The Emergence of Economic Rationality of GPT

Measurement

• The study measures economic rationality as consistency with utility maximization under budget constraints using revealed preference theory and the generalized axiom of revealed preference.A rationality score is derived from each group of 25 decisions within a given environment.Source: §1 · pp. 2–3

Experimental design

• GPT is instructed to allocate 100 points between two priced commodities across four environments, repeated 100 times to generate 10,000 tasks.The environments cover risky assets, immediate versus delayed rewards, payments to self versus another person, and meat versus tomatoes.Source: §1 · p. 3

Findings

• GPT demonstrates high rationality across risk, time, social, and food decisions and outperforms human subjects in experimental and literature benchmarks.The comparison uses a parallel experiment with 347 human subjects from a representative US sample.Source: §1 · p. 4

Robustness and limitations

• Rationality remains consistent across demographic settings and randomness specifications but drops significantly under alternative price framing and discrete choice.These results indicate strong overall rationality alongside context-sensitive decision-making limitations.Source: §1 · p. 4

Preference parameters

• Estimated preference parameters for GPT differ modestly from human subjects and exhibit substantially lower heterogeneity.The paper estimates preference parameters for both GPT and human subjects as part of the comparison.Source: §1 · p. 4

Contribution

• The study contributes to understanding LLM capabilities and caveats by showing that LLMs can act as rational decision makers while requiring further refinement for reliable decisions.The authors motivate this contribution by noting concerns about language understanding, behavioral bias, and context sensitivity.Source: §1 · p. 4

2 Experimental Method

• GPT-3.5-Turbo is evaluated through Python API experiments, enabling parameter adjustment and efficient large-scale testing.The model powers ChatGPT and is described as the most popular, stable, and cost-effective GPT variant.Source: §2 · p. 5

2.1 Design of the Baseline Condition

• The baseline instructs GPT to act as a human decision maker and includes 25 tasks with randomly generated prices to collect decisions for measuring rationality.Source: §2.1 · pp. 5–6
• The budget experiment endows decision makers with 100 points to choose bundles of two commodities, whose changing exchange rates support revealed-preference rationality tests.The four domains operationalize risk through contingent securities, time through immediate versus delayed rewards, social preferences through allocations between self and another subject, and food preferences through meat and tomatoes.Source: §2.1 · p. 6

2.2 Design of Conditions with Variations

• Robustness conditions vary temperature, price framing, choice format, and embedded demographics to test whether GPT’s decisions depend on randomness, presentation, or assigned characteristics.Temperature is increased to 0.5; price framing reverses the units statement; discrete choice presents 11 budget-line options; demographics vary gender, age, education, and minority status.Source: §2.2 · p. 7

2.3 Design of the Human Experiment

• A preregistered human experiment applies identical decision tasks to 347 representative US subjects randomly assigned across baseline, price-framing, and discrete-choice conditions.Instructions for humans and GPT are kept as similar as possible; temperature variation is inapplicable to humans.Source: §2.3 · p. 8
• The human experiment took place at The Wang Yanan Institute of Studies in Economics, Xiamen University.Source: §2.3 · p. 9
• All subjects provided informed consent before beginning the experiment.Source: §2.3 · p. 9
• Appendix D’s Table D1 reports the demographic characteristics of the experiment’s subjects.Source: §2.3 · p. 9

3.1 Revealed Preference Analysis

• Afriat’s theorem rationalizes a choice dataset by a continuous, concave, strictly increasing utility function if and only if choices satisfy GARP.The analysis uses well-behaved utility as the benchmark for revealed-preference rationality.Source: §3.1 · p. 9
• CCEI measures departures from rationality as the largest e ∈ [0, 1] for which a well-behaved U rationalizes choices; e = 1 indicates perfect GARP compliance.A CCEI below 1 represents the amount by which a budget constraint must be relaxed to remove violations.Source: §3.1 · p. 10
• The study also computes HMI, MPI, and MCI as robustness checks for departures from GARP.These indices are the Houtman-Maks, money pump, and minimum cost indices, respectively.Source: §3.1 · pp. 10–11

3.2 Structural Estimation for Preferences

• Structural estimation models risk and time choices with parameters for outcome or payment weights and curvature, including α, ρ, and the relative-risk-aversion measure θ = 1−ρ.For risk, α captures weighting of the better outcome and θ measures relative risk aversion; for time, α captures the weight on payment today and α > 0.5 denotes positive time preference.Source: §3.2 · p. 11
• Across all four preference domains, estimation is conditional on ρ ≤ 1 because the budget set makes ρ > 1 observationally equivalent to corner solutions at ρ = 1.Further details on estimating corner solutions are provided in the supplementary appendix.Source: §3.2 · p. 11
• Social and food preferences use CES utility, with α weighting self versus other payments or meat versus tomatoes and ρ governing curvature.For social preferences, α = 1 represents pure selfishness, α = 0.5 fair-mindedness, and α = 0 pure altruism; limiting ρ values correspond to efficiency-, Cobb–Douglas-, or equality-oriented behavior.Source: §3.2 · p. 12

4.1 Results from the Baseline Condition

• GPT observations surpass human subjects in rationality across all four domains using CCEI and additional HMI, MPI, and MCI indices.The CCEI comparison is significant at p < 0.01, while the additional-index comparison is significant at p < 0.1; 99.9% of simulated subjects violate GARP and have lower CCEI than GPT and humans.Source: §4.1 · pp. 13–15
• Across risk, time, social, and food preferences, 95, 89, 81, and 92 of 100 GPT observations respectively had CCEI = 1, with corresponding averages 0.998, 0.997, 0.997, and 0.999.Source: §4.1 · p. 13
• GPT is more responsive to price changes than humans in every preference domain: its Spearman coefficients are negative, whereas 96.1% of human observations are negative on average.The comparison is significant at p < 0.01 (two-sided two-sample t-tests), supporting stronger compliance with downward-sloping demand for GPT.Source: §4.1 · p. 15, Figure 2 · p. 16
• Compared with human subjects, GPT is closer to an expected-utility maximizer, more patient, more other-regarding and socially efficiency-oriented, and less fond of meat.Reported estimates are αr: 0.618 vs. 0.508, ρr: 0.335 vs. 0.488, αt: 0.513 vs. 0.504, ρt: 0.981 vs. 0.466, αs: 0.735 vs. 0.512, ρs: 0.330 vs. 0.520, and αf: 0.583 vs. 0.501 for Human vs. GPT.Source: §4.1 · p. 18
• GPT’s estimated preferences are less heterogeneous than humans’ preferences, whose individual-level parameter estimates are more dispersed.Similar patterns appear in individual-level estimations for GPT decision makers and human subjects.Source: §4.1 · p. 18

4.2 Results from the Conditions with Variations

• 4.7% and 9.8% of responses are invalid at temperatures 0.5 and 1, respectively, so variation analyses condition on valid answers.The study varies temperature, decision tasks, and demographic information while reporting mean CCEI and Spearman correlations with 95% confidence intervals.Source: §4.2 · p. 18
• Higher temperature leaves GPT’s rationality score and mean preference parameters statistically unchanged but increases heterogeneity in ρ_r, ρ_t, ρ_s, and ρ_f (p < 0.01).The findings suggest randomness increases stochasticity and creativity in language presentation, not rationality.Source: §4.2 · p. 19

Sensitive to Variation in the Decision Tasks

• Price framing significantly reduces GPT’s rationality across all four tasks; risk-preference CCEI falls to 0.901, with 34% below 0.9.CCEI values are significantly higher under baseline conditions than price framing (p < 0.01).Source: §4.2 · p. 19, Figure 4 · p. 21
• GPT is more affected than human subjects by price framing and discrete choices, with larger reductions in rationality and downward-sloping demand.The differences are supported by OLS regression analyses in Table D4.Source: §4.2 · p. 20
• Discrete choices also reduce GPT’s CCEI across all domains: risk 0.998 vs. 0.843, time 0.997 vs. 0.908, social 0.997 vs. 0.871, and food 0.999 vs. 0.780.All differences are significant at p < 0.01, and 51%, 32%, 33%, and 55% of observations fall below 0.9 in risk, time, social, and food.Source: §4.2 · p. 20, Figure 4 · p. 21

Insensitive to Demographic Information

• CCEI values, demand correlations, and estimated preference parameters are insensitive to demographic variations in GPT prompts, suggesting consistent decision quality across user groups.This contrasts with the human experiment and prior studies reporting demographic differences in rationality and preferences.Source: §4.2 · pp. 20–21

Contributions

• The study extends research on GPT by applying traditional decision-making tasks and systematic behavioral measures through revealed preference analysis.It demonstrates the effectiveness of experimental economics methods for studying artificial intelligence and positions GPT as a source of new experimental data and insights.Source: §5 · pp. 22–23

Main findings

• GPT displays high rationality in risk, time, social, and food-preference decisions, with performance largely unaffected by increased randomness or demographic characteristics.Demographic factors also do not significantly affect GPT’s estimated preference parameters.Source: §5 · pp. 22, 24

Context sensitivity

• GPT’s rationality drops under nonstandard price presentations and discrete choice sets, indicating sensitivity to decision contexts and linguistic frames.Under unfamiliar alternative-price tasks, GPT tends toward midpoint choices, whereas under discrete choices it tends toward the first or last option.Source: §5 · pp. 22, 24

Applications

• GPT’s rationality across domains suggests potential as a user-friendly, versatile AI-based decision-support tool for individuals and organizations.Unlike many decision-support algorithms requiring data input and training, GPT provides direct question-and-answer assistance.Source: §5 · p. 23

Limitations

• The study does not identify the mechanisms underlying GPT’s choices, leaving context sensitivity potentially attributable to training-data biases, insufficient alternative framing, or spurious correlations.The authors note that corpus-based heuristics may produce midpoint responses for unfamiliar price frameworks and endpoint responses for unfamiliar discrete choices.Source: §5 · p. 23

Scope and future research

• The conclusions are limited to revealed-preference rationality in a simple two-commodity environment, so broader rationality and realistic applications require further study.The authors call for research on supermarket shopping, portfolio choices, underlying mechanisms, and broader applications of artificial intelligent agents.Source: §5 · p. 24

A Method: GPT Experiment.

• GPT receives fixed system instructions, stored task background, and changing user prompts for comprehension checks and decision tasks across experimental conditions.The study sends message objects with system, assistant, and user roles; the system message remains fixed while assistant and user messages vary.Source: A Method: GPT Experiment · p. 34

A.1 Risk Preference

• In the risk experiment, GPT was instructed to act as a human decision maker, complete 25 rounds of decision-making tasks, use best judgment, and answer every round.Testing questions indicated understanding, with no misunderstandings across 25 simulations in each preference domain and condition.Source: §A.1 · p. 34

A.1.1 Baseline Condition

• In the baseline condition, GPT allocates 100 points between two assets with equal return probabilities and reports separate investments for Assets A and B.The prompt first tests whether GPT understands the 50% probabilities and the resulting returns before presenting the allocation task.Source: §A.1.1 · p. 35

A.1.2 Price Framing Condition

• The price-framing condition presents equivalent asset returns as points required per dollar, then asks GPT to allocate 100 points between the assets.For example, investing 90 points in Asset A at 1.25 points per dollar yields $72, while 10 points in Asset B at 5 points per dollar yields $2.Source: §A.1.2 · pp. 36–37

A.1.3 Discrete Choice Condition

• The discrete-choice condition gives GPT 11 paired options ($M, $N), each with a 50% chance of yielding either asset’s payoff, and asks it to choose the best option.The comprehension questions verify the equal probabilities, expected-return interpretation, and possibility of receiving the higher payoff.Source: §A.1.3 · p. 38
• The discrete-choice condition presents eleven paired options, (M1,N1) through (M11,N11), and asks which is best.Source: §A.1.3 · p. 39

A.2 Time Preference

• The time-preference protocol instructs the system to act as a human decision maker and complete 25 rounds using its best judgment.Source: §A.2 · p. 39
• The protocol requires an answer in every round; otherwise, the response is treated as a random choice.Source: §A.2 · p. 39

Baseline Condition

• GPT allocates 100 points between today and one month later, receiving cash immediately from today’s investment and a check after one month from the delayed investment.The allocation is elicited as separate point amounts for investing today and one month later.Source: §A.2.1 · p. 39
• Comprehension checks ask whether a participant can calculate returns from allocating 90 points today and 10 points one month later, with 0.8 dollars cash today and 0.2 dollars cashed one month later.Source: §A.2.1 · pp. 39–41
• An example allocates 75 points to today and 25 points to one month later, producing an immediate return of 60 dollars and a future return of 5 dollars.The passage describes the one-month-later return as guaranteed.Source: §A.2.1 · p. 41
• The decision task varies the per-point returns, specifying M dollars today and N dollars one month later, then asks GPT for its allocation.The reported implementation uses 25 continuous rounds with varying parameters M and N.Source: §A.2.1 · pp. 39, 41

A.2.2 Price Framing Condition

• The price-framing condition gives decision makers 100 points to allocate between today and one month later, with returns determined by separate conversion rates.The task requests the points invested today and one month later, with today’s payment in cash and the delayed payment as a check.Source: §A.2.2 · p. 41
• In the cited price-framing example, investing 90 points today at 1.25 points per dollar yields 72 dollars cash today; it also describes investing 10 points one month later.For today, each point yields 1/1.25 = 0.8 dollars cash, so 90 points yield 72 dollars cash.Source: §A.2.2 · p. 42
• The price-framing decision task varies conversion parameters M and N and asks for the allocation across today and one month later.The prompt specifies that investing every 1/M points today or 1/N points later returns one dollar at the corresponding date.Source: §A.2.2 · p. 43

A.2.3 Discrete Choice Condition

• The discrete-choice condition presents 11 options in the form ($M, $N), representing M dollars today and N dollars one month later, and asks GPT to select the best option.The task uses paired immediate and delayed payments rather than point allocations.Source: §A.2.3 · pp. 43–44
• The discrete-choice comprehension examples ask what return each option provides, when the delayed 2 dollars from ($72, $2) can be received, and which option is selected between ($40, $10) and ($72, $2).Source: §A.2.3 · pp. 43–44

A.3 Social Preference

• The social-preference condition assigns GPT 25 decision-making rounds and instructs it to act as a human decision maker using its best judgment.It requires an answer in every round and treats a missing answer as a random choice.Source: §A.3 · p. 44

A.3.1 Baseline Condition

• In the baseline condition, GPT allocates 100 points between itself and an anonymous counterpart without feedback across randomly matched rounds.Returns are specified separately for points allocated to each person, and GPT is asked to report allocations directly.Source: §A.3.1 · pp. 44–45
• The baseline protocol includes comprehension questions about returns, recipient identity, and whether to allocate points to the other person.Examples use allocations of 90 points to oneself and 10 to the other, with returns of 0.8 and 0.2 dollars per point.Source: §A.3.1 · p. 45

A.3.2 Price Framing Condition

• The price-framing condition preserves the 100-point allocation task but expresses returns as points required to obtain one dollar for each recipient.The decision task specifies rates of 1/M points per dollar for oneself and 1/N points per dollar for the other person.Source: §A.3.2 · pp. 46–47
• Price-framing comprehension questions ask GPT to calculate returns, identify who receives a specified amount, and decide whether to allocate to the other person.An example uses 1.25 points per dollar for oneself and 5 points per dollar for the other person.Source: §A.3.2 · p. 47

A.3.3 Discrete Choice Condition

• The discrete-choice condition presents 11 options in the form ($M, $N), representing the decision maker’s and the other person’s monetary returns.GPT is instructed to select only its best option in each round.Source: §A.3.3 · pp. 47–48
• Discrete-choice comprehension questions assess return interpretation, recipient identification, and selection between alternatives, including ($40, $10) versus ($72, $2).Source: §A.3.3 · p. 48

A.4 Food Preference

• The food-preference condition asks GPT to act as a human decision maker across 25 rounds and choose solutions it likes most.GPT must provide an answer in every round; otherwise, the response is treated as a random choice.Source: §A.4 · p. 49

• Each round gives the decision maker 100 points to divide between ham meat and tomato, receiving quantities corresponding to the points spent on each good.The prompt requests meat points first and tomato points second.Source: §A.4.1 · p. 49
• Comprehension questions test whether GPT understands the goods and how allocations convert into quantities.One example specifies 90 meat points and 10 tomato points, with returns of 0.8 Kg meat and 0.2 Kg tomato per point.Source: §A.4.1 · p. 49
• The decision task varies the quantities obtained per point, asking GPT to report its allocation and reasoning.The general formulation assigns M Kg meat per point and N Kg tomato per point.Source: §A.4.1 · p. 50

A.4.2 Price Framing Condition

• The price-framing condition gives the decision maker 100 points to divide between ham meat and tomato, with quantities determined by spending.GPT is asked to report meat and tomato point allocations separately.Source: §A.4.2 · p. 50
• In the worked example, spending 90 points on meat at 1.25 points per kilogram yields 90 / 1.25 = 72 kg; tomatoes cost 5 points per kilogram.Source: §A.4.2 · p. 51
• In the price-framing example, GPT allocates 80 points to meat and 20 points to tomatoes, citing preference for meat and its more favorable conversion rate.The response compares 1.25 points per kilogram for meat with 5 points per kilogram for tomatoes.Source: §A.4.2 · p. 51
• Price conversion rates are expressed as 1/M points per kilogram of meat and 1/N points per kilogram of tomato.The decision task asks GPT to provide its allocation under these rates.Source: §A.4.2 · p. 51

A.4.3 Discrete Choice Condition

• The discrete-choice condition presents 11 options, each written as a pair (M Kg, N Kg) specifying meat and tomato quantities.GPT is asked to identify the goods and report its best option.Source: §A.4.3 · pp. 51–52
• A discrete-choice example asks GPT to compare (40 Kg, 10 Kg) with (72 Kg, 2 Kg), and GPT selects the former for its more balanced quantities.GPT explains that the lower tomato quantity in the second option may not meet its needs.Source: §A.4.3 · p. 52

B.1 Design

• In the human experiment, subjects completed four randomized-order preference sections—risk, time, social, and food—with 25 decision tasks per domain following one format with randomly generated parameters.The human conditions were parallel to those in the GPT experiment.Source: §B.1 · p. 53
• The preregistered July 2023 experiment recruited 347 unique subjects from a representative US Prolific sample, with more than 110 subjects per condition and a 30.5-minute median duration.Subjects were randomly assigned to three conditions; the study was preregistered as AEARCTR-0011750.Source: §B.1 · p. 53

B.4 Risk Preference

• Risk-preference tasks allocated 100 points between two assets with a 50% chance of receiving either asset’s return, followed by allocation decisions across repeated rounds.The experiment used baseline, price-framing, and discrete-choice conditions to vary how the same risky allocation problem was presented.Source: §B.4 · p. 55, §B.4.1 · pp. 55–56

B.4.1 Baseline Condition

• The risk baseline expressed returns per invested point, whereas price framing expressed points required per dollar and discrete choice presented 11 ($M, $N) lottery options.The discrete-choice condition asked subjects to select their best option in each round.Source: §B.4.1 · p. 56, §B.4.2 · p. 57, §B.4.3 · p. 57

B.5 Time Preference

• Time-preference tasks asked subjects to allocate 100 points between receiving dollars today and a check cashable one month later.As in the other domains, subjects completed 25 rounds and one decision could be randomly selected to determine the bonus.Source: §B.5 · p. 58, §B.5.1 · p. 58

D: 100 dollars today]

• Participants allocated 100 points between today and one month later, with returns specified separately for each timing option.The task elicited allocations after decision-makers answered comprehension questions about timing, returns, and cash availability.Source: §B.5.2 · pp. 59–60

B.5.2 Price Framing Condition

• In the price-framing condition, returns were expressed as points required to obtain one dollar today or one month later.The decision task used 1/M points for one dollar today and 1/N points for one dollar later.Source: §B.5.2 · pp. 59–60

B.5.3 Discrete Choice Condition

• In the discrete-choice condition, participants selected their best option from 11 pairs of payments represented as ($M, $N).M denoted dollars received today and N denoted a check cashable one month later.Source: §B.5.3 · pp. 60–61

B.6 Social Preference

• The social-preference section consisted of 25 decision rounds, with one decision randomly selected to determine the participant’s bonus.Participants were instructed to provide an answer in every round and use their best judgment.Source: §B.6 · p. 61

B.6.1 Baseline Condition

• In the baseline social condition, participants allocated 100 points between themselves and an anonymous matched subject without feedback across rounds.Returns depended on the points allocated to each person, and participants reported allocations to themselves and the other person separately.Source: §B.6.1 · pp. 61–62

B.6.2 Price Framing Condition

• The social price-framing condition used point costs for generating one dollar for oneself or the other person.The decision task expressed these rates as 1/M points for one dollar for oneself and 1/N points for one dollar for the other person.Source: §B.6.2 · pp. 62–63

B.6.3 Discrete Choice Condition

• In the social discrete-choice condition, participants chose their best option from 11 ($M, $N) allocations specifying payments to themselves and another person.Participants were randomly matched with a new anonymous subject in each round, with no feedback across rounds.Source: §B.6.3 · p. 64
• The discrete-choice condition tests comprehension with multiple-choice and open-ended questions before asking participants to select the best of 11 ($M_i,$N_i) options.The comprehension questions cover interpreting allocations and comparing alternatives such as ($40, $10) and ($72, $2).Source: §B.6.3 · p. 64

B.7 Food Preference

• The food-preference section gives participants 25 hypothetical decision rounds, requires an answer in every round, and promises a fixed $50 bonus if selected for realization.Source: §B.7 · p. 64

B.7.1 Baseline Condition

• In the baseline condition, decision makers spend 100 points between ham meat and tomato, reporting meat points first and tomato points second.The quantities obtained depend on per-point yields M Kg of meat and N Kg of tomato.Source: §B.7.1 · p. 65, C: 0.8 Kg meat and 0.2 Kg tomato; D:… · p. 65

B.7.2 Price Framing Condition

• The price-framing condition uses the same 100-point allocation but expresses prices as 1/M points per kilogram of meat and 1/N points per kilogram of tomato.Comprehension checks require converting spending into quantities, illustrated by prices of 1.25 points for meat and 5 points for tomato.Source: §B.7.2 · p. 65, [MCQ; A: Meat and tomato; B: Meat… · p. 66

B.7.3 Discrete Choice Condition

• The food discrete-choice condition presents 11 options as (M Kg, N Kg) bundles and asks participants to identify their best option after comprehension checks.Example checks ask participants to interpret (72 Kg, 2 Kg) and choose between (40 Kg, 10 Kg) and (72 Kg, 2 Kg).Source: §B.7.3 · p. 66, [MCQ; A: Meat and tomato; B: Meat… · p. 66, C: 72 Kg meat and 0 Kg tomato; D: 100… · p. 67

B.8.1 Baseline

• Incentives randomly select 1 out of every 30 subjects and one decision for implementation, with outcomes paid according to the selected decision’s domain.Baseline implementations include random asset outcomes, immediate or one-month payments, anonymous matching for social allocations, and a fixed $50 payment for the hypothetical food task.Source: §B.8.1 · pp. 67–68

B.8.2 Price Framing

• The procedure frames asset decisions as investing every 1/M points in Asset A for a 1-dollar return, mentions 1/N points for Asset B, and randomly selects one decision for implementation.Source: §B.8.2 · pp. 68–69

B.8.3 Discrete Choice

• Discrete-choice conditions present 11 options for risky, intertemporal, social, and food decisions, with selected choices implemented through the corresponding random or hypothetical payment rule.Risk choices randomize between M and N dollars, intertemporal choices pay today and after one month, social choices affect both matched participants, and food choices remain hypothetical with a fixed $50 payment.Source: §B.8.3 · pp. 70–71

C.1 Preference Estimation

• The preference-estimation specification derives first-order conditions for optimal choice (x1, x2) given prices (p1, p2), linking relative quantity responses to relative prices conditional on ρ.The specification also relates ρ to the correlation coefficient between logarithmic relative quantity and price rates.Source: §C.1 · p. 72
• For risk preference, as ρr →1, the decision maker allocates all expenditure to the security.Source: §C.1 · p. 72
• In risk, as ρr decreases, the decision-maker smooths payments more across securities when prices change, indicating greater risk aversion.Higher ρr instead implies stronger movement toward the lower-priced option.Source: §C.1 · p. 72
• In time preference, ρt approaching 1 shifts all expenditure to the lower-priced period, whereas lower ρt indicates less fungibility across periods.Source: §C.1 · p. 72
• In social preference, ρs approaching 1 concentrates expenditure on the lower-priced subject, whereas lower ρs produces more equal payoff allocation.Source: §C.1 · p. 72
• In food preference, ρf approaching 1 concentrates expenditure on lower-priced goods, whereas lower ρf distributes meat and tomatoes more evenly.The latter pattern indicates a greater tendency toward equality.Source: §C.1 · pp. 72–73
• Preference parameters are estimated from a bounded expenditure-share function using nonlinear Tobit maximum likelihood, yielding α and ρ for all four domains.The approach follows expenditure-share methods because ln(x1/x2) is undefined for corner solutions.Source: §C.1 · p. 73

Bronars Power

• 99.9% of uniformly random simulated subjects reject GARP, establishing that the experiment’s 25-choice budget sets have power to detect violations.The benchmark subjects choose uniformly at random across allocations on each budget line and face randomly generated budget sets.Source: §C.2 · p. 74

Predictive Success

• GPT observations and human subjects outperform the hypothetical benchmark in predictive success across risk, time, social, and food preferences.Predictive success is defined as the GARP pass rate minus (1 − Bronars power).Source: §C.2 · p. 74

Selten Score

• Average Selten scores for GPT observations and human subjects are significantly greater than zero in all four domains.The significance level is p < 0.01 using a two-sided two-sample t-test.Source: §C.2 · pp. 74–75

Bootstrap Power

• Bootstrap estimates using 10,000 synthetic subjects and 25 choices drawn from actual decision-makers’ budget sets provide a robustness check on GARP rejection probabilities.This method relies on preference heterogeneity, and indifferent preferences can produce a low probability of GARP violation; the results align with preference parameter estimates.Source: §C.2 · p. 75

Conclusion

• Together, the analyses show that the budget sets have power to detect rationality violations and that GPT observations and human subjects have high rationality.The conclusion covers the benchmark, predictive-success, Selten-score, and bootstrap analyses.Source: §C.2 · p. 75

Rationality scores

• Cumulative-distribution figures compare GPT observations with human and simulated subjects across CCEI, HMI, MPI, and MCI in risk, time, social, and food preferences.The figures present one set of rationality-index comparisons for each preference domain.Source: Figure D2 · p. 77, Figure D3 · p. 78, Figure D4 · p. 79

Robustness variations

• Additional figures examine GPT’s quantity-share relationships with log-price ratios across baseline, price-framing, discrete-choice, and temperature variations.The plots cover all four preference domains and include fitted lines, while temperature figures report CCEI and Spearman’s correlation distributions.Source: Figure D6 · p. 81, Figure D7 · p. 82, Figure D8 · p. 83

Preference parameters

• Baseline aggregate preference parameters are compared between GPT and human subjects, with all comparisons statistically significant at 1% except αt.The notes state that aggregate parameters cover risk, time, social, and time preference and use two-sample two-sided t-tests.Source: Table D2 · p. 101, D Result · p. 101

Individual-level parameters

• At the individual level, all GPT–human preference-parameter comparisons are statistically significant at 1%, while GPT variations do not differ significantly from baseline at 10%.The individual-level summary covers risk, time, social, and time preference parameters and uses two-sample two-sided t-tests.Source: Table D3 · p. 102, D Result · p. 102