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arxiv: 2606.22226 · v1 · pith:ITC4MUALnew · submitted 2026-06-20 · 💻 cs.GT · cs.AI· cs.IT· math.IT

Quantifying Theoretical AI Alignment Guarantees: Receiver-Utility Bounds in Bayesian Persuasion

Eric Yachbes , Eva Tardos This is my paper

Pith reviewed 2026-06-26 10:32 UTC · model grok-4.3

classification 💻 cs.GT cs.AIcs.ITmath.IT
keywords Bayesian persuasionreceiver utility boundsmisaligned signalingbit-string priorsAI alignmentinformation designsender-optimal schemes
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The pith

Receiver bit-guessing utility under sender-optimal signals is at most 1.5 times the prior-only baseline.

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

The paper models an AI sender that observes a bit-string world state and chooses signals to maximize the expected number of bits the human receiver guesses as 1. The receiver wants to maximize its own expected number of correct guesses. For any prior μ the authors prove that the highest receiver utility achievable by a sender-optimal signal is at most 1.5 times the receiver utility obtained from the prior alone. The bound tightens to an additive ηn loss when the prior is η-close to the product of its marginals. A concrete six-bit prior shows the ratio can reach 39/31, ruling out any universal improvement to 5/4.

Core claim

For a prior μ over {0,1}^n, let R0(μ) be the receiver's expected correct guesses using only the prior and let Rmax(μ) be the maximum receiver expected correct guesses over all signaling schemes that are optimal for the sender. Then Rmax(μ)/R0(μ) ≤ 3/2 for every μ. When μ(x) ≥ (1−η)π_μ(x) for all x, the stronger additive bound Rmax(μ) ≤ R0(μ) + ηn holds. There exists a six-bit prior achieving exactly 39/31.

What carries the argument

The ratio Rmax(μ)/R0(μ) of receiver utilities in the Bayesian persuasion game where sender utility equals expected number of 1-guesses.

If this is right

  • Receiver utility cannot exceed 1.5 times the prior baseline under any sender-optimal scheme.
  • When the prior is η-close to its independent product, the excess receiver utility is at most ηn.
  • No universal bound of 5/4 or better holds, because the six-bit example attains 39/31.
  • The 3/2 bound is therefore the best constant that works for all finite-bit-string priors.

Where Pith is reading between the lines

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

  • The same linear-utility structure may allow similar ratio bounds in other finite-state persuasion settings with misaligned sender objectives.
  • Extending the model to continuous states or non-linear receiver utilities would require new proof techniques.
  • The six-bit construction supplies an explicit worst-case instance that can be used to test numerical solvers for larger n.

Load-bearing premise

The world state is a finite bit string and both players' payoffs are linear in the number of bits guessed correctly or guessed as 1.

What would settle it

A prior μ for which some sender-optimal signal yields receiver utility strictly larger than 1.5 times R0(μ).

read the original abstract

Misalignment can change how information moves from an AI agent to a human user. We model this as an information advantage: the AI agent observes the world state, while the human receiver only knows a prior and must act after seeing the agent's signal. A strategic AI sender may withhold evidence or garble information in order to steer the human's decision. We ask how much useful information can still reach the human when the AI optimizes a misaligned objective. We study a Bayesian persuasion model in which the world state is a bit string, the human receiver wants to guess the bits correctly, and a single AI sender wants the receiver to guess as many bits as possible as $1$. For a prior $\mu$, let $R_0(\mu)$ be the receiver's utility from using only the prior, and let $R_{\max}(\mu)$ be the largest receiver utility among signaling schemes that are optimal for the sender. We prove $R_{\max}(\mu)/R_0(\mu)\leq 3/2$. This bound improves for priors close to the independent product prior with the same marginals: if $\mu(x)\geq (1-\eta)\pi_\mu(x)$ for every state $x$, then $R_{\max}(\mu)\leq R_0(\mu)+\eta n$. We also give a six-bit prior for which $R_{\max}(\mu)/R_0(\mu)=39/31>5/4$, so no universal $5/4$ bound is possible.

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

0 major / 2 minor

Summary. The manuscript models misalignment in a Bayesian persuasion game on state space {0,1}^n. The receiver's utility is the expected number of correctly recovered bits; the sender's utility is the expected number of bits reported as 1. For prior μ, R0(μ) is the receiver's utility under the prior alone and Rmax(μ) is the highest receiver utility attainable by any signaling scheme that is optimal for the sender. The paper proves Rmax(μ)/R0(μ) ≤ 3/2 for every μ, shows that the ratio improves to Rmax(μ) ≤ R0(μ) + ηn when μ(x) ≥ (1−η)πμ(x) for all x, and exhibits an explicit 6-bit prior attaining ratio 39/31, ruling out any universal 5/4 bound.

Significance. If the stated theorems hold, the work supplies explicit, parameter-free quantitative guarantees on information loss under misalignment inside a fully formalized finite-state persuasion model. The 3/2 upper bound, the η-closeness refinement, and the concrete 6-bit witness that separates 5/4 from the true constant are all strengths; the setting requires no continuity, measurability, or equilibrium-selection assumptions beyond the standard Bayesian-persuasion definitions.

minor comments (2)
  1. [§1] §1: The introduction would benefit from a one-paragraph high-level outline of the proof strategy for the 3/2 bound before the formal statements.
  2. Notation: The definition of the product prior πμ could be stated once in a displayed equation rather than inline in the abstract and again in the body.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive evaluation of the manuscript, including the recognition of the parameter-free 3/2 bound, the η-closeness refinement, and the explicit 6-bit example separating 5/4 from the true constant. We are pleased by the recommendation to accept.

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper defines R_0(μ) as receiver utility from the prior alone and R_max(μ) as the maximum receiver utility over sender-optimal signaling schemes, both directly from the fixed finite-state Bayesian persuasion model with explicit bit-string utilities. The 3/2 bound, the η-improved bound, and the 39/31 counterexample are stated as theorems proved inside this model; no parameters are fitted to data, no self-citations are invoked as load-bearing premises, and no quantity is redefined in terms of itself. The derivation therefore remains self-contained against the model primitives.

Axiom & Free-Parameter Ledger

0 free parameters · 3 axioms · 0 invented entities

The paper rests on standard domain assumptions of Bayesian persuasion applied to the stated utilities; no free parameters or invented entities are introduced.

axioms (3)
  • domain assumption The world state is a bit string of length n.
    Explicit in the model description.
  • domain assumption Receiver utility equals expected number of correctly guessed bits.
    Stated as the human's objective.
  • domain assumption Sender utility equals expected number of bits guessed as 1.
    Stated as the AI's objective.

pith-pipeline@v0.9.1-grok · 5813 in / 1434 out tokens · 27930 ms · 2026-06-26T10:32:14.929667+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

8 extracted references · 8 canonical work pages

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