Extrapolating Volition with Recursive Information Markets

Abhimanyu Pallavi Sudhir; Long Tran-Thanh

cs.GTApr 8, 2026

Extrapolating Volition with Recursive Information Markets

Authors: Abhimanyu Pallavi Sudhir, Long Tran-Thanh

Organizations: University of Warwick, Coventry, United Kingdom

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.

Figures & tables

$\mathbf{P}(I_{1},I_{2})$	$I_{1}$	$I_{2}$	$\mathbf{P}(E\mid I_{1},I_{2})$
$15/32$	$0$	$0$	$0.08$
$15/32$	$0$	$1$	$0.08$
$1/24$	$1$	$0$	$0.5$
$1/48$	$1$	$1$	$0.2$

Table 1. A distribution exhibiting the fact-checking effect.

Choice set	True utilities	Information Offers
$\mathcal{X}$	$U:\mathcal{X}\to\mathbb{R}$	$\mathcal{I}=\{\mathbf{0},\mathbf{I}_{1},\mathbf{I}_{2},\dots\}$
$\mathcal{X}^{1}=\mathcal{I}$	$U^{1}:\mathcal{X}^{1}\to\mathbb{R}$	$\mathcal{I}^{1}=\{\mathbf{0},\mathbf{I}^{1}_{1},\mathbf{I}^{1}_{2},\dots\}$
$\mathcal{X}^{2}=\mathcal{I}^{1}$	$U^{2}:\mathcal{X}^{2}\to\mathbb{R}$	$\mathcal{I}^{2}=\{\mathbf{0},\mathbf{I}^{2}_{1},\mathbf{I}^{2}_{2}\dots\}$
$\dots$	$\dots$	$\dots$

Table 2. Successive decision problems, naive approach

Panel of Figure 1 — Figure 1. Recursive Inspection as an imperfect recall game; nodes are labelled by the information available for making the decision at that node. Note how the decision tree is in the reverse order of the inspection order: $x^{N}$ is decided first, and $x^{0}$ last.

Panel of Figure 2 — Figure 2. The Recursive Inspection Protocol

Panel of Figure 4 — Figure 4. Screenshots from the infonomy-server platform

Value of Information

Value of information studies whether acquiring information can improve decisions enough to justify its cost.

See all 37 papers

Not All Information Is Worth Asking For: Decision-Informed Information Seeking with LLMs
Oct 23, 2026Seunghan Lee, Jun Seo, Junhyeok Kang +9LLM Decision-Making Value of Information
LG AI Research
Information Aggregation with AI Agents
Apr 21, 2026Spyros GalanisAI Agent Evaluation Multi-Agent Reasoning
Department of Economics, University of Durham
Strategic Exploitation in LLM Agent Markets: A Simulation Framework for E-Commerce Trust
May 11, 2026Shijun Lei, Quang Nguyen, Swapneel S Mehta +7Human Behavior Simulation Agent-Based Modeling
Northwestern Polytechnical University · Boston University · Fudan University +3

Oct 23, 2026J/K move · Enter open · S save

Not All Information Is Worth Asking For: Decision-Informed Information Seeking with LLMs

Seunghan Lee, Jun Seo, Junhyeok Kang, Jaehoon Lee+8

LG AI Research

LLM Decision-Making Value of Information

Open paper AskPDF arXiv

Large language models (LLMs) are increasingly used to support decisions under incomplete information, where deciding what to look up and when to stop matters as much as the final answer. However, LLMs fall into an information trap: They pay for checks, i.e., costly pieces of evidence, that cannot change their decision or are not worth their cost, and they keep asking when the evidence is already sufficient. To this end, we propose Decision-Informed Value-of-information Acquisition (DIVA), a simple yet effective procedure for LLM information seeking based on the decision value of evidence. DIVA 1) lets the LLM specify a small decision model, i.e., how likely a bad outcome is and how each check would shift this probability, through short numeric questions and 2) values each candidate check by how much its imagined outcomes improve the decision net of its cost, stopping when no check is worth its cost. Its variant, DIVA-U, further accounts for the LLM's uncertain estimates of how strongly each check shifts this probability. DIVA is training-free and applies to any LLM. Across four domains and 20 LLMs, DIVA-U has lower regret, i.e., value lost relative to the best possible decision, than every LLM baseline on real-world data, mainly by stopping once evidence suffices, and DIVA cuts the regret of the best LLM baseline by 75% in synthetic scenarios where every check's reliability is given. Code: github.com/seunghan96/diva.

Abstract

Value of Information

Explore similar work

Not All Information Is Worth Asking For: Decision-Informed Information Seeking with LLMs

Information Aggregation with AI Agents

Strategic Exploitation in LLM Agent Markets: A Simulation Framework for E-Commerce Trust