1% ============================================================================2% Introduction (WP 26)3% Author: Simon-Pierre Boucher — simon-pierre.boucher@uqo.ca4% Numbers: results/evaluation*/summary.csv, contrasts.csv, cost.csv, repeat_variation.json,5% results/fundamental/eval_vs_resale_contrasts.csv, results/ledger/*.jsonl6% ============================================================================7\section{Introduction}8\label{sec:introduction}910Few numbers matter as much to a household, a lender or a municipality as the value of a dwelling, and few are as hard to observe. A transaction price is realised once, under the particular circumstances of one buyer and one seller; between transactions the value must be estimated, and the estimate governs how much a bank will lend, how much tax the owner pays, and at what price a listing is pitched. For most of the twentieth century the estimate was produced by an appraiser applying the sales-comparison method to a handful of recent sales. Over the last two decades automated valuation models, descended from the hedonic regression of \citet{rosen1974hedonic} and now dominated by gradient-boosted trees, have taken over the volume end of this work, with accuracy that rivals or exceeds manual appraisal in liquid markets and deteriorates, as appraisal does, in thin ones \citep{kok2017big, bogin2020appraisal, mullainathan2017machine}. The appraisal they replace is itself known to be a biased instrument: appraisers shrink toward comparables and anchor on the contract price, so that the recorded price partly reflects the valuation that financed it \citep{quan1991price, eriksen2019influence, calem2021appraising}.1112Large language models have entered this landscape with a different proposition. A model that can read a dossier of attributes, comparable sales and market indicators, reason about them in words and return a number is, in form, an appraiser, and a committee of such models given distinct roles, a comparables specialist, a market economist, an underwriter, a skeptic, is, in form, a valuation panel. The multi-agent literature in machine learning has argued that such committees improve on a single model when their members debate: independent answers are exchanged, criticised and revised, and the revised answers are aggregated \citep{du2023improving, liang2024encouraging}. If that argument carries over to valuation, the lender of the near future will consult a deliberating panel of artificial analysts rather than a regression. The question this paper asks is whether the deliberation adds anything. Put precisely: does communication among heterogeneous autonomous valuation agents add measurable information about the value of a property, beyond what the same agents know before they communicate, beyond what the same inference budget buys from one agent, and beyond what a strong tabular model extracts from the same data?1314The question is open because two literatures give opposite answers to it. The theory of forecast combination says that the value of a crowd is bounded by the correlation of its errors \citep{bates1969combination, clemen1985limits}, that diversity rather than individual ability is what averaging rewards \citep{hong2004groups}, and that social influence on a network is wise only when no member dominates \citep{degroot1974reaching, golub2010naive}; experiments with human crowds find that even mild exposure to others' estimates narrows the range of opinion without improving its centre \citep{lorenz2011how}, although decentralised exchange can help under the right structure \citep{becker2017network, navajas2018aggregated}. The language-model literature is divided along the same line. Against the early debate results stand findings that majority voting over independent samples captures most of the gain \citep{wang2022selfconsistency}, that debate rarely beats voting at matched cost \citep{smit2024should, wu2025can}, that similar models debating converge on the majority view including its errors \citep{estornell2024multi}, and that homogeneous agents with uniform updating cannot improve expected correctness by debating at all \citep{zhu2026demystifying}. Since the gains attributed to deliberation are routinely obtained by spending the same tokens on repeated sampling \citep{brown2024large, snell2024scaling}, any test of deliberation must separate communication from compute. In real estate, the handful of recent papers that apply language models to valuation use one model at a time: they report competitive point estimates and overconfident intervals from in-context examples \citep{geerts2025performance}, improve a boosted AVM with text features extracted by a model \citep{faxvaag2025incorporating}, fine-tune a model for quantile prediction \citep{vedula2025quantile}, or ask whether a model has internalised user-cost logic \citep{li2026large}. None has tested a deliberating committee against information-matched and cost-matched controls on registered transactions.1516We answer the question with a preregistered experiment on 631,866 arm's-length residential sales registered in Quebec between January 2021 and October 2026, drawn from the public land register and joined to the municipal assessment roll (422,542 houses, 122,976 condominium units and 86,348 small multi-unit buildings). The sample is split chronologically into a training window to June 2024, a validation window to March 2025, a test window from April to December 2025 and an untouched 2026 holdout, with a spatial holdout of three entire regions and a prospective set of 1,182 sales registered after the protocol was frozen. Every arm of the experiment receives the same information set, defined by a cutoff on the day before the sale and enforced by an audit of nine leakage checks, and the same opportunity to select comparables. Four non-agentic baselines, a hedonic regression, a hierarchical model with a repeat-sales adjustment, a tuned gradient-boosted model and an automated valuation model with as-of comparable features and conformal intervals, are fitted on the training window and tuned on validation only. Seven agentic arms share one evidence packet per property: a single generalist model; twelve role-specialised agents with least-privilege views of the packet, aggregated without communication; the same twelve agents in a structured debate of one, two or four rounds of critique and revision; the debate with a blinded skeptic and deterministic verification of citations and adjustments; a placebo committee with generic prompts on the same views; a full-view variant that removes the evidence partition; and a cost-matched single agent sampled twelve times and self-refined. The agents are drawn from two providers at identical list prices and assigned to roles by a seeded balanced permutation, so that a provider contrast is not a budget contrast. Every number in the paper traces to a stored transcript, and the four primary contrasts, each paired on the same properties and tested by a block bootstrap over municipality-by-month cells with Holm's correction \citep{cameron2008bootstrap, holm1979simple}, were written down before any test property was valued.1718The experiment is built on a model of valuation as decentralised information aggregation that tells us what to expect and what would count as evidence. Under correlated signals the equal-weight pool of $K$ agents has a mean-squared error floor of $\rho\sigma^{2}$ that no committee size removes; a revision rule in which agents move toward the committee statistic contracts the dispersion of their estimates by $(1-\lambda)^{r}$ after $r$ rounds without changing the pooled error, so that convergence is a measure of the anchoring weight, not of accuracy; evidence exchange lowers the pooled error only when it redistributes weight toward evidence outside the common view, and can raise it when it concentrates attention on evidence that is already popular; permuting role prompts while holding the evidence views fixed leaves the error distribution unchanged under additive separability; and no linear deliberation can beat the best pool of the round-0 estimates. Each proposition is mapped to a preregistered contrast, and the mapping is what allows a null result to be read as a finding rather than as an absence of one.1920The result is a precise null on deliberation and a more nuanced picture of the committee. On the test subsample at the mid-tier models, the single model reaches a mean absolute log error of 0.166, the twelve independent roles 0.159, the two-round debate 0.158, the debate with skeptic and verification 0.158, the placebo committee 0.157 and the cost-matched single agent 0.163; the automated valuation model scores 0.171 on the full test partition and 0.163 on the same eighty properties. Every preregistered paired contrast includes zero: the debate improves on the independent committee by 0.001 log points with a 95 percent interval of $[-0.006, 0.005]$, on the placebo committee by nothing at all, $[-0.005, 0.006]$, on the cost-matched single agent by 0.006, $[-0.017, 0.004]$, and on the AVM by 0.005, $[-0.033, 0.026]$, with Holm-adjusted $p$-values of one. The intervals rule out relative improvements from deliberation larger than about four percent against the independent committee and about seven percent against the compute-matched agent, which is not quite the two percent threshold that the preregistration set as the falsification criterion; we return to this in Section~\ref{sec:limitations}. Rounds of debate behave exactly as the theory predicts: the interquartile range of the agents' log estimates falls by roughly half after the first round and keeps falling, the anchoring index of the revisions is 0.7 to 0.8, and accuracy does not move. In the 2026 holdout and in the prospective set the debate is marginally worse than the independent committee, by 0.003 and 0.009 log points. The committees are not inaccurate: they are statistically indistinguishable from the AVM on the test subsample, and their median absolute percentage error is lower. But their intervals are about thirty percent narrower than the AVM's conformal intervals and cover 86 to 89 percent of prices at a nominal 90 percent, 78 to 81 percent at the small-model tier, and in the 2026 holdout the three agentic arms overvalue by ten log points where the AVM is unbiased, a drift that no amount of deliberation corrects because every agent in the committee shares it. The committee's explanations are faithful in the narrow sense the audit can verify, every cited evidence identifier exists in the packet, 96 to 99 percent of stated adjustments lie within forty percent of the raw comparable price and about 99 percent of points lie inside the hull of the adjusted comparables, but faithful explanations do not translate into calibrated intervals. A two-round debate costs about 1.52 US dollars and 5.6 minutes per property, against 0.23 dollars for the independent committee and about two cents for a single model; the AVM costs nothing at the margin. Finally, on the 92,089 sales with a later resale, the gradient-boosted baselines lie measurably closer to the market-adjusted resale value than the realised first price does; the same test for the agentic arms is specified but deferred, because too few of the evaluated properties have yet resold.2122The paper makes four contributions. The first is a design that isolates communication from its confounds. The independent committee supplies the round-0 estimates of the debate, so that their difference is communication and nothing else; the cost-matched single agent supplies the same tokens without roles or communication; the placebo committee supplies the same views and mechanics without mandates; the full-view variant supplies the same mandates without the partition; and the information set, the comparable pool, the providers and the budget are held fixed across all of them. To our knowledge no evaluation of language-model deliberation in any domain has run all of these controls on the same properties under a frozen protocol. The second is the theory, which is elementary but, we think, clarifying: it shows that the convergence statistics on which debate systems are often judged are uninformative about accuracy, identifies the single channel through which communication can add information, and shows that the placebo contrast identifies prompt-evidence complementarity rather than the value of role diversity. The third is the Quebec evidence itself, the first on language-model valuation in the province and, to our knowledge, the first to use registered sales from a public land register rather than listing or portal data, with a leakage-defended as-of pipeline, chronological, spatial and prospective holdouts, calibration at four levels, a faithfulness audit, measured run-to-run variation and full cost accounting, and with the distinction between transaction-price prediction and fundamental value kept explicit throughout. The fourth is the set of open artefacts: the code, the configuration, the role prompts with their hashes, the freeze record, the ledgers and the evaluation outputs are released, together with a labelled synthetic dataset and a mock provider that allow the entire pipeline to run without keys or proprietary data, so that the null can be challenged by extending the same runs rather than by repeating them.2324Three bodies of prior work are closest. The hedonic and AVM literature, from \citet{rosen1974hedonic} to the tabular benchmarks of \citet{kok2017big} and \citet{bogin2020appraisal}, provides the baselines and the standard that any new method must meet; the Quebec hedonic studies reviewed in Section~\ref{sec:literature} provide the institutional antecedents. The forecast-combination and social-learning literature, from \citet{bates1969combination} and \citet{clemen1985limits} to \citet{golub2010naive} and \citet{lorenz2011how}, provides the propositions, which we restate for a committee with an explicit evidence partition and a provider structure. The multi-agent debate literature, from \citet{du2023improving} to the sceptical results of \citet{smit2024should}, \citet{estornell2024multi} and \citet{zhu2026demystifying}, provides the hypothesis under test and the warning that compute must be matched; our contribution relative to it is a domain with a continuous, noisy, selected target and strong non-neural baselines, and a design in which the channels those papers conflate are separately identified. We do not claim priority for applying language models to property valuation, which \citet{geerts2025performance}, \citet{faxvaag2025incorporating}, \citet{vedula2025quantile} and others have done; our claim is about what deliberation among such models does and does not add. The policy relevance follows from the finding rather than preceding it: if committees of agents built on two or three foundation models are no more accurate than a tabular model, systematically narrower in their stated uncertainty, and jointly biased when the market moves, then the concern about algorithmic monoculture raised by \citet{kleinberg2021algorithmic} and \citet{bommasani2022picking} applies to collateral valuation with particular force, and the welfare model of Section~\ref{sec:welfare} shows why the variance of system losses, not their mean, is where that concern bites.2526The remainder of the paper is organised as follows. Section~\ref{sec:literature} reviews the five literatures on which the study draws and states what it adds. Section~\ref{sec:theory} sets out the model of valuation as information aggregation, defines the objects that the empirical work can and cannot identify, and derives the propositions. Section~\ref{sec:setting} describes the Quebec records and the institutional facts that shape the identification strategy, and Section~\ref{sec:data} the sample, the partitions, the information-set rules and the leakage audit. Section~\ref{sec:architecture} describes the evidence packet, the roles, the output contract, the providers, the protocols and the audit trail, and Section~\ref{sec:design} the arms, the preregistered hypotheses, the metrics, the inference and the freeze. Section~\ref{sec:results} reports the main results, Section~\ref{sec:ablations} the ablations and robustness checks, including the rounds grid, the provider committees, the spatial holdout and the prospective set, and Section~\ref{sec:calibration} the calibration and faithfulness audits. Section~\ref{sec:fundamental} triangulates fundamental value with repeat sales, rents and user cost. Section~\ref{sec:welfare} works out what the accuracy results do and do not imply for buyers, sellers and lenders. Section~\ref{sec:limitations} records the limitations, and Section~\ref{sec:conclusion} concludes. The appendices contain the reproducibility record, the role prompts, the output contract, additional tables and the proofs.27