly to sample composition rather than to the
  2. [Abstract; Section 5.1.4; Section 8] Section 5.1.4 correctly notes that REU (and RDU) are nested between EUT-rationalizability and FOSD-rationalizability under multiple priors, and that REU is not nonparametrically characterizable given cardinal indeterminacy of the ambiguity–scale product. The abstract and conclusion nonetheless speak of “greater empirical scope for non-EUT models” under uncertainty. That claim is accurate at the class level (˜e** bounds the entire multiple-prior class), but the paper should state more sharply in the abstract/introduction that the wedge does not identify which multiple-prior specification (kinked RDU vs. smooth REU, or generalized kinked) is responsible, and that separating them is left for future work. As written, a casual reader may over-read the result as validating specific ambiguity models rather than the multiple-prior FOSD layer.
minor comments (6)
  1. [Figure 1; Figures 3–4] Figure 1 and Figures 3–4 use survival functions with 95% CI braces; the braces are helpful but visually dense near the upper tail. Consider a companion table of selected percentiles (e.g., 25/50/75/90) for e*, ˜e**, e**, e*** under uncertainty and risk to make the layered gaps easier to cite.
  2. [Section 3, footnote 6] Footnote 6 on random incentives and hedging is careful and cites Baillon, Halevy, and Li (2022a,b). Given how central this design premise is to measured ambiguity aversion, a one-paragraph discussion in the main text of Section 3 (rather than only a long footnote) would improve accessibility for experimental readers.
  3. [Section 7.2, Figure 5] In Section 7.2, Figure 5 shows mean e***(π1) with CIs; the text states the same holds for e** and at the individual level but omits those figures “to economize on space.” A short online appendix figure for e**(π1) would make the “uniform prior is approximately optimal” claim fully transparent.
  4. [Throughout] Typographical/consistency: “Ahnet al.” appears without a space or non-breaking space before “et al.” in several places (e.g., early Introduction); standardize to “Ahn et al.” throughout. Also “Demboet al.” same issue.
  5. [Section 6] Section 6 illustrative subjects: the table of scores for IDs 703, 629, 921, 340, 407, 612 reports e** = e*** for all six; a brief sentence explaining why that equality holds for these particular patterns (near-equalization or corner behavior) would help readers who are new to the nested scores.
  6. [Front matter] JEL codes and keywords are fine; consider adding “revealed preference” more prominently if the journal’s keyword list allows, since that is the paper’s methodological core.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: nested CCEI scores are definitional by preference-class inclusion, but empirical gaps, KS tests, DiD, and power simulations are data-driven from independent observations.

full rationale

The paper applies standard Afriat/GARP/CCEI and GRID revealed-preference tests (extended from Polisson-Quah-Renou 2020 and the authors' companion risk paper) to the Ahn et al. (2014) portfolio data under uncertainty, and compares score distributions to an independent subject pool under risk. Nesting 1 ≥ e* ≥ ˜e** ≥ e** ≥ e*** follows immediately from the nested families of utility functions (well-behaved o FOSD-multiple-priors o FOSD-uniform o EUT-uniform); this is definitional bookkeeping, not a circular derivation of the central claim. The claim itself—comparable e*/e*** distributions across domains plus a larger ˜e**–e** wedge under uncertainty—is measured from the observed choices via nonparametric inequalities, Kolmogorov–Smirnov tests, subject-level difference-in-differences on subsamples, and a Bronars-style simulation of unstructured FOSD violations. No free parameters are fitted and then re-labeled as predictions; no uniqueness theorem is imported to forbid alternatives; self-citations supply the risk-experiment data and the computational method but do not force the comparative magnitudes. Residual design premises (random incentives, inability to separate RDU from REU) are acknowledged limitations, not circular reductions. Honest non-finding of circularity is therefore warranted.

Assumptions & free parameters 0 free parameters · 5 assumptions · 1 invented entities

The paper is nonparametric revealed-preference analysis of existing experimental data. It imports standard Afriat/GARP machinery, FOSD monotonicity, and the GRID method; the only paper-specific construct is the multiple-prior FOSD layer that accommodates the RDU/REU classes already in the literature. No free parameters are fitted to generate the central comparative claims.

assumptions (5)
  • standard math Afriat's theorem: a finite dataset is rationalizable by a continuous increasing utility iff it satisfies GARP
    Used throughout Section 5 to define e* and the nested efficiency indices.
  • domain assumption FOSD monotonicity under the objectively known probability structure (state 2 has probability 1/3, states 1 and 3 share 2/3)
    Defines ~e** (multiple-prior FOSD-rationalizability); Section 5.1.2.
  • domain assumption Symmetry of the rationalizing utility across the two uncertain states
    Imposed because the experiment treats states 1 and 3 symmetrically; Section 5.1.2.
  • domain assumption Uniform prior is the natural single-prior benchmark under the experimental design
    Adopted for e** and e***; Section 7.2 verifies it approximately maximizes single-prior scores.
  • standard math Nishimura-Ok-Quah (2017) strengthening of GARP for FOSD-rationalizability and Polisson-Quah-Renou (2020) GRID method for EUT-rationalizability
    Computational engines for the nested scores; Section 5.
invented entities (1)
  • FOSD-rationalizability under multiple priors (~e**) independent evidence
    purpose: Nonparametric upper bound on the entire class of multiple-prior models (RDU and REU) without committing to a functional form
    Defined in Section 5.1.2 as the new intermediate layer between basic rationalizability and uniform-prior FOSD; it is a definitional construct, not a new physical or preference object.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Ever since Ellsberg." pith.science (2026). https://pith.science/paper/Q74NM5KK

@misc{pith2026260709355,
  author       = {Pith},
  title        = {Pith review of: Ever since Ellsberg},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Q74NM5KK}},
  note         = {Machine review of arXiv:2607.09355}
}
read the original abstract

Ellsberg's famous paradox challenged Savage's subjective expected utility theory (EUT) -- which reduces uncertainty to risk -- by suggesting an aversion toward ambiguity. We provide a revealed preference test of the full set of axioms underpinning subjective EUT under uncertainty and compare it to an analogous test of objective EUT under risk. We find that individual choices are as consistent with utility maximization and expected utility maximization under uncertainty as they are under risk. Nevertheless, there is greater empirical scope for non-EUT models under uncertainty than under risk, and the absolute and relative consistency of EUT and non-EUT models vary considerably across subjects.

Figures

Figures reproduced from arXiv: 2607.09355 by the authors.

Figure 1
Figure 1. Distributions of Rationalizability Scores [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Subject Behavior Each panel shows all 50 choices for a single subject in terms of token shares, except for panel (c) which is in terms of budget shares. Each vertex of the unit simplex corresponds to a full allocation to one of the three securities. (a) ID 703 is consistent with infinite risk aversion; (b) ID 629 is consistent with risk neutrality; (c) ID 921 is consistent with the maximization of logarithmic von Ne… view at source ↗
Figure 3
Figure 3. Distributions of Rationalizability Scores (Uncertainty vs. Risk) [PITH_FULL_IMAGE:figures/full_fig_p024_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Distributions of FOSD-Rationalizability Scores (Uncertainty vs. Risk) [PITH_FULL_IMAGE:figures/full_fig_p025_4.png]
Figure 5
Figure 5. Figure 5: EUT-Rationalizability Scores under Single Priors [PITH_FULL_IMAGE:figures/full_fig_p026_5.png]
Figure 6
Figure 6. Figure 6: Individual-Level Rationalizability Scores [PITH_FULL_IMAGE:figures/full_fig_p028_6.png]
Figure 7
Figure 7. Figure 7: Differences-in-Differences in Individual-Level Rationalizability Scores [PITH_FULL_IMAGE:figures/full_fig_p029_7.png]
Figure 8
Figure 8. Figure 8: Power of Testing FOSD-Rationalizability The horizontal axis shows different score value bins for FOSD-rationalizability under the uniform prior (e ††). The vertical axis represents the gap between FOSD-rationalizability under multiple priors versus under the uniform pr…

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Revealed Rationality: Label-Free Evaluation and Regularization from Representation Theorems

    econ.TH 2026-08 conditional novelty 6.0 of 10

    Representation theorems from decision theory yield label-free, exhaustive rationality checks and continuous penalties for LLM behavior.

Reference graph

Works this paper leans on

175 extracted references · cited by 1 Pith paper

  1. [1]

    Ok , date-added =

    Hiroki Nishimura and Efe A. Ok , date-added =. Utility Representation of an Incomplete and Nontransitive Preference Relation , volume =. Journal of Economic Theory , pages =

  2. [2]

    Incomplete Preferences and Rational Intransitivity of Choice , volume =

    Michael Mandler , date-added =. Incomplete Preferences and Rational Intransitivity of Choice , volume =. Games and Economic Behavior , number =

  3. [3]

    Comparative Incompleteness: Measurement, Behavioral Manifestations and Elicitation , volume =

    Edi Karni and Marie-Louise Vier. Comparative Incompleteness: Measurement, Behavioral Manifestations and Elicitation , volume =. Journal of Economic Behavior and Organization , pages =

  4. [4]

    Ok , date-added =

    Kfir Eliaz and Efe A. Ok , date-added =. Indifference or Indecisiveness? Choice-Theoretic Foundations of Incomplete Preferences , volume =. Games and Economic Behavior , number =

  5. [5]

    Incomplete Preferences: Modeling, Representations, and Behavioral Implications , year =

    Edi Karni , date-added =. Incomplete Preferences: Modeling, Representations, and Behavioral Implications , year =

  6. [6]

    On the Representation of Incomplete Preferences under Uncertainty with Indecisiveness in Tastes and Beliefs , volume =

    Gil Riella , date-added =. On the Representation of Incomplete Preferences under Uncertainty with Indecisiveness in Tastes and Beliefs , volume =. Economic Theory , pages =

  7. [7]

    Subjective Expected Utility with Incomplete Preferences , volume =

    Tsogbadral Galaabaatar and Edi Karni , date-added =. Subjective Expected Utility with Incomplete Preferences , volume =. Econometrica , number =

  8. [8]

    Ok and Pietro Ortoleva and Gil Riella , date-added =

    Efe A. Ok and Pietro Ortoleva and Gil Riella , date-added =. Incomplete Preferences under Uncertainty: Indecisiveness in Beliefs versus Tastes , volume =. Econometrica , number =

Show all 175 references
  1. [9]

    Ok , date-added =

    Juan Dubra and Fabio Maccheroni and Efe A. Ok , date-added =. Expected Utility Theory without the Completeness Axiom , volume =. Journal of Economic Theory , number =

  2. [10]

    Regret Theory: A New Foundation , volume =

    Enrico Diecidue and Jeeva Somasundaram , date-added =. Regret Theory: A New Foundation , volume =. Journal of Economic Theory , number =

  3. [11]

    Skew-Symmetric Additive Representations of Preferences , volume =

    Yutaka Nakamura , date-added =. Skew-Symmetric Additive Representations of Preferences , volume =. Journal of Mathematical Economics , number =

  4. [12]

    Regret Theory with General Choice Sets , volume =

    John Quiggin , date-added =. Regret Theory with General Choice Sets , volume =. Journal of Risk and Uncertainty , number =

  5. [13]

    An Axiomatic Foundation for Regret Theory , volume =

    Robert Sugden , date-added =. An Axiomatic Foundation for Regret Theory , volume =. Journal of Economic Theory , number =

  6. [14]

    Fishburn , date-added =

    Peter C. Fishburn , date-added =. Non-transitive Measurable Utility for Decision under Uncertainty , volume =. Journal of Mathematical Economics , number =

  7. [15]

    Fishburn , date-added =

    Peter C. Fishburn , date-added =. SSB Utility Theory and Decision-Making under Uncertainty , volume =. Mathematical Social Sciences , number =

  8. [16]

    Randomize at Your Own Risk: On the Observability of Ambiguity Aversion , volume =

    Aur. Randomize at Your Own Risk: On the Observability of Ambiguity Aversion , volume =. Econometrica , number =

  9. [17]

    Experimental Elicitation of Ambiguity Attitude Using the Random Incentive System , volume =

    Aur\'elien Baillon and Yoram Halevy and Chen Li , date-added =. Experimental Elicitation of Ambiguity Attitude Using the Random Incentive System , volume =. Experimental Economics , pages =

  10. [18]

    Randomization and Ambiguity Aversion , volume =

    Shaowei Ke and Qi Zhang , date-added =. Randomization and Ambiguity Aversion , volume =. Econometrica , number =

  11. [19]

    Preferences for Flexibility and Randomization under Uncertainty , volume =

    Kota Saito , date-added =. Preferences for Flexibility and Randomization under Uncertainty , volume =. American Economic Review , number =

  12. [20]

    Chambers and Paul J

    Yaron Azrieli and Christopher P. Chambers and Paul J. Healy , date-added =. Incentives in Experiments: A Theoretical Analysis , volume =. Journal of Political Economy , number =

  13. [21]

    Abraham Wald's complete class theorem and Knightian uncertainty , volume =

    Christoph Kuzmics , date-added =. Abraham Wald's complete class theorem and Knightian uncertainty , volume =. Games and Economic Behavior , pages =

  14. [22]

    Unintended Hedging in Ambiguity Experiments , volume =

    J\"org Oechssler and Alex Roomets , date-added =. Unintended Hedging in Ambiguity Experiments , volume =. Economics Letters , number =

  15. [23]

    Randomization Devices and the Elicitation of Ambiguity-Averse Preferences , volume =

    Sophie Bade , date-added =. Randomization Devices and the Elicitation of Ambiguity-Averse Preferences , volume =. Journal of Economic Theory , number =

  16. [24]

    Wakker , date-added =

    Aur\'elien Baillon and Zhenxing Huang and Asli Selim and Peter P. Wakker , date-added =. Measuring Ambiguity Attitudes for All (Natural) Events , volume =. Econometrica , number =

  17. [25]

    Dimmock and Roy Kouwenberg and Peter P

    Stephen G. Dimmock and Roy Kouwenberg and Peter P. Wakker , date-added =. Ambiguity Attitudes in a Large Representative Sample , volume =. Management Science , number =

  18. [26]

    Hey , date-added =

    Anna Conte and John D. Hey , date-added =. Assessing Multiple Prior Models of Behaviour under Ambiguity , volume =. Journal of Risk and Uncertainty , number =

  19. [27]

    Hey and Gianna Lotito and Anna Maffioletti , date-added =

    John D. Hey and Gianna Lotito and Anna Maffioletti , date-added =. The Descriptive and Predictive Adequacy of Theories of Decision Making under Uncertainty/Ambiguity , volume =. Journal of Risk and Uncertainty , pages =

  20. [28]

    Trautmann and Gijs van de Kuilen , booktitle =

    Stefan T. Trautmann and Gijs van de Kuilen , booktitle =. Ambiguity Attitudes , year =

  21. [29]

    The Ellsberg Paradox and Risk Aversion: An Anticipated Utility Approach , volume =

    Uzi Segal , date-added =. The Ellsberg Paradox and Risk Aversion: An Anticipated Utility Approach , volume =. International Economic Review , number =

  22. [30]

    Objective Imprecise Probabilistic Information, Second Order Beliefs and Ambiguity Aversion: An Axiomatization , year =

    Rapha\"el Giraud , booktitle =. Objective Imprecise Probabilistic Information, Second Order Beliefs and Ambiguity Aversion: An Axiomatization , year =

  23. [31]

    Ahn , date-added =

    David S. Ahn , date-added =. Ambiguity Without a State Space , volume =. Review of Economic Studies , number =

  24. [32]

    A Bayesian Approach to Uncertainty Aversion , volume =

    Yoram Halevy and Vincent Feltkamp , date-added =. A Bayesian Approach to Uncertainty Aversion , volume =. Review of Economic Studies , number =

  25. [33]

    Testing Ambiguity Models through the Measurement of Probabilities for Gains and Losses , volume =

    Aur\'elien Baillon and Han Bleichrodt , date-added =. Testing Ambiguity Models through the Measurement of Probabilities for Gains and Losses , volume =. American Economic Journal: Microeconomics , number =

  26. [34]

    Wakker , date-added =

    Mohammed Abdellaoui and Aur\'elien Baillon and Laetitia Placido and Peter P. Wakker , date-added =. The Rich Domain of Uncertainty: Source Functions and Their Experimental Implementation , volume =. American Economic Review , number =

  27. [35]

    Zame , date-added =

    Peter Bossaerts and Paolo Ghirardato and Serena Guarnaschelli and William R. Zame , date-added =. Ambiguity in Asset Markets: Theory and Experiment , volume =. Review of Financial Studies , number =

  28. [36]

    Ellsberg Revisited: An Experimental Study , volume =

    Yoram Halevy , date-added =. Ellsberg Revisited: An Experimental Study , volume =. Econometrica , number =

  29. [37]

    Machina and Marciano Siniscalchi , booktitle =

    Mark J. Machina and Marciano Siniscalchi , booktitle =. Ambiguity and Ambiguity Aversion , year =

  30. [38]

    Decision Theory unver Ambiguity , volume =

    Johanna Etner and Meglena Jeleva and Jean-Marc Tallon , date-added =. Decision Theory unver Ambiguity , volume =. Journal of Economic Surveys , number =

  31. [39]

    Wakker , date-added =

    Peter P. Wakker , date-added =. Prospect Theory: For Risk and Ambiguity , year =

  32. [40]

    Ambiguity and Second-Order Belief , volume =

    Kyoungwon Seo , date-added =. Ambiguity and Second-Order Belief , volume =. Econometrica , number =

  33. [41]

    Nau , date-added =

    Robert F. Nau , date-added =. Uncertainty Aversion with Second-Order Utilities and Probabilities , volume =. Management Science , number =

  34. [42]

    A Theory of Subjective Compound Lotteries , volume =

    Haluk Ergin and Faruk Gul , date-added =. A Theory of Subjective Compound Lotteries , volume =. Journal of Economic Theory , number =

  35. [43]

    Attitude Toward Imprecise Information , volume =

    Thibault Gajdos and Takashi Hayashi and Jean-Marc Tallon and Jean-Christophe Vergnaud , date-added =. Attitude Toward Imprecise Information , volume =. Journal of Economic Theory , number =

  36. [44]

    Preferences Over Sets of Lotteries , volume =

    Wojciech Olszewski , date-added =. Preferences Over Sets of Lotteries , volume =. Review of Economic Studies , number =

  37. [45]

    Differentiating Ambiguity and Ambiguity Attitude , volume =

    Paolo Ghirardato and Fabio Maccheroni and Massimo Marinacci , date-added =. Differentiating Ambiguity and Ambiguity Attitude , volume =. Journal of Economic Theory , number =

  38. [46]

    Subjective Probability and Expected Utility Without Additivity , volume =

    David Schmeidler , date-added =. Subjective Probability and Expected Utility Without Additivity , volume =. Econometrica , number =

  39. [47]

    Knight , date-added =

    Frank H. Knight , date-added =. Risk, Uncertainty, and Profit , year =

  40. [48]

    Quah , date-added =

    Aluma Dembo and Shachar Kariv and Matthew Polisson and John K.-H. Quah , date-added =. Ever since Allais , volume =. Journal of Political Economy , number =

  41. [49]

    Epstein , date-added =

    Larry G. Epstein , date-added =. Are Probabilities Used in Markets? , volume =. Journal of Economic Theory , number =

  42. [50]

    Machina and D

    Mark J. Machina and D. Schmeidler , date-added =. A More Robust Definition of Subjective Probability , volume =. Econometrica , number =

  43. [51]

    A Smooth Model of Decision Making under Ambiguity , volume =

    Peter Klibanoff and Massimo Marinacci and Sujoy Mukerji , date-added =. A Smooth Model of Decision Making under Ambiguity , volume =. Econometrica , number =

  44. [52]

    Maxmin Expected Utility with Non-Unique Prior , volume =

    Itzhak Gilboa and David Schmeidler , date-added =. Maxmin Expected Utility with Non-Unique Prior , volume =. Journal of Mathematical Economics , number =

  45. [53]

    Risk, Ambiguity, and the Savage Axioms , volume =

    Daniel Ellsberg , date-added =. Risk, Ambiguity, and the Savage Axioms , volume =. Quarterly Journal of Economics , number =

  46. [54]

    Savage , date-added =

    Leonard J. Savage , date-added =. The Foundations of Statistics , year =

  47. [55]

    Bewley , date-added =

    Truman F. Bewley , date-added =. Knightian Decision Theory. Part I , volume =. Decisions in Economics and Finance , pages =

  48. [56]

    Anderson , date-added =

    Robert M. Anderson , date-added =. Core Theory with Strongly Convex Preferences , volume =. Econometrica , number =

  49. [57]

    Charness and U

    G. Charness and U. Gneezy and A. Imas , date-added =. Experimental Methods: Eliciting Risk Preferences , volume =. Journal of Economic Behavior and Organization , pages =

  50. [58]

    C. A. Holt and S. K. Laury , date-added =. Risk Aversion and Incentive Effects , volume =. American Economic Review , number =

  51. [59]

    Starmer and R

    C. Starmer and R. Sugden , date-added =. Testing Alternative Explanations of Cyclical Choices , volume =. Economica , number =

  52. [60]

    Loomes and C

    G. Loomes and C. Starmer and R. Sugden , date-added =. Observing Violations of Transitivity by Experimental Methods , volume =. Econometrica , number =

  53. [61]

    Loomes and C

    G. Loomes and C. Starmer and R. Sugden , date-added =. Preference Reversal: Information-Processing Effect or Rational Non-Transitive Choice? , volume =. Economic Journal , number =

  54. [62]

    Tversky , date-added =

    A. Tversky , date-added =. Intransitivity of Preferences , volume =. Psychological Review , number =

  55. [63]

    Fudenberg and W

    D. Fudenberg and W. Gao and A. Liang , date-added =. How Flexible Is That Functional Form? Quantifying the Restrictiveness of Theories , year =. Review of Economics and Statistics , number =

  56. [64]

    Fudenberg and J

    D. Fudenberg and J. Kleinberg and A. Liang and S. Mullainathan , date-added =. Measuring the Completeness of Economic Models , volume =. Journal of Political Economy , number =

  57. [65]

    Ellis and S

    K. Ellis and S. Kariv and E. Ozbay , date-added =. The Predictivity of Theories of Choice Under Uncertainty , year =

  58. [66]

    Ellis and S

    K. Ellis and S. Kariv and E. Ozbay , date-added =. Predicting and Understanding Individual-Level Choice under Risk , year =

  59. [67]

    H. R. Varian , date-added =. Non-Parametric Analysis of Optimizing Behavior with Measurement Error , volume =. Journal of Econometrics , number =

  60. [68]

    Approximate Expected Utility Rationalization , volume =

    Federico Echenique and Taisuke Imai and Kota Saito , date-added =. Approximate Expected Utility Rationalization , volume =. Journal of the European Economic Association , number =

  61. [69]

    Andreoni and L

    J. Andreoni and L. Vesterlund , date-added =. Which is the Fair Sex? Gender Differences in Altruism , volume =. Quarterly Journal of Economics , number =

  62. [70]

    The Distributional Preferences of Americans, 2013--2016 , volume =

    Raymond Fisman and Pamela Jakiela and Shachar Kariv and Silvia Vannutelli , date-added =. The Distributional Preferences of Americans, 2013--2016 , volume =. Experimental Economics , pages =

    2013

  63. [71]

    Casalino and Raymond Fisman and Shachar Kariv and Daniel Markovits , date-added =

    Jing Li and Lawrence P. Casalino and Raymond Fisman and Shachar Kariv and Daniel Markovits , date-added =. Experimental Evidence of Physician Social Preferences , volume =. Proceedings of the National Academy of Sciences , number =

  64. [72]

    Hu and J

    G. Hu and J. Li and J. K.-H. Quah and R. Tang , date-added =. A Theory of Revealed Indirect Preference , year =

  65. [73]

    Lanier and B

    J. Lanier and B. Miao and J. K.-H. Quah and S. Zhong , date-added =. Intertemporal Consumption with Risk: A Revealed Preference Analysis , year =. Review of Economics and Statistics , pages =

  66. [74]

    Andreoni and C

    J. Andreoni and C. Sprenger , date-added =. Estimating Time Preferences from Convex Budgets , volume =. American Economic Review , number =

  67. [75]

    Barseghyan and F

    L. Barseghyan and F. Molinari and M. Thirkettle , date-added =. Discrete Choice under Risk with Limited Consideration , volume =. American Economic Review , number =

  68. [76]

    Breig and P

    Z. Breig and P. Feldman , date-added =. Revealing Risky Mistakes Through Revisions , volume =. Journal of Risk and Uncertainty , pages =

  69. [77]

    Nielsen and J

    K. Nielsen and J. Rehbeck , date-added =. When Choices Are Mistakes , volume =. American Economic Review , number =

  70. [78]

    Dietrich and A

    F. Dietrich and A. Staras and R. Sugden , date-added =. Savage's Response to Allais as Broomean Reasoning , volume =. Journal of Economic Methodology , number =

  71. [79]

    Murphy , date-added =

    Samiran Banerjee and James H. Murphy , date-added =. A Simplified Test for Preference Rationality of Two-Commodity Choice , volume =. Experimental Economics , pages =

  72. [80]

    Quah , date-added =

    Matthew Polisson and John K.-H. Quah , date-added =. Rationalizability, Cost-Rationalizability, and Afriat's Efficiency Index , year =

  73. [81]

    Manzini and M

    P. Manzini and M. Mariotti , date-added =. On the Representation of Incomplete Preferences over Risky Alternatives , volume =. Theory and Decision , number =

  74. [82]

    Consistency of Preference: The Two-Commodity Case , volume =

    Hugh Rose , date-added =. Consistency of Preference: The Two-Commodity Case , volume =. Review of Economic Studies , number =

  75. [83]

    Blavatskyy and A

    P. Blavatskyy and A. Ortmann and V. Panchenko , date-added =. On the Experimental Robustness of the Allais Paradox , volume =. American Economic Journal: Microeconomics , number =

  76. [84]

    Loewenstein and E

    G. Loewenstein and E. Haisley , booktitle =. The Economist as Therapist: Methodological Ramifications of `Light' Paternalism , year =

  77. [85]

    R. H. Thaler and C. R. Sunstein , date-added =. Libertarian Paternalism , volume =. American Economic Review , number =

  78. [86]

    Kariv and D

    S. Kariv and D. Silverman , date-added =. An Old Measure of Decision-Making Quality Sheds New Light on Paternalism , volume =. Journal of Institutional and Theoretical Economics , number =

  79. [87]

    Camerer and S

    C. Camerer and S. Issacharoff and G. Loewenstein and T. O'Donoghue and M. Rabin , date-added =. Regulation for Conservatives: Behavioral Economics for `Asymmetric Paternalism' , volume =. University of Pennsylvania Law Review , pages =

  80. [88]

    Loomes and R

    G. Loomes and R. Sugden , date-added =. Testing for Regret and Disappointment in Choice Under Uncertainty , volume =. Economic Journal , pages =

  81. [89]

    Regret Theory: An Alternative Theory of Rational Choice under Uncertainty , volume =

    Graham Loomes and Robert Sugden , date-added =. Regret Theory: An Alternative Theory of Rational Choice under Uncertainty , volume =. Economic Journal , number =

  82. [90]

    Fishburn , date-added =

    Peter C. Fishburn , date-added =. Nontransitive Measurable Utility , volume =. Journal of Mathematical Psychology , number =

  83. [91]

    Bell , date-added =

    David E. Bell , date-added =. Regret in Decision Making under Uncertainty , volume =. Operations Research , number =

  84. [92]

    Carvalho and D

    L. Carvalho and D. Silverman , date-added =. Complexity and Sophistication , volume =. Journal of Political Economy Microeconomics , number =

  85. [93]

    Echenique and T

    F. Echenique and T. Imai and K. Saito , date-added =. Testable Implications of Models of Intertemporal Choice: Exponential Discounting and Its Generalizations , volume =. American Economic Journal: Microeconomics , number =

  86. [94]

    Varian , date-added =

    Hal R. Varian , date-added =. Goodness-of-Fit in Optimizing Models , volume =. Journal of Econometrics , number =

  87. [95]

    Dziewulski , date-added =

    P. Dziewulski , date-added =. Just-Noticeable Difference as a Behavioural Foundation of the Critical Cost-Efficiency Index , volume =. Journal of Economic Theory , pages =

  88. [96]

    L. S. Carvalho and S. Meier and S. W. Wang , date-added =. Poverty and Economic Decision-Making: Evidence from Changes in Financial Resources at Payday , volume =. American Economic Review , number =

  89. [97]

    Decision Making under Uncertainty: An Experimental Study in Market Settings , year =

    Federico Echenique and Taisuke Imai and Kota Saito , date-added =. Decision Making under Uncertainty: An Experimental Study in Market Settings , year =

  90. [98]

    Chambers and Federico Echenique and Kota Saito , date-added =

    Christopher P. Chambers and Federico Echenique and Kota Saito , date-added =. Testing Theories of Financial Decision Making , volume =. Proceedings of the National Academy of Sciences , number =

  91. [99]

    C. P. Chambers and C. Liu and S.-K. Martinez , date-added =. A Test for Risk-Averse Expected Utility , volume =. Journal of Economic Theory , pages =

  92. [100]

    Savage in the Market , volume =

    Federico Echenique and Kota Saito , date-added =. Savage in the Market , volume =. Econometrica , number =

  93. [101]

    Kubler and L

    F. Kubler and L. Selden and X. Wei , date-added =. What Are Asset Demand Tests of Expected Utility Really Testing? , volume =. Economic Journal , number =

  94. [102]

    Kubler and L

    F. Kubler and L. Selden and X. Wei , date-added =. Asset Demand Based Tests of Expected Utility Maximization , volume =. American Economic Review , number =

  95. [103]

    Bayer and Subir Bose and Matthew Polisson and Ludovic Renou , date-added =

    Ralph-C. Bayer and Subir Bose and Matthew Polisson and Ludovic Renou , date-added =. IFS Working Papers , title =

  96. [104]

    R. C. Green and S. Srivastava , date-added =. Expected Utility Maximization and Demand Behavior , volume =. Journal of Economic Theory , number =

  97. [105]

    H. R. Varian , date-added =. Estimating Risk Aversion from Arrow-Debreu Portfolio Choice , volume =. Econometrica , number =

  98. [106]

    H. R. Varian , date-added =. Nonparametric Tests of Models of Investor Behavior , volume =. Journal of Financial and Quantitative Analysis , number =

  99. [107]

    Varian , date-added =

    Hal R. Varian , date-added =. Non-Parametric Tests of Consumer Behaviour , volume =. Review of Economic Studies , number =

  100. [108]

    Vermeulen , date-added =

    F. Vermeulen , date-added =. Foundations of Revealed Preference: Introduction , volume =. Economic Journal , number =

  101. [109]

    H. R. Varian , date-added =. Revealed Preference and its Applications , volume =. Economic Journal , number =

  102. [110]

    Erwin Diewert , date-added =

    W. Erwin Diewert , date-added =. Afriat's Theorem and Some Extensions to Choice under Uncertainty , volume =. Economic Journal , number =

  103. [111]

    S. N. Afriat , date-added =. Afriat's Theorem and the Index Number Problem , volume =. Economic Journal , number =

  104. [112]

    C. P. Chambers and F. Echenique , date-added =. Revealed Preference Theory , year =

  105. [113]

    Crawford and B

    I. Crawford and B. Empirical Revealed Preference , volume =. Annual Reviews , pages =

  106. [114]

    Varian , date-added =

    Hal R. Varian , date-added =. The Nonparametric Approach to Demand Analysis , volume =. Econometrica , number =

  107. [115]

    Erwin Diewert , date-added =

    W. Erwin Diewert , date-added =. Afriat and Revealed Preference Theory , volume =. Review of Economic Studies , number =

  108. [116]

    H. S. Houthakker , date-added =. Revealed Preference and the Utility Function , volume =. Economica , number =

  109. [117]

    P. A. Samuelson , date-added =. The Problem of Integrability in Utility Theory , volume =. Economica , number =

  110. [118]

    P. A. Samuelson , date-added =. Consumption Theory in Terms of Revealed Preference , volume =. Economica , number =

  111. [119]

    P. A. Samuelson , date-added =. A Note on the Pure Theory of Consumer's Behaviour , volume =. Economica , number =

  112. [120]

    J. D. Hey and C. Orme , date-added =. Investigating Generalizations of Expected Utility Theory Using Experimental Data , volume =. Econometrica , number =

  113. [121]

    Choices, Values, and Frames , year =

  114. [122]

    D. W. Harless and C. F. Camerer , date-added =. The Predictive Utility of Generalized Expected Utility Theories , volume =. Econometrica , number =

  115. [123]

    Recent Developments in Modeling Preferences: Uncertainty and Ambiguity , volume =

    Colin Camerer and Martin Weber , date-added =. Recent Developments in Modeling Preferences: Uncertainty and Ambiguity , volume =. Journal of Risk and Uncertainty , number =

  116. [124]

    Individual Decision Making , year =

    Colin Camerer , booktitle =. Individual Decision Making , year =

  117. [125]

    W. T. Harbaugh and K. Krause and T. R. Berry , date-added =. GARP for Kids: On the Development of Rational Choice Behavior , volume =. American Economic Review , number =

  118. [126]

    Andreoni and J

    J. Andreoni and J. Miller , date-added =. Giving According to GARP: An Experimental Test of the Consistency of Preferences for Altruism , volume =. Econometrica , number =

  119. [127]

    Mattei , date-added =

    A. Mattei , date-added =. Full-Scale Real Tests of Consumer Behavior using Experimental Data , volume =. Journal of Economic Behavior and Organization , number =

  120. [128]

    Sippel , date-added =

    R. Sippel , date-added =. An Experiment on the Pure Theory of Consumer's Behaviour , volume =. Economic Journal , number =

  121. [129]

    J. C. Cox , date-added =. On Testing the Utility Hypothesis , volume =. Economic Journal , number =

  122. [130]

    Cappelen and Shachar Kariv and Erik

    Alexander W. Cappelen and Shachar Kariv and Erik. The Development Gap in Economic Rationality of Future Elites , volume =. Games and Economic Behavior , pages =

  123. [131]

    Prelec , date-added =

    D. Prelec , date-added =. The Probability Weighting Function , volume =. Econometrica , number =

  124. [132]

    Diecidue and P

    E. Diecidue and P. P. Wakker , date-added =. On the Intuition of Rank-Dependent Utility , volume =. Journal of Risk and Uncertainty , number =

  125. [133]

    Abdellaoui , date-added =

    M. Abdellaoui , date-added =. A Genuine Rank-Dependent Generalization of the von Neumann-Morgenstern Expected Utility Theorem , volume =. Econometrica , number =

  126. [134]

    Wakker , date-added =

    P. Wakker , date-added =. Separating Marginal Utility and Probabilistic Risk Aversion , volume =. Theory and Decision , pages =

  127. [135]

    Two-Stage Lotteries without the Reduction Axiom , volume =

    Uzi Segal , date-added =. Two-Stage Lotteries without the Reduction Axiom , volume =. Econometrica , number =

  128. [136]

    M. E. Yaari , date-added =. The Dual Theory of Choice under Risk , volume =. Econometrica , number =

  129. [137]

    M. J. Machina , date-added =. Review of `Generalized Expected Utility Theory: The Rank-Dependent Model' , volume =. Journal of Economic Literature , number =

  130. [138]

    Bronars , date-added =

    Stephen G. Bronars , date-added =. The Power of Nonparametric Tests of Preference Maximization , volume =. Econometrica , number =

  131. [139]

    Zame and Bertil Tungodden and Erik

    William R. Zame and Bertil Tungodden and Erik. Linking Social and Personal Preferences: Theory and Experiment , volume =. Journal of Political Economy , number =

  132. [140]

    Le Comportement de l'Homme Rationnel devant le Risque: Critique des Postulats et Axiomes de l'Ecole Americaine , volume =

    Maurice Allais , date-added =. Le Comportement de l'Homme Rationnel devant le Risque: Critique des Postulats et Axiomes de l'Ecole Americaine , volume =. Econometrica , number =

  133. [141]

    Estimating Ambiguity Aversion in a Portfolio Choice Experiment , volume =

    David Ahn and Syngjoo Choi and Douglas Gale and Shachar Kariv , date-added =. Estimating Ambiguity Aversion in a Portfolio Choice Experiment , volume =. Quantitative Economics , number =

  134. [142]

    Dow and Shachar Kariv , date-added =

    Jing Li and William H. Dow and Shachar Kariv , date-added =. Social Preferences of Future Physicians , volume =. Proceedings of the National Academy of Sciences , number =

  135. [143]

    Distributional Preferences and Political Behavior , volume =

    Raymond Fisman and Pamela Jakiela and Shachar Kariv , date-added =. Distributional Preferences and Political Behavior , volume =. Journal of Public Economics , pages =

  136. [144]

    The Distributional Preferences of an Elite , volume =

    Raymond Fisman and Pamela Jakiela and Shachar Kariv and Daniel Markovits , date-added =. The Distributional Preferences of an Elite , volume =. Science , number =

  137. [145]

    How Did the Great Recession Impact Social Preferences? , volume =

    Raymond Fisman and Pamela Jakiela and Shachar Kariv , date-added =. How Did the Great Recession Impact Social Preferences? , volume =. Journal of Public Economics , pages =

  138. [146]

    Individual Preferences for Giving , volume =

    Raymond Fisman and Shachar Kariv and Daniel Markovits , date-added =. Individual Preferences for Giving , volume =. American Economic Review , number =

  139. [147]

    Halevy and G

    Y. Halevy and G. Mayraz , date-added =. Identifying Rule-Based Rationality , volume =. Review of Economics and Statistics , number =

  140. [148]

    Relaxed Optimization: How Close Is a Consumer to Satisfying First-Order Conditions? , volume =

    Geoffroy de Clippel and Kareen Rozen , date-added =. Relaxed Optimization: How Close Is a Consumer to Satisfying First-Order Conditions? , volume =. Review of Economics and Statistics , number =

  141. [149]

    Ok and John K.-H

    Hiroki Nishimura and Efe A. Ok and John K.-H. Quah , date-added =. A Comprehensive Approach to Revealed Preference Theory , volume =. American Economic Review , number =

  142. [150]

    Afriat , date-added =

    Sydney N. Afriat , date-added =. On a System of Inequalities in Demand Analysis: An Extension of the Classical Method , volume =. International Economic Review , number =

  143. [151]

    Afriat , date-added =

    Sydney N. Afriat , date-added =. Efficiency Estimation of Production Functions , volume =. International Economic Review , number =

  144. [152]

    K. J. Arrow , date-added =. The Role of Securities in the Optimal Allocation of Risk-bearing , volume =. Review of Economic Studies , number =

  145. [153]

    A Theory of Disappointment Aversion , volume =

    Faruk Gul , date-added =. A Theory of Disappointment Aversion , volume =. Econometrica , number =

  146. [154]

    Machina , date-added =

    Mark J. Machina , date-added =. `Expected Utility' Analysis without the Independence Axiom , volume =. Econometrica , number =

  147. [155]

    Rational Behavior, Uncertain Prospects, and Measurable Utility , volume =

    Jacob Marschak , date-added =. Rational Behavior, Uncertain Prospects, and Measurable Utility , volume =. Econometrica , number =

  148. [156]

    Afriat , date-added =

    Sydney N. Afriat , date-added =. The Construction of Utility Functions from Expenditure Data , volume =. International Economic Review , number =

  149. [157]

    Parametric Recoverability of Preferences , volume =

    Yoram Halevy and Dotan Persitz and Lanny Zrill , date-added =. Parametric Recoverability of Preferences , volume =. Journal of Political Economy , number =

  150. [158]

    Who Is (More) Rational? , volume =

    Syngjoo Choi and Shachar Kariv and Wieland M\"uller and Dan Silverman , date-added =. Who Is (More) Rational? , volume =. American Economic Review , number =

  151. [159]

    Masatlioglu and C

    Y. Masatlioglu and C. Raymond , date-added =. A Behavioral Analysis of Stochastic Reference Dependence , volume =. American Economic Review , number =

  152. [160]

    Kahneman and A

    D. Kahneman and A. Tversky , date-added =. Prospect Theory: An Analysis of Decision under Risk , volume =. Econometrica , number =

  153. [161]

    Developments in Non-Expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk , volume =

    Chris Starmer , date-added =. Developments in Non-Expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk , volume =. Journal of Economic Literature , number =

  154. [162]

    Savage's Axioms Usually Imply Violation of Strict Stochastic Dominance , volume =

    Peter Wakker , date-added =. Savage's Axioms Usually Imply Violation of Strict Stochastic Dominance , volume =. Review of Economic Studies , number =

  155. [163]

    Stochastic Dominance in Regret Theory , volume =

    John Quiggin , date-added =. Stochastic Dominance in Regret Theory , volume =. Review of Economic Studies , number =

  156. [164]

    B. K. Reference-Dependent Risk Attitudes , volume =. American Economic Review , number =

  157. [165]

    Tversky and D

    A. Tversky and D. Kahneman , date-added =. Advances in Prospect Theory: Cumulative Representation of Uncertainty , volume =. Journal of Risk and Uncertainty , number =

  158. [166]

    Generalized Expected Utility Theory: The Rank-Dependent Model , year =

    John Quiggin , date-added =. Generalized Expected Utility Theory: The Rank-Dependent Model , year =

  159. [167]

    A Theory of Anticipated Utility , volume =

    John Quiggin , date-added =. A Theory of Anticipated Utility , volume =. Journal of Economic Behavior and Organization , number =

  160. [168]

    S. H. Chew , date-added =. Axiomatic Utility Theories with the Betweenness Property , volume =. Annals of Operations Research , number =

  161. [169]

    Dekel , date-added =

    E. Dekel , date-added =. An Axiomatic Characterization of Preferences under Uncertainty: Weakening the Independence Axiom , volume =. Journal of Economic Theory , number =

  162. [170]

    Theory of Games and Economic Behavior , year =

    John von Neumann and Oskar Morgenstern , date-added =. Theory of Games and Economic Behavior , year =

  163. [171]

    Debreu , booktitle =

    G. Debreu , booktitle =. Topological Methods in Cardinal Utility Theory , year =

  164. [172]

    Debreu , booktitle =

    G. Debreu , booktitle =. Representation of a Preference Ordering by a Numerical Function , year =

  165. [173]

    Consistency and Heterogeneity of Individual Behavior under Uncertainty , volume =

    Syngjoo Choi and Raymond Fisman and Douglas Gale and Shachar Kariv , date-modified =. Consistency and Heterogeneity of Individual Behavior under Uncertainty , volume =. American Economic Review , number =

  166. [174]

    Quah and Ludovic Renou , date-modified =

    Matthew Polisson and John K.-H. Quah and Ludovic Renou , date-modified =. Revealed Preferences over Risk and Uncertainty , volume =. American Economic Review , number =

  167. [175]

    Gale and Shachar Kariv , date-modified =

    Syngjoo Choi and Raymond Fisman and Douglas M. Gale and Shachar Kariv , date-modified =. Revealing Preferences Graphically: An Old Method Gets a New Tool Kit , volume =. American Economic Review: AEA Papers and Proceedings , number =

Pith tools

Reviewed July 13, 2026 · model on record in the stance chip above.