pith. machine review for the scientific record. sign in

arxiv: 2604.08606 · v1 · submitted 2026-04-08 · 💻 cs.GT · cs.AI· econ.TH

Recognition: unknown

Extrapolating Volition with Recursive Information Markets

Abhimanyu Pallavi Sudhir , Long Tran-Thanh
Authors on Pith no claims yet

Pith reviewed 2026-05-10 17:15 UTC · model grok-4.3

classification 💻 cs.GT cs.AIecon.TH
keywords information marketsLLM buyersvalue of informationinspection paradoxrecursive mechanismsextrapolated volitionAI alignmentscalable oversight
0
0 comments X

The pith

Recursive information markets with LLM buyers that forget inspected data price information according to its true value.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines a mechanism to fix information markets where buyers face an asymmetry: inspecting a piece of information gives it away for free, so no one pays. Large language models serve as buyers that can inspect then forget the content, breaking the paradox. The authors focus on a recursive version of this setup and analyze it using a value-of-information approach to check whether sellers are paid exactly what the information is worth to the eventual user. This approach matters for building reliable markets in data and for scaling oversight of advanced AI systems through processes related to extrapolated volition.

Core claim

The recursive LLM-buyer information market resolves the buyer's inspection paradox by letting the model inspect information, compute its value, and then forget the details before deciding on purchase. Formal analysis through the value-of-information paradigm shows that this design creates incentives for information to be priced and supplied in line with its actual worth, with the recursion allowing repeated application across layers of evaluation.

What carries the argument

The recursive information market mechanism in which LLM buyers inspect, value, and forget information to eliminate the inspection paradox while preserving value-of-information incentives.

If this is right

  • Information sellers receive payments that match the true downstream value of what they provide.
  • The mechanism supports repeated, layered evaluation suitable for oversight tasks.
  • Applications emerge in AI alignment where successive rounds can extrapolate preferences or values.
  • Market efficiency improves because buyers no longer need to pay without first verifying content.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same forgetting step could be adapted to other buyer types if reliable deletion protocols are engineered.
  • Testing with current LLMs in simulated recursive markets would reveal whether value calculations remain accurate across multiple rounds.
  • Connections to prediction markets suggest the approach might generalize beyond static information to dynamic forecasts.

Load-bearing premise

LLM buyers can reliably forget inspected information without any residual effects that would let them retain value or distort the market's pricing signals.

What would settle it

A controlled market simulation in which an LLM buyer retains usable fragments of inspected information and still refuses to pay full price, showing the forgetting step fails to preserve incentives.

Figures

Figures reproduced from arXiv: 2604.08606 by Abhimanyu Pallavi Sudhir, Long Tran-Thanh.

Figure 1
Figure 1. Figure 1: Recursive Inspection as an imperfect recall game; [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The Recursive Inspection Protocol Unfortunately, our marginal value mechanism does not satisfy this hope. Take the following example. Example 6.1. Suppose our decision problem is {0, 1} and: • in our prior judgement, 0 is the better choice: E[𝑈 (0)] = 1, E[𝑈 (1)] = 0 • 𝐼1 tells us 1 is better: E[𝑈 (0)|𝐼1] = 0, E[𝑈 (1)|𝐼1] = 1 • 𝐼2 refutes 𝐼1 and says 0 is better: E[𝑈 (0)|𝐼1, 𝐼2] = 1 and E[𝑈 (1)|𝐼1, 𝐼2] = 0… view at source ↗
Figure 3
Figure 3. Figure 3: Screenshots from the infonomy-server platform of defending the correct information”—and we may also use the expression for such a shortfall as a measure of how good a particular scalable oversight protocol is. REFERENCES [1] George A Akerlof. 1978. The market for “lemons”: Quality uncertainty and the market mechanism. In Uncertainty in economics. Elsevier, 235–251. [2] K. J. Arrow. 1972. Economic Welfare a… view at source ↗
read the original abstract

One of the impediments to the efficiency of information markets is the inherent information asymmetry present in them, exacerbated by the "buyer's inspection paradox" (the buyer cannot mitigate the asymmetry by "inspecting" the information, because in doing so the buyer obtains the information without paying for it). Previous work has suggested that using Large Language Model (LLM) buyers to inspect and purchase information could overcome this information asymmetry, as an LLM buyer can simply "forget" the information it inspects. In this work, we analyze this mechanism formally through a "value-of-information" paradigm, i.e. whether it incentivizes information to be priced and provided in accordance with its "true value". We focus in particular on our new recursive version of the mechanism, which we believe has a range of applications including in AI alignment research, where it is related to Extrapolated Volition and Scalable Oversight.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper proposes a recursive information market mechanism in which LLM buyers inspect and then 'forget' signals to overcome the buyer's inspection paradox in information markets. It analyzes the mechanism via a value-of-information paradigm, claiming that the resulting prices reflect the true marginal value of information, and highlights applications to extrapolating volition and scalable oversight in AI alignment.

Significance. If the central incentive-compatibility claim holds, the construction would supply a market-based method for eliciting and pricing information according to its contribution to extrapolated preferences, with direct relevance to AI alignment techniques that rely on recursive oversight. The paper's emphasis on a parameter-free equilibrium (if derived) and the explicit link to extrapolated volition would constitute a substantive contribution to both mechanism design and alignment research.

major comments (3)
  1. [§3] §3 (Recursive Mechanism Definition): The value-of-information equilibrium is asserted to price information at its 'true value,' yet the manuscript supplies no explicit recursive equation or fixed-point characterization showing how the forgetting operator propagates marginal value across levels. Without this derivation, it is impossible to verify that the claimed alignment between market price and true value is a derived property rather than an assumption.
  2. [§4] §4 (Value-of-Information Analysis): The incentive-compatibility argument rests on the exogenous assumption that an LLM buyer can perfectly forget inspected information. No formal operator, retention model, or proof of incentive compatibility is given; partial retention would alter willingness-to-pay at subsequent recursion levels and undermine the equilibrium claim.
  3. [§5] §5 (Application to Extrapolated Volition): The link between the market prices and extrapolated volition is stated but not formalized. No theorem or proposition demonstrates that the equilibrium prices converge to the volition-extrapolation functional under the recursive construction.
minor comments (2)
  1. [§3] Notation for the forgetting operator is introduced informally; a compact mathematical definition would improve readability.
  2. [Introduction] The abstract and introduction both refer to 'true value' without an initial formal definition; this should be supplied before the value-of-information analysis.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments, which correctly identify opportunities to strengthen the formal foundations of the recursive mechanism. We will revise the manuscript to incorporate explicit derivations and propositions addressing the points raised, while preserving the core conceptual contributions.

read point-by-point responses

  1. Referee: [§3] §3 (Recursive Mechanism Definition): The value-of-information equilibrium is asserted to price information at its 'true value,' yet the manuscript supplies no explicit recursive equation or fixed-point characterization showing how the forgetting operator propagates marginal value across levels. Without this derivation, it is impossible to verify that the claimed alignment between market price and true value is a derived property rather than an assumption.

    Authors: We agree that the manuscript would be improved by an explicit recursive characterization. The current draft describes the mechanism and its value-of-information properties at a conceptual level but does not supply the fixed-point equation. In the revision we will add a formal recursive definition in §3 that models the forgetting operator as a state reset and derives the equilibrium condition under which market prices equal marginal value across recursion levels. revision: yes

  2. Referee: [§4] §4 (Value-of-Information Analysis): The incentive-compatibility argument rests on the exogenous assumption that an LLM buyer can perfectly forget inspected information. No formal operator, retention model, or proof of incentive compatibility is given; partial retention would alter willingness-to-pay at subsequent recursion levels and undermine the equilibrium claim.

    Authors: The paper treats perfect forgetting as an ideal property of the LLM buyer that resolves the inspection paradox, as noted in the abstract. We acknowledge that no formal operator or incentive-compatibility proof is provided. The revision will introduce a mathematical forgetting operator and prove incentive compatibility under the perfect-forgetting case; we will also discuss the sensitivity to partial retention as a limitation. revision: partial

  3. Referee: [§5] §5 (Application to Extrapolated Volition): The link between the market prices and extrapolated volition is stated but not formalized. No theorem or proposition demonstrates that the equilibrium prices converge to the volition-extrapolation functional under the recursive construction.

    Authors: The connection to extrapolated volition is presented as a motivating application rather than a fully derived result. The manuscript does not contain a convergence theorem. In the revised version we will add a proposition in §5 that states the conditions under which recursive market prices converge to the volition-extrapolation functional, building directly on the value-of-information analysis. revision: yes

Circularity Check

0 steps flagged

No circularity: formal analysis remains independent of inputs

full rationale

The paper's core derivation applies a value-of-information paradigm to the recursive information market to determine whether prices align with true value, treating LLM forgetting as an exogenous assumption rather than a derived quantity. No equations or steps reduce the claimed incentive alignment to a self-definition, fitted parameter renamed as prediction, or load-bearing self-citation chain. The mechanism's recursive structure and applications to extrapolated volition are presented as extensions of prior suggestions without the central result being forced by construction from those inputs. The analysis is therefore self-contained against external benchmarks of the paradigm.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Ledger extracted from abstract only; full paper may introduce additional parameters or assumptions.

axioms (1)
  • domain assumption LLM buyers can forget inspected information without affecting subsequent market behavior or value assessment
    Required to overcome the buyer's inspection paradox as described.
invented entities (1)
  • Recursive information market no independent evidence
    purpose: To enable extrapolation of volition for AI alignment applications
    New recursive extension of the base mechanism introduced in the work.

pith-pipeline@v0.9.0 · 5451 in / 1161 out tokens · 52448 ms · 2026-05-10T17:15:15.920982+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

46 extracted references · 18 canonical work pages · 1 internal anchor

  1. [1]

    George A Akerlof. 1978. The market for “lemons”: Quality uncertainty and the market mechanism. InUncertainty in economics. Elsevier, 235–251

    1978

  2. [2]

    K. J. Arrow. 1972.Economic Welfare and the Allocation of Resources for Invention. Macmillan Education UK, London, 219–236. https://doi.org/10.1007/978-1-349- 15486-9_13

    work page doi:10.1007/978-1-349- 1972

  3. [3]

    Moshe Babaioff, Robert Kleinberg, and Renato Paes Leme. 2012. Optimal mech- anisms for selling information. InProceedings of the 13th ACM Conference on Electronic Commerce(Valencia, Spain)(EC ’12). Association for Computing Ma- chinery, New York, NY, USA, 92–109. https://doi.org/10.1145/2229012.2229024

    work page doi:10.1145/2229012.2229024 2012

  4. [4]

    Michael Ben-Or, Oded Goldreich, Shafi Goldwasser, Johan Håstad, Joe Kilian, Silvio Micali, and Phillip Rogaway. 1990. Everything provable is provable in zero-knowledge. InAdvances in Cryptology – CRYPTO 1988 - Proceedings (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intel- ligence and Lecture Notes in Bioinformatics)...

    work page doi:10.1007/0-387-34799-2_4 1990

  5. [5]

    Dirk Bergemann, Alessandro Bonatti, and Alex Smolin. 2018. The Design and Price of Information.The American Economic Review108, 1 (2018), 1–48. arXiv:26527944

    2018

  6. [6]

    Samuel R. Bowman, Jeeyoon Hyun, Ethan Perez, Edwin Chen, Craig Pettit, Scott Heiner, Kamil˙e Lukoši¯ut˙e, Amanda Askell, Andy Jones, Anna Chen, Anna Goldie, Azalia Mirhoseini, Cameron McKinnon, Christopher Olah, Daniela Amodei, Dario Amodei, Dawn Drain, Dustin Li, Eli Tran-Johnson, Jackson Kernion, Jamie Kerr, Jared Mueller, Jeffrey Ladish, Joshua Landau,...

    work page doi:10.48550/arxiv.2211.03540 2022

  7. [7]

    Collin Burns, Pavel Izmailov, Jan Hendrik Kirchner, Bowen Baker, Leo Gao, Leopold Aschenbrenner, Yining Chen, Adrien Ecoffet, Manas Joglekar, Jan Leike, Ilya Sutskever, and Jeffrey Wu. 2024. Weak-to-Strong Generalization: Eliciting Strong Capabilities With Weak Supervision. InProceedings of the 41st International Conference on Machine Learning. PMLR, 4971–5012

    2024

  8. [8]

    Vitalik Buterin. 2024. From prediction markets to info finance. https://vitalik.eth. limo/general/2024/11/09/infofinance.html. https://vitalik.eth.limo/general/2024/ 11/09/infofinance.html Accessed: April 13, 2026

    2024

  9. [9]

    Stephen Casper, Xander Davies, Claudia Shi, Thomas Krendl Gilbert, Jérémy Scheurer, Javier Rando, Rachel Freedman, Tomek Korbak, David Lindner, Pedro Freire, Tony Tong Wang, Samuel Marks, Charbel-Raphael Segerie, Micah Carroll, Andi Peng, Phillip J.K. Christoffersen, Mehul Damani, Stewart Slocum, Usman Recursive Information Markets GAIW’26, May 2026, Paph...

    2026

  10. [10]

    Junjie Chen, Minming Li, and Haifeng Xu. 2022. Selling Data To a Machine Learner: Pricing via Costly Signaling. InProceedings of the 39th International Conference on Machine Learning. PMLR, 3336–3359

    2022

  11. [11]

    Paul Christiano, Buck Shlegeris, and Dario Amodei. 2018. Supervising strong learners by amplifying weak experts. arXiv:1810.08575 [cs.LG] https://arxiv.org/ abs/1810.08575

    work page Pith review arXiv 2018

  12. [12]

    Vincent Conitzer. 2009. Prediction markets, mechanism design, and cooperative game theory. InProceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence(Montreal, Quebec, Canada)(UAI ’09). AUAI Press, Arlington, Virginia, USA, 101–108

    2009

  13. [13]

    Paul Dütting, Vahab Mirrokni, Renato Paes Leme, Haifeng Xu, and Song Zuo

  14. [14]

    2024 , isbn =

    Mechanism Design for Large Language Models. InProceedings of the ACM on Web Conference 2024 (WWW ’24). Association for Computing Machinery, New York, NY, USA, 144–155. https://doi.org/10.1145/3589334.3645511

    work page doi:10.1145/3589334.3645511 2024

  15. [15]

    Alireza Fallah, Michael Jordan, Ali Makhdoumi, and Azarakhsh Malekian

  16. [16]

    https: //api.semanticscholar.org/CorpusID:267682401

    On Three-Layer Data Markets.ArXivabs/2402.09697 (2024). https: //api.semanticscholar.org/CorpusID:267682401

    work page arXiv 2024

  17. [17]

    2015.Vingean Reflection: Reliable Reasoning for Self-Improving Agents

    Benja Fallenstein and Nate Soares. 2015.Vingean Reflection: Reliable Reasoning for Self-Improving Agents. Technical Report 2015-2. MIRI. https://intelligence. org/files/VingeanReflection.pdf

    2015

  18. [18]

    Amirata Ghorbani and James Zou. 2019. Data Shapley: Equitable Valuation of Data for Machine Learning. InProceedings of the 36th International Conference on Machine Learning (Proceedings of Machine Learning Research, Vol. 97), Ka- malika Chaudhuri and Ruslan Salakhutdinov (Eds.). PMLR, 2242–2251. https: //proceedings.mlr.press/v97/ghorbani19c.html

    2019

  19. [19]

    Goldreich

    O. Goldreich. 2001.Foundations of Cryptography: Volume 1, Basic Tools. Cambridge University Press. https://books.google.co.uk/books?id=oo3RzgEACAAJ

    2001

  20. [20]

    Danny Halawi, Fred Zhang, Chen Yueh-Han, and Jacob Steinhardt. 2024. Ap- proaching Human-Level Forecasting with Language Models. https://doi.org/10. 48550/arXiv.2402.18563 arXiv:2402.18563 [cs]

    work page arXiv 2024

  21. [21]

    Lewis Hammond and Sam Adam-Day. 2024. Neural Interactive Proofs. InICML 2024 Next Generation of AI Safety Workshop

    2024

  22. [22]

    Robin Hanson. 2002. Logarithmic Market Scoring Rules for Modular Combina- torial Information Aggregation.The Journal of Prediction Markets1, 1 (January 2002), 3–15. https://doi.org/10.5750/jpm.v1i1.417

    work page doi:10.5750/jpm.v1i1.417 2002

  23. [23]

    Robin Hanson. 2011. IP+ Like Barbed Wire?

    2011

  24. [24]

    Robin Hanson. 2011. Rah Efficient IP

    2011

  25. [25]

    R. Howard. 1966. Information Value Theory.IEEE Transactions on Systems Science and Cybernetics2, 1 (1966), 22–26. https://doi.org/10.1109/tssc.1966.30007

    work page doi:10.1109/tssc.1966.30007 1966

  26. [26]

    Evan Hubinger. 2020. AI Safety via Market Making — LessWrong

    2020

  27. [27]

    Evan Hubinger. 2020. Alignment proposals and complexity classes. https://www.lesswrong.com/posts/N64THGX7XNCqRtvPG/alignment- proposals-and-complexity-classes. Retrieved April 13, 2026from https://www.lesswrong.com/posts/N64THGX7XNCqRtvPG/alignment- proposals-and-complexity-classes Accessed: April 13, 2026

    2020

  28. [28]

    Russell Impagliazzo and Moti Yung. 1987. Direct Minimum-Knowledge Computa- tions. InA Conference on the Theory and Applications of Cryptographic Techniques on Advances in Cryptology (CRYPTO ’87). Springer-Verlag, Berlin, Heidelberg, 40–51

    1987

  29. [29]

    Geoffrey Irving, Paul Christiano, and Dario Amodei. 2018. AI Safety via Debate. https://doi.org/10.48550/arXiv.1805.00899 arXiv:1805.00899 [cs, stat]

    work page internal anchor Pith review doi:10.48550/arxiv.1805.00899 2018

  30. [30]

    H. W. Kuhn, K. J. Arrow, E. W. Barankin, D. Blackwell, R. Bott, N. Dalkey, M. Dresher, D. Gale, D. B. Gillies, I. Glicksberg, O. Gross, S. Karlin, H. W. Kuhn, J. P. Mayberry, J. W. Milnor, T. S. Motzkin, J. von Neumann, H. Raiffa, L. S. Shapley, M. Shiffman, F. M. Stewart, G. L. Thompson, and R. M. Thrall. 1953.Extensive games and the problem of informati...

    1953

  31. [31]

    Nian Li, Chen Gao, Mingyu Li, Yong Li, and Qingmin Liao. 2024. EconAgent: Large Language Model-Empowered Agents for Simulating Macroeconomic Activities. InProceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), Lun-Wei Ku, Andre Martins, and Vivek Srikumar (Eds.). Association for Computational Lingu...

    work page doi:10.18653/v1/2024.acl-long.829 2024

  32. [32]

    D. V. Lindley. 1956. On a Measure of the Information Provided by an Experiment. The Annals of Mathematical Statistics27, 4 (1956), 986–1005. http://www.jstor. org/stable/2237191

    work page arXiv 1956

  33. [33]

    Manelli and Daniel R

    Alejandro M. Manelli and Daniel R. Vincent. 2006. Bundling as an optimal selling mechanism for a multiple-good monopolist.Journal of Economic Theory127, 1 (2006), 1–35. https://doi.org/10.1016/j.jet.2005.08.007

    work page doi:10.1016/j.jet.2005.08.007 2006

  34. [34]

    Daniel Paleka, Abhimanyu Pallavi Sudhir, Alejandro Alvarez, Vineeth Bhat, Adam Shen, Evan Wang, and Florian Tramèr. 2024. Consistency Checks for Language Model Forecasters. InThe Thirteenth International Conference on Learning Repre- sentations

    2024

  35. [35]

    Raiffa and R

    H. Raiffa and R. Schlaifer. 1961.Applied Statistical Decision Theory. Division of Research, Graduate School of Business Adminitration, Harvard University. https://books.google.co.uk/books?id=wPBLAAAAMAAJ

    1961

  36. [36]

    Samuelson and W.D

    P.A. Samuelson and W.D. Nordhaus. 2009.Economics. McGraw-Hill Education. https://books.google.co.uk/books?id=eS5ZAAAAYAAJ

    2009

  37. [37]

    Park, and Philip E

    Philipp Schoenegger, Indre Tuminauskaite, Peter S. Park, and Philip E. Tetlock

  38. [38]

    Schoenegger, I

    Wisdom of the Silicon Crowd: LLM Ensemble Prediction Capabilities Rival Human Crowd Accuracy. https://doi.org/10.48550/arXiv.2402.19379 arXiv:2402.19379 [cs]

    work page doi:10.48550/arxiv.2402.19379

  39. [39]

    George J Stigler. 1961. The economics of information.Journal of political economy 69, 3 (1961), 213–225

    1961

  40. [40]

    Abhimanyu Pallavi Sudhir, Jackson Kaunismaa, and Arjun Panickssery. 2025. A Benchmark for Scalable Oversight Mechanisms. InICLR 2025 Workshop on Bidi- rectional Human-AI Alignment. https://openreview.net/forum?id=mzLBxX84VI

    2025

  41. [41]

    Emanuel Tewolde, Brian Hu Zhang, Caspar Oesterheld, Manolis Zampetakis, Tuomas Sandholm, Paul Goldberg, and Vincent Conitzer. 2024. Imperfect-recall games: equilibrium concepts and their complexity. InProceedings of the Thirty- Third International Joint Conference on Artificial Intelligence(Jeju, Korea)(IJCAI ’24). Article 332, 11 pages. https://doi.org/1...

    work page doi:10.24963/ijcai.2024/332 2024

  42. [42]

    Kristine Thomassen, Siril Vassbø, Espen Solheim-Kile, and Jardar Lohne. 2016. Public-Private Partnership: Transaction Costs of Tendering.Procedia Computer Science100 (2016), 818–825. https://doi.org/10.1016/j.procs.2016.09.230 Interna- tional Conference on ENTERprise Information Systems/International Conference on Project MANagement/International Conferen...

    work page doi:10.1016/j.procs.2016.09.230 2016

  43. [43]

    Van Alstyne

    Marshall V. Van Alstyne. 1999. A proposal for valuing information and instru- mental goods. InProceedings of the 20th International Conference on Information Systems(Charlotte, North Carolina, USA)(ICIS ’99). Association for Information Systems, USA, 328–345

    1999

  44. [44]

    Van Alstyne

    Marshall V. Van Alstyne. 1999. A Proposal for Valuing Information and Instru- mental Goods. InProceedings of the 20th International Conference on Information Systems (ICIS ’99). Association for Information Systems, USA, 328–345

    1999

  45. [45]

    Martin Weiss, Nasim Rahaman, Manuel Wuthrich, Yoshua Bengio, Li Erran Li, Bernhard Schölkopf, and Christopher Pal. 2024. Redesigning Information Markets in the Era of Language Models. InFirst Conference on Language Modeling

    2024

  46. [46]

    Birdwatch: Crowd wisdom and bridging algorithms can inform understanding and reduce the spread of misinfor- mation.arXiv preprint arXiv:2210.15723, 2022

    Stefan Wojcik, Sophie Hilgard, Nick Judd, Delia Mocanu, Stephen Ragain, M. B. Fallin Hunzaker, Keith Coleman, and Jay Baxter. 2022. Birdwatch: Crowd Wisdom and Bridging Algorithms can Inform Understanding and Reduce the Spread of Misinformation. arXiv:2210.15723 [cs.SI] https://arxiv.org/abs/2210. 15723 A BASIC RESULTS ABOUT V ALUE-OF-INFORMATION We inclu...

    work page arXiv 2022