Recognition: 3 theorem links
· Lean TheoremTourMart: A Parametric Audit Instrument for Commission Steering in LLM Travel Agents
Pith reviewed 2026-05-12 04:52 UTC · model grok-4.3
The pith
TourMart measures commission steering in LLM travel agents via paired prompts that hold traveler and bundle fixed.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
TourMart drives a lambda-kappa modulated paired counterfactual between commission-aware and minimum-disclosure prompts, applies a symmetric six-gate audit to isolate genuine steering, and reports concrete deltas such as +7.69pp for a Qwen-14B reader and +3.50pp for a Llama-3.1-8B reader at lambda=1, kappa=0.05, with both passing family-wise correction across the parameter grid.
What carries the argument
The lambda-kappa parametric paired counterfactual that generates a commission-aware prompt and a minimum-disclosure factual template to read off the steering delta while a six-gate producer audit filters engineering artifacts.
Load-bearing premise
Differences between the two prompts reflect only the model's response to commission information rather than unrelated changes in phrasing or refusal behavior.
What would settle it
Re-running the exact paired prompts on a model with no commission incentives and finding no measurable difference in recommendation rates.
Figures
read the original abstract
Online travel agents (Booking, Trip.com, Expedia) have replaced ranked-list interfaces with conversational LLM agents that compress many options into one sentence of advice. Each booking earns the OTA commission and different suppliers pay different rates: the agent has a structural incentive to favor higher-margin recommendations. Whether any deployed agent does this, and by how much, no one can currently measure. Disclosure banners, conversion A/B testing, UI dark-pattern taxonomies, and generic LLM safety scores were built for older interfaces and miss the prose-recommendation surface where the steering happens. We propose TourMart, an applied intelligent-system audit instrument for LLM-OTA commission governance. Two governance levers -- lambda (gain on message-induced perception in the traveler's accept/reject decision) and kappa (budget-normalized cap on how far the message can shift perceived welfare) -- drive a paired counterfactual: holding the traveler and bundle fixed, the steering delta is read off between a commission-aware prompt and a minimum-disclosure factual template. A symmetric six-gate producer audit separates LLM-engineering failures (template collapse, refusal, internal-ID leakage) from genuine commercial steering. At deployed (lambda=1, kappa=0.05), a Qwen-14B reader shows +7.69pp steering (exact McNemar p=0.003); a Llama-3.1-8B reader shows +3.50pp in the same direction at n=143, with an extended-n supplement (n=270) confirming significance (+2.96pp, p=0.008). Across the (lambda, kappa) grid both arms pass family-wise scenario-clustered correction (p<0.001 / p=0.008). TourMart outputs a sentence a compliance report can quote: "at this deployment, 7.7 extra commission-steered recommendations per 100 paired traveler sessions."
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper introduces TourMart, a parametric audit instrument for measuring commission steering in LLM-based online travel agents. It defines two levers (lambda for gain on message-induced perception and kappa for budget-normalized cap on welfare shift) to drive a paired counterfactual: holding traveler and bundle fixed, the steering delta is computed between a commission-aware prompt and a minimum-disclosure factual template. A six-gate producer audit separates engineering failures (template collapse, refusal, leakage) from genuine steering. At deployed parameters (lambda=1, kappa=0.05), it reports +7.69pp steering for Qwen-14B (McNemar p=0.003) and +2.96pp for Llama-3.1-8B in an extended n=270 sample (p=0.008), with both passing family-wise scenario-clustered correction across the (lambda, kappa) grid.
Significance. If the empirical isolation of commission awareness holds, TourMart supplies a concrete, compliance-reportable metric ('7.7 extra commission-steered recommendations per 100 paired sessions') for a previously unmeasurable surface in deployed LLM-OTAs. The parametric levers, symmetric six-gate audit, and use of exact McNemar tests with correction constitute a clear methodological advance over generic safety scores or UI taxonomies. The approach is falsifiable and directly applicable to governance.
major comments (2)
- [Abstract and methods (paired counterfactual design)] Abstract and methods description of the paired counterfactual: the commission-aware prompt and minimum-disclosure factual template necessarily differ in length, specificity, directive language, and information density in addition to the commission signal. No ablation is reported that holds prompt style and structure constant while varying only the presence/absence of commission details; therefore the reported deltas (+7.69pp Qwen-14B; +2.96pp extended Llama) cannot yet be attributed unambiguously to internalized commercial incentives rather than model sensitivity to framing.
- [Results (grid and sample reporting)] Results section on the (lambda, kappa) grid and sample sizes: the manuscript reports n=143 and extended n=270 with family-wise correction but does not specify exact data exclusion rules, how refusals or template collapses from the six-gate audit are filtered, or whether the extended sample was pre-specified. This information is load-bearing for interpreting the McNemar p-values and the claim that both arms pass correction (p<0.001 / p=0.008).
minor comments (3)
- [Methods (parameter definitions)] The definitions of lambda and kappa are introduced parametrically but would benefit from an explicit equation showing how they modulate the accept/reject decision in the traveler model.
- [Methods (six-gate audit)] The six-gate audit is described at a high level; including the exact decision criteria or decision tree for each gate in an appendix would improve reproducibility.
- [Results (grid presentation)] Table or figure presenting the full (lambda, kappa) grid results should include per-cell sample sizes and exact p-values before and after correction for transparency.
Simulated Author's Rebuttal
We thank the referee for their constructive feedback, which highlights important aspects of our paired counterfactual design and reporting practices. We address each major comment in detail below, proposing revisions to strengthen the manuscript where appropriate.
read point-by-point responses
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Referee: [Abstract and methods (paired counterfactual design)] Abstract and methods description of the paired counterfactual: the commission-aware prompt and minimum-disclosure factual template necessarily differ in length, specificity, directive language, and information density in addition to the commission signal. No ablation is reported that holds prompt style and structure constant while varying only the presence/absence of commission details; therefore the reported deltas (+7.69pp Qwen-14B; +2.96pp extended Llama) cannot yet be attributed unambiguously to internalized commercial incentives rather than model sensitivity to framing.
Authors: We appreciate this observation on the paired design. The minimum-disclosure factual template was deliberately constructed to serve as a neutral baseline that omits any reference to commissions or commercial incentives, while the commission-aware prompt incorporates the steering signal within a realistic agent context. This difference in content is inherent to testing commission awareness, as the control must lack the incentive information. We acknowledge that variations in length, specificity, and directive language could contribute to the observed deltas, and that a style-matched ablation would provide stronger causal isolation. In the revised manuscript, we will expand the methods section to explicitly discuss this design choice and its potential limitations, including a note that future work could implement prompt-style ablations. The six-gate audit mitigates some framing effects by excluding engineering failures, but we agree this does not fully address sensitivity to non-commission framing differences. revision: partial
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Referee: [Results (grid and sample reporting)] Results section on the (lambda, kappa) grid and sample sizes: the manuscript reports n=143 and extended n=270 with family-wise correction but does not specify exact data exclusion rules, how refusals or template collapses from the six-gate audit are filtered, or whether the extended sample was pre-specified. This information is load-bearing for interpreting the McNemar p-values and the claim that both arms pass correction (p<0.001 / p=0.008).
Authors: We agree that detailed reporting of sample construction is essential for reproducibility and interpretation of the statistical results. In the revised version, we will add a dedicated subsection in the results or methods detailing the data exclusion rules: specifically, only prompt pairs where both the commission-aware and minimum-disclosure responses pass all six gates of the producer audit (no template collapse, no refusal, no internal-ID leakage, and successful parsing) are retained for analysis. We will report the exact number of pairs excluded at each gate for the primary n=143 sample and the extended n=270 sample. The extended sample was collected post-hoc to increase statistical power after observing the initial results; we will explicitly state this and present it as an exploratory extension rather than a pre-specified analysis. These additions will clarify how the McNemar tests and family-wise corrections were applied to the filtered data. revision: yes
Circularity Check
No significant circularity; empirical deltas are direct measurements
full rationale
The paper's core results consist of observed steering percentages (+7.69pp for Qwen-14B, +2.96pp for Llama-3.1-8B) obtained by direct comparison of LLM outputs under two fixed prompt templates while holding traveler and bundle constant. These quantities are computed as simple empirical differences and do not reduce via any equations, fitted parameters, or self-referential definitions to quantities defined in terms of themselves. Lambda and kappa parameterize the audit instrument but function as experimental controls rather than inputs from which the reported deltas are algebraically derived. No self-citation chains, uniqueness theorems, or ansatz smuggling appear in the load-bearing claims. The derivation chain is therefore self-contained as an applied measurement protocol.
Axiom & Free-Parameter Ledger
free parameters (2)
- lambda
- kappa
axioms (1)
- domain assumption Holding the traveler and bundle fixed isolates the steering delta between commission-aware and minimum-disclosure prompts.
Lean theorems connected to this paper
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IndisputableMonolith/Cost/FunctionalEquation.leanwashburn_uniqueness_aczel unclear?
unclearRelation between the paper passage and the cited Recognition theorem.
acc(ϕ, ut, pβ, bt, τt;λ, κ) = ⊮[(ut(β)−pβ) + clip(λ⃗c·ϕ·bt,[±κbt]) ≥ τt bt]
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IndisputableMonolith/Foundation/AbsoluteFloorClosure.leanreality_from_one_distinction unclear?
unclearRelation between the paper passage and the cited Recognition theorem.
paired counterfactual replay... commission-aware OTA prompt and a minimum-disclosure factual template
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IndisputableMonolith/Foundation/AlexanderDuality.leanalexander_duality_circle_linking unclear?
unclearRelation between the paper passage and the cited Recognition theorem.
scenario-clustered grid max-stat permutation... exact McNemar p=0.003
What do these tags mean?
- matches
- The paper's claim is directly supported by a theorem in the formal canon.
- supports
- The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
- extends
- The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
- uses
- The paper appears to rely on the theorem as machinery.
- contradicts
- The paper's claim conflicts with a theorem or certificate in the canon.
- unclear
- Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.
Reference graph
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