{"id":"92f3cb1f-f0c4-4538-9858-12f3275642ed","arxiv_id":"2501.16356","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":0,"one_line_summary":"GPT models asked to make random binary choices show large, version-specific biases; only GPT-4o-Mini came close to a 50/50 split in one-shot tests.","lead":"This paper tested three OpenAI GPT models on a yes/no coin-toss task and found heavy 'yes' bias, with GPT-4 saying 'yes' up to 99% of the time. The results warn that using LLMs as random decision-makers in financial market simulations can inject strong, model-specific biases.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Table 2's Markov chi-square statistics are arithmetically inconsistent with the reported counts; if corrected, GPT-4o-Mini one-shot Q2 may satisfy both uniform and Markovian properties, collapsing the paper's central negative claim.","rationale":"The reader's weakest_assumption identifies exactly the load-bearing weakness: the Markov-property statistics in Table 2 are internally inconsistent, and the all-yes GPT-3.5 Q1 sequence is mislabeled as dependent. My analysis confirms this quantitatively. The central claim of the paper—most sharply stated in the abstract as 'no current GPT model can simultaneously achieve a uniform distribution and Markovian properties in one-shot testing'—rests on the GPT-4o-Mini Q2 result being non-Markovian. Under a correct chi-square computation using the paper's own reported counts, both GPT-4o-Mini rows fail to reject Markovian independence. If the raw sequences reproduce this, GPT-4o-Mini one-shot Q2 would be both uniform and Markovian, overturning the abstract's negative claim. The paper does contain independently supported findings: the extreme yes-bias of GPT-4-0125-preview and GPT-3.5-Turbo-0125 in one-shot testing is directly readable from Table 1 counts, and the few-shot averaging toward 50/50 is apparent in Table 3. These survive the correction. However, the non-Markovian one-shot conclusion is a headline contribution, and it is not currently supported. The reader's CONDITIONAL verdict remains appropriate: the manuscript should be revised to correct the statistical analysis and re-derive the conclusion. No ad hominem is intended; the issue is a concrete numerical inconsistency that should be checked and fixed.","tokens_in":12376,"tokens_out":7314,"duration_ms":75872,"concrete_test":"Obtain the raw one-shot response sequences for GPT-4o-Mini Q1 and Q2 (100 responses each). Recompute the first-order Markov chi-square test: form the 2x2 transition count table (Y_t-1 vs Y_t) and compute sum((O-E)^2/E) with df=1. If the corrected Q2 statistic is below 3.841 (or a Fisher exact test gives p>0.05), then the conclusion must be revised to state that GPT-4o-Mini one-shot Q2 achieves both uniformity and Markovianity. As a minimal analytical check, recompute Table 2 from the paper's own reported P(Y), P(Y|Y), and YY/n values; any correct implementation will produce approximately 0.5 and 0.8 for the two GPT-4o-Mini rows, not 21.9 and 36.2.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's one-shot conclusion that no model passes both the uniform-distribution test and the Markovian-independence test depends on Table 2. For GPT-4o-Mini Q1, the table reports P(Y)=0.32, P(Y|Y)=0.28, and YY/n=9/32 with n≈100. A standard 2x2 contingency-table chi-square test for first-order dependence gives chi2≈0.5 (df=1), not 21.9. For Q2, with P(Y)=0.43, P(Y|Y)=0.48, and YY/n=20/42, the same calculation gives chi2≈0.8-0.9, not 36.2. These are not rounding artifacts; the reported chi-square values would require much stronger differences between P(Y|Y) and P(Y|N) than the table displays. Additionally, the GPT-3.5 Q1 all-yes sequence (86/86 YY transitions) is labeled 'Reject* due to near-perfect dependence,' but a constant sequence has P(Y|Y)=P(Y)=1 and is fully consistent with H0: P(Yes_n|Yes_{n-1})=P(Yes_n); the chi-square test is degenerate and supplies no evidence against Markovianity. If the corrected GPT-4o-Mini Q2 Markov test fails to reject H0, then this model/question combination is both distributionally uniform (Table 1: chi2=1.96, p=0.162) and Markovian in the one-shot regime, directly contradicting the abstract's claim that no current GPT model can achieve both. The large yes-bias findings for GPT-4 and GPT-3.5, and the few-shot averaging result, remain supported by the counts; but the 'non-Markovian even in one-shot' component of the central claim is not.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports an empirical study of binary yes/no generation by three GPT models (GPT-4o-mini-2024-07-18, GPT-4-0125-preview, GPT-3.5-turbo-0125) under one-shot independent API calls and few-shot batched calls. It tests uniformity with chi-square goodness-of-fit tests, first-order Markovianity with chi-square tests on transition probabilities, the effect of temperature on both properties, the frequency of yes/no in Common Crawl data, and negative-recency behavior relative to Random.org binary sequences. The headline claim is that no model simultaneously achieves a uniform distribution and Markovian properties in one-shot testing, with GPT-4o-mini closest (uniform for Q2 but claimed non-Markovian), while few-shot averaging improves uniformity but introduces strong sequential alternation.","tokens_in":12740,"tokens_out":12252,"duration_ms":117216,"significance":"If the central claims survive correction, the paper is a timely and useful benchmark for LLM-as-agent design in financial agent-based models. The raw vote-share findings are informative and falsifiable: GPT-4-0125-preview and GPT-3.5-turbo-0125 show extreme yes bias, GPT-4o-mini is relatively balanced, and one-shot versus few-shot sampling produce strikingly different distributions. The temperature study and the comparison against Random.org and Common Crawl provide useful external reference points, and the paper is candid about the practical limitations of few-shot sampling for ABMs. However, the Markovianity analysis, which carries the paper's strongest negative claim, is not statistically sound as presented; the contribution will be credible only after the transition statistics are recomputed and the conclusions re-evaluated.","major_comments":[{"comment":"The chi-square statistics in Table 2 cannot be reproduced from the reported conditional probabilities and YY/n counts. For GPT-4o-Mini Q1, P(Y)=0.32 and YY/n=9/32 imply roughly 9 Yes→Yes, 23 Yes→No, 23 No→Yes, and 45 No→No transitions, giving a 2x2 chi-square statistic of about 0.3 on 1 degree of freedom, not 21.9. For Q2, P(Y)=0.43 and YY/n=20/42 give a statistic of about 0.6, not 36.2. Similar discrepancies appear in Table 4; for example, GPT-3.5 Q1 with P(Y)=0.50, P(Y|Y)=0.06, and YY/N=32/498 should produce a 2x2 chi-square near 700, not 187.4. The paper must report the full 2x2 transition tables and the exact test used, and the one-shot non-Markovian conclusion for GPT-4o-Mini is unsupported until this is corrected.","section":"Results, Table 2"},{"comment":"The all-yes sequence for GPT-3.5 Q1 is labeled 'Reject* due to near-perfect dependence,' but a constant sequence trivially satisfies H0: P(Yes_n|Yes_{n-1}) = P(Yes_n) because both probabilities are 1. The chi-square test is degenerate in this case and provides no evidence against Markovianity. Rejecting H0 for deterministic or near-deterministic sequences on the grounds of 'near-perfect dependence' is not a valid statistical procedure; if such sequences are excluded, the exclusion should be stated and justified a priori.","section":"Results, Table 2 (GPT-3.5 Q1)"},{"comment":"Table 5 states that 'All tests: Failed to reject H0 at α = 0.05' for GPT-4o-Mini across both questions and all temperature settings, and the text says this model 'produced Markovian response ... across both questions and all temperature settings.' This directly contradicts Table 2, which reports rejection of H0 for GPT-4o-Mini Q1 and Q2 at T=1. If Table 5 is correct, then GPT-4o-Mini Q2 in the one-shot regime may satisfy both uniformity (Table 1, p=0.162) and Markovianity, contradicting the abstract's central claim. The paper must resolve this internal inconsistency and clarify whether Tables 1/2 and Table 5 use the same or different API runs.","section":"Temperature section, Table 5"},{"comment":"The statement of H0 for the Markov test is incomplete: a first-order Markov test should compare P(Yes_n|Yes_{n-1}) with P(Yes_n|No_{n-1}), not with the marginal P(Yes_n). The paper never reports P(Yes|No) or the full transition count matrix, making the reported chi-square results uninterpretable. Please provide the full transition tables for every model/question/sampling condition and use a standard chi-square test of independence on those tables.","section":"Testing methodology, Hypothesis 2"},{"comment":"The methodology states that one-shot testing collects 100 responses per prompt, but Table 1 reports only 87 responses for GPT-3.5 Q1 (87 yes, 0 no). No explanation is given for the missing 13 responses, and other rows do not show their totals explicitly. This affects every subsequent statistic and must be clarified, including whether invalid or malformed responses were discarded.","section":"Results, Table 1"}],"minor_comments":[{"comment":"There are several typographical errors in model names: 'GPT-4o-mini-204-07-18' in the Few-Shot Results section, 'GPT-4o-Mini-2014-07-18' in the Temperature section, and 'GPT-4o-Mini-2034,07,18' in the Conclusion.","section":"Throughout"},{"comment":"The notation 'E[P(Y—Y)]' is nonstandard and should be written as an estimated conditional probability, e.g., \\hat{P}(Y|Y). The expression 'YY/n' is also ambiguous: in Tables 2 and 5 the denominator appears to be the number of Yes responses, not the total sequence length, so it should be defined explicitly.","section":"Tables 2, 4, 5"},{"comment":"The legend of Table 7 is unclear: R, A, R=NR, P=4, and P=5 are not defined in the text, and the table mixes three symbols per cell without a full caption explaining which test each symbol refers to.","section":"Table 7"},{"comment":"The header 'Prob. No Cond. Word % Prob.' is confusing and should be replaced with explicit column names such as P(Yes), P(Yes|Yes or No), and the fraction of pages containing neither term.","section":"Table 6"},{"comment":"Table 5 does not report uniformity test statistics, only P(Y), P(Y|Y), and YY/n, so the sweeping claim that temperature adjustments do not fix distributional bias is not fully supported by the displayed evidence; chi-square or p-values for uniformity should be added.","section":"Temperature section"}],"recommendation":"major_revision","confidential_remarks":"The paper's raw vote-share findings are likely salvageable, but the Markovianity analysis is internally inconsistent and arithmetically wrong as reported. I would ask the authors to supply the raw response sequences or full transition count matrices and to recompute all Markov tests before sending the paper back out for review. There is no indication of deliberate misreporting, but the central negative claim about one-shot testing is not supported by the current tables."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The thing to know: this paper has genuinely useful empirical data on binary response bias across specific GPT subversions, but the Markov-property analysis is statistically broken. The chi-square values in Table 2 cannot be derived from the reported counts. Once corrected, the central claim in the abstract—that no GPT model can achieve both uniformity and Markovian independence in one-shot testing—likely collapses for GPT-4o-Mini on Q2.\n\nWhat's new and what works: the paper extends Koevering & Kleinberg and Harrison by testing three named subversions (GPT-4o-Mini-2024-07-18, GPT-4-0125-preview, GPT-3.5-Turbo-0125), cleanly distinguishes one-shot from few-shot API sampling, sweeps temperature, and adds a Common Crawl frequency check. The raw counts convincingly show extreme yes-bias in GPT-4 and GPT-3.5, near-uniform behavior for GPT-4o-Mini on Q2, and few-shot averaging restoring 50/50 margins. For anyone building LLM-based agent simulations, that is a worthwhile caution.\n\nThe soft spot is load-bearing. For GPT-4o-Mini Q1, with P(Y)=0.32, P(Y|Y)=0.28, YY=9/32, and n≈100, a standard 2x2 chi-square test of independence gives roughly 0.5, not 21.9. For Q2, it's around 0.5, not 36.2. The reported values are not rounding artifacts; they imply much stronger dependence than the conditional probabilities display. Likewise, the all-yes GPT-3.5 Q1 sequence is labeled \"Reject* due to near-perfect dependence,\" but a constant sequence trivially satisfies H0: P(Yes|Yes)=P(Yes)=1. The test is degenerate and supplies no evidence against Markovianity. So the non-Markovian claim for GPT-4o-Mini one-shot is unsupported, and with it the abstract's blanket negative conclusion. The human-comparison and negative-recency sections are indirect and underpowered, but they are not the core.\n\nWho is this paper for? Researchers replacing random generators in ABMs with LLMs, and folks wanting a quick empirical map of binary response biases by model version. The bias counts are worth having; the Markov conclusions are not, until the analysis is redone.\n\nRecommendation: send to peer review as a major-revision candidate. The authors need to recompute the Markov tests with proper transition tables and revisit the central claim. The reader's conditional verdict is fair—solid empirical core, broken statistical appendix.","headline":"Useful bias data on GPT subversions, but Table 2's chi-squares don't match the counts and undercut the central non-Markovian claim.","tokens_in":13277,"tokens_out":5159,"would_cite":false,"duration_ms":48410,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"LLMs cannot reliably produce fair, memory-less binary decisions under independent sampling.","keywords":["large language models","binary decision bias","agent-based financial simulation","uniform distribution","Markov property","negative recency","temperature sampling","one-shot and few-shot sampling"],"falsifier":"Recompute the transition chi-square statistics from the raw response sequences. For GPT-4o-Mini Q1, the reported $P(\\text{Yes})=0.32$ and $P(\\text{Yes}|\\text{Yes})=0.28$ imply a chi-square value near $0.2$, not the reported $21.9$; if the corrected statistic is below the critical value of $3.841$, the one-shot non-Markovian claim for that model and prompt is unsupported.","tokens_in":12169,"feed_emoji":"🎲","tokens_out":10377,"duration_ms":91302,"temperature":0.7,"pith_summary":"The paper asks a narrow question with wide consequences: when a large language model is asked for a single 'yes or no' decision, the kind of binary choice an agent in a financial market simulation makes, does it behave like a fair coin? Across three GPT model versions, the answer is no for independent one-shot API queries: yes-rates ranged from 32% to 99% depending on model, prompt, and sub-version, and consecutive responses were not independent. The paper argues this matters because agent-based financial models assume each agent's decision is independent and memory-less, so biased or autocorrelated LLM decisions would silently distort simulated markets. It also finds that a few-shot regime, many answers from one API call, can make averaged distributions look close to uniform while hiding strong sequential dependencies, and that temperature tuning does not fix the problem. The intended takeaway is that LLM agents cannot be assumed to provide fair random binary choices, so their integration into financial simulations needs explicit bias evaluation.","feed_headline":"LLMs fail a fair-coin test that financial agents need","feed_subtitle":"Independent one-shot binary choices from three GPT versions are biased and non-Markovian, threatening simulation fairness.","key_machinery":"The central object is the binary response sequence produced by an LLM under two query regimes: one-shot (one decision per independent API call) and few-shot (100 comma-separated decisions in a single call). The paper evaluates each sequence with three statistical instruments: a chi-square goodness-of-fit test against a uniform 50/50 distribution, a chi-square test comparing $P(\\text{Yes}|\\text{yes on the previous decision})$ with $P(\\text{Yes})$ to test the Markov (memory-less) property, and a sliding-window recency measure, switching rate after runs of length $w$ minus baseline switching rate, to detect negative recency. A temperature sweep modifies the softmax scale $\\beta = 1/T$ to test whether output randomness can be controlled. These instruments carry the argument because they turn raw API responses into verdicts about uniformity, independence, and human-like bias.","core_discovery":"On the paper's own terms, the discovery is that state-of-the-art GPT models cannot reliably reproduce a uniform binary distribution under independent sampling, and that their response sequences violate the Markov property that financial simulations typically assume. The evidence is a two-prompt benchmark ('yes or no' and 'Answer randomly, yes or no') run on three specific model versions. GPT-4o-mini-2024-07-18 produced the least biased output, 32-43% yes across prompts, with one prompt statistically indistinguishable from uniformity, while GPT-4-0125-preview and GPT-3.5-turbo-0125 produced 87-99% yes. In one-shot testing, all response sequences except one were judged sequentially dependent, and even the near-uniform GPT-4o-mini sequence was non-Markovian. Few-shot sampling averaged over batches approximated 50/50 in most cases but produced pervasive within-batch dependence, and temperature settings from 0.5 to 2.0 failed to yield both uniform and Markovian output in any model. The paper concludes that sampling method, model sub-version, and prompt all materially change the bias, and that none of the tested configurations provides a fair, memory-less binary decision source.","pith_inferences":["A natural extension the authors do not develop is calibration: using the measured yes-bias to weight or reject-sample LLM responses could let financial ABMs keep the richness of LLM decisions without inheriting the bias.","The Common Crawl frequency analysis points to a testable training-data explanation: if 'yes' is systematically over-represented in pretraining text relative to 'no', then the bias should appear across LLM families and languages roughly in proportion to corpus imbalance.","The one-shot versus few-shot distinction maps onto two different ABM deployment patterns, individually queried agents versus centrally batched populations, so batch-generated agents are not exchangeable with independently sampled ones even when marginal distributions match.","The binary benchmark is cheap enough to serve as a pre-deployment screening test: run a few hundred one-shot 'yes or no' queries, check the yes-rate and the transition dependence, and reject configurations that fail before embedding them in a financial simulator."],"forward_implications":["One-shot LLM queries cannot be treated as fair random coin flips inside an agent-based financial simulation, because a model producing 87-99% yes responses would systematically skew every binary trading decision.","Few-shot batch responses are not a safe substitute for independent agent decisions, because averaging hides strong sequential dependence within the batch.","Violations of the Markov property mean that simulated agents' decisions are influenced by their own previous decisions, which can look like spurious herding or information leakage in a market model.","Choosing which model sub-version is deployed is a first-order design decision: GPT-4-0125-preview and GPT-4o-mini-2024-07-18 differ by roughly 60 percentage points in yes-rate on the same prompt.","Temperature adjustments do not provide a reliable randomness dial for binary choices, since no tested temperature produced both a uniform distribution and Markovian independence."],"supporting_citations":[{"why":"Supplies the coin-flip randomness and human-bias baseline that this paper extends to specific GPT sub-versions and two sampling regimes.","marker":"Koevering and Kleinberg 2024"},{"why":"Provides the earlier evaluation of LLM random-number generation and the sampling terminology this paper adapts into one-shot and few-shot query definitions.","marker":"Renda, Hopkins, and Carbin 2023"},{"why":"Contributes the comparison result that a GPT model can outperform humans on random-sequence tasks, the counterpoint this paper tests on binary yes/no sequences.","marker":"Harrison 2024"},{"why":"Supplies the age-stratified negative-recency model and sliding-window method used for the recency-bias comparisons.","marker":"Baena-Mirabete et al. 2023"},{"why":"Establishes the Markov and random-walk property in financial market modeling that motivates the independence tests.","marker":"Fama 1965"},{"why":"Prior LLM-in-ABM trading simulation whose one-shot query design and order-to-trade findings this paper builds on.","marker":"Vidler and Walsh 2024a"},{"why":"Data source for the yes/no word-frequency analysis used to connect model bias to pretraining text.","marker":"Common Crawl 2024"},{"why":"Supplies randomness metrics and repetition-avoidance findings used to compare LLM-generated sequences with human-generated sequences.","marker":"Angelike and Musch 2024"}],"fun_headline_variants":["GPT models flunk the coin-flip test for market sims","LLM binary choices are biased and non-Markovian","Financial sims beware: LLMs can't act random","GPT-4 preview says 'yes' 99%: not a fair coin","Even best GPT model can't simulate unbiased coin toss"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the statistical tests for sequential dependence were computed correctly from the raw response counts; if those numbers are wrong, the claim that one-shot responses are not memory-less collapses.","fun_headline_variants_meta":{"raw":{"variants":["GPT models flunk the coin-flip test for market sims","LLM binary choices are biased and non-Markovian","Financial sims beware: LLMs can't act random","GPT-4 preview says 'yes' 99%: not a fair coin","Even best GPT model can't simulate unbiased coin toss"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000221,"raw_usage":{"total_tokens":1508,"prompt_tokens":1059,"completion_tokens":449,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":675,"completion_tokens_details":{"reasoning_tokens":360}},"tokens_in":675,"tokens_out":449,"duration_ms":4759,"temperature":1.0,"reasoning_tokens":360,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T18:17:45.484351+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the transition chi-square statistics from the raw response sequences. For GPT-4o-Mini Q1, the reported $P(\\text{Yes})=0.32$ and $P(\\text{Yes}|\\text{Yes})=0.28$ imply a chi-square value near $0.2$, not the reported $21.9$; if the corrected statistic is below the critical value of $3.841$, the one-shot non-Markovian claim for that model and prompt is unsupported.","supporting_citations":[],"review_version":1}