1% ============================================================================2\section{Related Literature}3\label{sec:literature}4% ============================================================================56This paper draws on five literatures, reviewed briefly below before we state what the study adds and what it does not claim.78\subsection{Hedonic Models and Automated Valuation}9\label{subsec:lit_hedonic}1011The hedonic approach treats a dwelling as a bundle of characteristics whose implicit prices are revealed in equilibrium \citep{rosen1974hedonic}; applied reviews document wide variation in functional form, attributes and spatial treatment \citep{malpezzi2003hedonic, sirmans2005composition}, and \citet{hill2013hedonic} surveys the resulting index methods. Repeat-sales indexes \citep{bailey1963regression, case1987prices} abstract from attribute measurement but require repeated transfers. Spatial dependence is first-order: \citet{pace1998spatial} and \citet{pace1998spatiotemporal} introduce spatial and spatiotemporal autoregressive structures for real estate, systematised by \citet{lesage2009introduction}. For Quebec, the closest hedonic antecedents are the Quebec City and Montreal studies of Des Rosiers, Th\'eriault and Dub\'e on access and neighbourhood factors \citep{desrosiers2000sorting}, transit investments \citep{dube2014spatial}, the joint determination of price and time on the market \citep{dube2016spatiotemporal} and residential reconversions \citep{dube2023residential}. On the automated-valuation side, \citet{mullainathan2017machine} frame prediction as a distinct econometric task; \citet{kok2017big}, \citet{mayer2019estimation} and \citet{perezrave2019machine} compare manual appraisal, hedonic updating and big-data regression; gradient-boosted trees \citep{chen2016xgboost, prokhorenkova2018catboost} remain the strongest tabular baselines \citep{grinsztajn2022why}; \citet{bogin2020appraisal} show that both AVM and appraisal accuracy deteriorate in thin rural markets; and listing text adds information at the margin \citep{nowak2017textual, shen2021information, zhang2024describe}.1213\subsection{Appraisal Accuracy and Bias}14\label{subsec:lit_appraisal}1516\citet{quan1991price} model appraisal as signal extraction with shrinkage toward comparables, and \citet{northcraft1987experts} show that professionals anchor on listing prices. \citet{cho1996empirical} link appraisal to redlining and \citet{nakamura2010how} to house-price uncertainty. Purchase-mortgage data reveal confirmation bias toward contract prices, with a sharply asymmetric appraisal-to-contract ratio \citep{calem2021appraising, eriksen2019influence, eriksen2020contract}, and low appraisals pull contract prices down \citep{fout2022when}. \citet{agarwal2015collateral} measure the collateral-valuation response of constrained borrowers, \citet{agarwal2020regulation} ask whether regulation de-biases appraisers, and \citet{shui2018appraisal} find no quality difference between appraisals routed through management companies and others. Racial valuation gaps are documented by \citet{howell2018neighborhoods}, \citet{howell2021increasing}, \citet{perry2018devaluation} and \citet{freddiemac2021racial}, and \citet{fuster2022predictably} show that algorithmic credit decisions reshape such disparities. These findings motivate our treatment of prices as noisy, possibly biased proxies.1718\subsection{Information Aggregation and Deliberation}19\label{subsec:lit_aggregation}2021The case for averaging independent judgements \citep{galton1907vox, surowiecki2004wisdom} is formalised in the forecast-combination literature \citep{bates1969combination, clemen1989combining, timmermann2006forecast}, where trimmed, extremised or logit-pooled aggregates dominate simple means when forecasts are miscalibrated \citep{ranjan2010combining, satopaa2014combining, jose2014trimmed}. The value of a crowd is bounded by the correlation of its errors \citep{clemen1985limits}, and diversity often matters more than individual ability \citep{hong2004groups, lamberson2012optimal, davisstober2014when}. Social influence is double-edged: averaging on a network is wise only if no agent is too influential \citep{degroot1974reaching, golub2010naive}, Bayesian learning on networks has its own limits \citep{acemoglu2011bayesian}, sequential observation produces cascades \citep{bikhchandani1992theory}, and public signals crowd out private information \citep{morris2002social}. Experimentally, \citet{lorenz2011how} find that mild social influence narrows the diversity of estimates and undermines crowd wisdom, \citet{becker2017network} find that decentralised communication can improve accuracy, \citet{navajas2018aggregated} report that small deliberating groups outperform large non-interacting crowds, and \citet{prelec2017solution} recover the truth from meta-knowledge when the majority is wrong.2223The literature on large language models (LLMs) revisits these questions with artificial agents. Multi-agent debate was proposed to improve factuality and reasoning \citep{du2023improving, liang2024encouraging, chan2023chateval}, building on the debate paradigm of \citet{irving2018ai} and on evidence that persuasive debaters help weaker judges \citep{khan2024debating, michael2023debate}; frameworks such as CAMEL, AutoGen, MetaGPT and generative agents \citep{li2023camel, wu2023autogen, hong2023metagpt, park2023generative} made role-based agent societies easy to build, and \citet{guo2024large} survey the design space. Whether debate adds information beyond ensembling is contested. \citet{wang2022selfconsistency} show that majority voting over independent samples captures much of the gain; \citet{smit2024should}, \citet{wang2024rethinking}, \citet{kaesberg2025voting} and \citet{wu2025can} find that debate often fails to beat voting at matched cost and that majority pressure suppresses independent correction; \citet{estornell2024multi} show that debate among similar models converges to the majority view, including shared misconceptions; and \citet{zhu2026demystifying} show that with homogeneous agents and uniform updating debate cannot improve expected correctness. The compute-scaling results of \citet{chen2024more}, \citet{li2024more}, \citet{brown2024large} and \citet{snell2024scaling} are decisive for our design: any benefit of deliberation must be separated from more samples or more inference compute. Finally, LLMs are calibrated only under some elicitation schemes and are frequently overconfident \citep{kadavath2022language, tian2023just, xiong2024can}, and their stated reasoning is not always faithful to the computation behind the answer \citep{turpin2023language, lanham2023measuring}; we therefore evaluate explanations by the faithfulness standard of \citet{jacovi2020towards} rather than by plausibility.2425\subsection{LLMs as Forecasters and Valuers}26\label{subsec:lit_llmvaluation}2728\citet{halawi2024approaching} approach human crowd accuracy on forecasting tournaments, and \citet{schoenegger2024wisdom} find that an ensemble of twelve LLMs rivals a human crowd whereas single models lag it \citep{schoenegger2023large}. In real estate, prior work is recent and sparse. \citet{geerts2025performance} evaluate single LLMs on international housing datasets with in-context examples and report competitive point estimates but overconfident intervals and weak spatial reasoning; \citet{faxvaag2025incorporating} use LLM-extracted listing-text features to improve a gradient-boosting AVM; \citet{vedula2025quantile} fine-tune LLMs for quantile price prediction; \citet{chen2024predicting} compare ChatGPT with machine learning for Shanghai rents; \citet{bae2025housing} propose a single-model valuation and reasoning pipeline; and \citet{li2026large} ask whether one LLM internalises user-cost logic when valuing dwellings for surveyed UK households. None implements deliberation among specialised agents, cost-matched comparisons with ensembles and strong non-LLM baselines on arm's-length transactions, or a joint evaluation of calibration and explanation faithfulness.2930\subsection{Uncertainty, Evaluation and Model Comparison}31\label{subsec:lit_uncertainty}3233Proper scoring rules \citep{matheson1976scoring, gneiting2007strictly, gneiting2014probabilistic} and quantile loss \citep{koenker1978regression} reward calibrated and sharp predictive distributions, and conformal prediction \citep{vovk2005algorithmic, lei2018distribution, romano2019conformalized, angelopoulos2023gentle} provides finite-sample coverage against which LLM-elicited intervals are benchmarked. Accuracy comparisons use \citet{diebold1995comparing} with the correction of \citet{harvey1997testing}, the conditional framework of \citet{giacomini2006tests} and the model confidence set of \citet{hansen2011model}; dependence across properties, neighbourhoods and time is handled by block and stationary bootstraps \citep{kunsch1989jackknife, politis1994stationary} and clustered bootstrap inference \citep{cameron2008bootstrap}, and multiplicity by \citet{holm1979simple}.3435\subsection{Fundamental Value and Transaction Prices}36\label{subsec:lit_fundamental}3738A transaction price is the outcome of search and bargaining, not an observation of fundamental value. The user-cost framework \citep{poterba1984tax, himmelberg2005assessing} and variance decompositions of the rent-price ratio \citep{campbell2009what} define fundamental value through discounted housing services, financing costs, taxes, risk and expected appreciation, and evidence of predictable returns and extrapolative expectations \citep{case1989efficiency, glaeser2017extrapolative} implies persistent deviations from fundamentals. Search frictions \citep{wheaton1990vacancy, han2015microstructure}, seller loss aversion \citep{genesove2001loss} and collateral constraints \citep{stein1995prices, kiyotaki1997credit, iacoviello2005house, mian2011house} add transaction-specific noise and liquidity premia; official Canadian and Quebec data products \citep{statcan2024chsp, mamh2024manuel} frame the institutional setting. Finally, \citet{kleinberg2021algorithmic} show that algorithmic monoculture can lower welfare even when each algorithm is individually more accurate, and \citet{bommasani2022picking} document outcome homogenisation when decision-makers share a model; because our agents rest on a few foundation models, correlated errors are a market-design concern as well as a statistical one.3940\subsection{Position of This Paper}41\label{subsec:lit_position}4243The paper makes three contributions. First, it brings the theory of aggregation under correlated signals to bear on LLM deliberation, deriving testable conditions on correlation, diversity and communication structure under which deliberation reduces or increases mean-squared valuation error. Second, it provides, to our knowledge, the first evaluation of specialised multi-agent deliberation for residential valuation on arm's-length transactions that is matched on information, compute and provider against hedonic, repeat-sales, gradient-boosting, AVM and single-LLM baselines, reporting calibration, tail errors and explanation faithfulness alongside point accuracy. Third, it separates transaction-price prediction from fundamental value, triangulated with repeat sales, rents and user-cost diagnostics, in a Quebec setting with hedonic but no LLM-based evidence. We do not claim to be the first to apply LLMs to property valuation, to study multi-agent debate, or to model Quebec housing; the novelty lies in the joint design that isolates whether communication among heterogeneous agents adds information, and in reporting a negative answer should the data support it.44