Informativeness Gap in AI and Decision Making

• Informativeness gap is a concept describing the discrepancy between nominal information availability and the actual epistemic value derived by different users.
• It operationalizes across domains such as generative AI, reasoning evaluation, web search, and statistical estimation through formal metrics and comparative analyses.
• The gap arises from mechanisms like overreliance on proxy objectives, misallocated attention, and local coherence bias, influencing educational outcomes and decision-making.

Searching arXiv for the supplied paper and closely related work on “informativeness gap” across generative AI, reasoning evaluation, calibration, and information completeness. Searching arXiv for (Morisco, 25 Mar 2026) and related papers. “Informativeness gap” denotes a systematic disparity between information that is nominally available and the epistemic value, completeness, or decision usefulness that is actually realized. In the current literature, the phrase is often an interpretive label rather than the authors’ own term. In generative AI, it corresponds to a “generative AI knowledge gap” in which users with different epistemic competencies derive different knowledge quality from the same output (Morisco, 25 Mar 2026). In reasoning evaluation, it appears as a discrepancy between stepwise correctness and stepwise contribution toward the answer (Prasad et al., 2023). In web search, it becomes the difference between the full information spectrum and the subset actually observed during browsing (Khanna, 12 Oct 2025). In decision theory for predictive models, it is formalized as the maximum normalized payoff advantage one predictor offers over another across all decision-making tasks (Feng et al., 16 Jul 2025).

1. Conceptual scope

Across the supplied literature, the concept has three recurring features. First, it is relational rather than intrinsic: the gap is defined between a full corpus and a viewed subset, between a comprehensive answer and a partial answer, between a predictor and a competing predictor, or between the same AI output and different users’ resulting knowledge states. Second, it is usually epistemic rather than merely lexical: what matters is not token overlap or verbosity, but whether additional material improves accuracy, contextual adequacy, reliability, or downstream utility. Third, it is often interaction-dependent: informativeness is not always a property of the text alone, but of the relation between text, user, task, and reference structure.

This makes “informativeness gap” a family resemblance concept spanning informational inequality, model evaluation, search behavior, prediction, and statistical estimation. In some settings the gap is a shortfall from an ideal reference; in others it is a mismatch between two desiderata that are often conflated, such as correctness and contribution.

Setting	Formal or operational quantity	Interpretation
Generative AI use	$$\mathbb{E}[Q(K_u)\mid u\in G_1] \neq \mathbb{E}[Q(K_u)\mid u\in G_2]$$	Unequal epistemic yield from the same AI exposure (Morisco, 25 Mar 2026)
Reasoning chains	$\mathrm{info\mbox{-}gain}^{(i)}_{pvi}=pvi(s^{(i)}\to\hat{a}\mid s^{(<i)})$	Incremental usefulness of a reasoning step (Prasad et al., 2023)
Predictors	$$\mathsf{IG}(\pi,\sigma)=\sup_{(A,u)\in\mathcal{U}}(\mathsf{EU}_\pi-\mathsf{EU}_\sigma)$$	Maximum payoff advantage across decision tasks (Feng et al., 16 Jul 2025)
GMM estimation	$$\Delta_k=\frac{\sigma_{\theta_k g}\sigma_{gg}^{-1}\sigma_{g\theta_k}}{\sigma_{\theta_k\theta_k}}$$	Share of estimator variance explained by moments (Yu et al., 29 Jun 2026)
Web search	$G_n=1-I_{\text{completeness},n}$	Unobserved portion of the information spectrum (Khanna, 12 Oct 2025)

2. Generative AI and informational inequality

The most explicit social-theoretic formulation comes from the proposal to extend knowledge-gap theory and digital-divide research to generative AI (Morisco, 25 Mar 2026). The central claim is that generative AI shifts the locus of informational inequality away from access and basic usage toward interpretation and evaluation. Classical knowledge-gap theory emphasized differential acquisition of factual knowledge as information flows increase. Digital-divide research added first-level divides in access, second-level divides in usage and digital skills, and third-level divides in outcomes. The generative AI extension argues that these are no longer sufficient because many AI systems are widely available and require no specialized technical expertise to obtain fluent outputs.

The critical stage becomes post-exposure processing. Generative AI “shifts the point of interaction from retrieval to interpretation”: the system produces tailored answers on demand, often with low source transparency, and the user’s main task becomes assessing plausibility, relevance, completeness, and reliability (Morisco, 25 Mar 2026). The paper treats education as the main explanatory variable. Higher levels of education are assumed to correlate with more frequent questioning of outputs, more comparison with other sources, and more active reflection on system limitations such as hallucinations, lack of up-to-date data, and bias. Lower levels of education are assumed to correlate with more direct reliance on outputs, less systematic verification, and weaker contextualization. This bundle is named the “epistemic dimensions of AI use.”

The paper’s reconstructed formalization makes the point directly. Let $I$ be the information produced by a generative AI system in response to prompt $p$, let $K_u$ denote the knowledge state of user $u$ after interacting with $I$, and let $\mathrm{info\mbox{-}gain}^{(i)}_{pvi}=pvi(s^{(i)}\to\hat{a}\mid s^{(<i)})$0 capture epistemic quality. An informativeness gap exists between groups $\mathrm{info\mbox{-}gain}^{(i)}_{pvi}=pvi(s^{(i)}\to\hat{a}\mid s^{(<i)})$1 and $\mathrm{info\mbox{-}gain}^{(i)}_{pvi}=pvi(s^{(i)}\to\hat{a}\mid s^{(<i)})$2 if, for similar prompts and the same system,

$\mathrm{info\mbox{-}gain}^{(i)}_{pvi}=pvi(s^{(i)}\to\hat{a}\mid s^{(<i)})$3

with the difference associated with epistemic competencies rather than access or basic usage (Morisco, 25 Mar 2026). On this view, the gap is not in the raw output $\mathrm{info\mbox{-}gain}^{(i)}_{pvi}=pvi(s^{(i)}\to\hat{a}\mid s^{(<i)})$4 but in the “epistemic quality—accuracy, contextual adequacy, and reliability—of the information they derive” from the same output.

The same framework also implies longitudinal dynamics. Repeated AI use, combined with differential evaluation, can reinforce already advantaged users and entrench misperceptions among less critical users. The paper further suggests that the gap may be larger in high-stakes, complex, or contentious domains such as health and politics than in everyday practical knowledge, because contextualization errors there are harder to detect and more consequential (Morisco, 25 Mar 2026).

3. Formalizations in reasoning, prediction, and estimation

In reasoning evaluation, the gap is formalized as a discrepancy between being correct and being informative (Prasad et al., 2023). ReCEval treats a reasoning chain as an informal proof from input context $\mathrm{info\mbox{-}gain}^{(i)}_{pvi}=pvi(s^{(i)}\to\hat{a}\mid s^{(<i)})$5 to predicted answer $\mathrm{info\mbox{-}gain}^{(i)}_{pvi}=pvi(s^{(i)}\to\hat{a}\mid s^{(<i)})$6 and decomposes each step into Reasoning Content Units. Correctness is judged by whether each conclusion is supported by premises and consistent with prior context. Informativeness is a separate axis: each step should provide new information helpful toward deriving $\mathrm{info\mbox{-}gain}^{(i)}_{pvi}=pvi(s^{(i)}\to\hat{a}\mid s^{(<i)})$7. Step-level informativeness is defined as conditional pointwise V-information,

$\mathrm{info\mbox{-}gain}^{(i)}_{pvi}=pvi(s^{(i)}\to\hat{a}\mid s^{(<i)})$8

This makes the gap observable in two directions: a step can be correct but uninformative because it is redundant or irrelevant, or informative but incorrect because it increases answer predictability through a misleading shortcut (Prasad et al., 2023).

In predictive decision theory, the gap becomes explicitly cardinal (Feng et al., 16 Jul 2025). For binary outcomes, a possibly miscalibrated predictor is represented by its prediction distribution $\mathrm{info\mbox{-}gain}^{(i)}_{pvi}=pvi(s^{(i)}\to\hat{a}\mid s^{(<i)})$9 and true conditional frequency function $$\mathsf{IG}(\pi,\sigma)=\sup_{(A,u)\in\mathcal{U}}(\mathsf{EU}_\pi-\mathsf{EU}_\sigma)$$0. The informativeness gap of predictor $$\mathsf{IG}(\pi,\sigma)=\sup_{(A,u)\in\mathcal{U}}(\mathsf{EU}_\pi-\mathsf{EU}_\sigma)$$1 relative to predictor $$\mathsf{IG}(\pi,\sigma)=\sup_{(A,u)\in\mathcal{U}}(\mathsf{EU}_\pi-\mathsf{EU}_\sigma)$$2 is

$$\mathsf{IG}(\pi,\sigma)=\sup_{(A,u)\in\mathcal{U}}(\mathsf{EU}_\pi-\mathsf{EU}_\sigma)$$3

the maximum normalized payoff advantage one predictor offers over the other across all decision problems. This strictly generalizes U-Calibration and Calibration Decision Loss and recovers Blackwell informativeness as a special case when both predictors are perfectly calibrated (Feng et al., 16 Jul 2025).

In misspecification-robust GMM, the relevant quantity is the informativeness of the estimator with respect to its moments (Yu et al., 29 Jun 2026). For parameter component $$\mathsf{IG}(\pi,\sigma)=\sup_{(A,u)\in\mathcal{U}}(\mathsf{EU}_\pi-\mathsf{EU}_\sigma)$$4,

$$\mathsf{IG}(\pi,\sigma)=\sup_{(A,u)\in\mathcal{U}}(\mathsf{EU}_\pi-\mathsf{EU}_\sigma)$$5

measures the share of asymptotic variance explained by sampling variation in the moments. Under correct specification, $$\mathsf{IG}(\pi,\sigma)=\sup_{(A,u)\in\mathcal{U}}(\mathsf{EU}_\pi-\mathsf{EU}_\sigma)$$6; under misspecification it can fall below one, even when the Hansen $$\mathsf{IG}(\pi,\sigma)=\sup_{(A,u)\in\mathcal{U}}(\mathsf{EU}_\pi-\mathsf{EU}_\sigma)$$7-test does not reject. The natural “gap” here is $$\mathsf{IG}(\pi,\sigma)=\sup_{(A,u)\in\mathcal{U}}(\mathsf{EU}_\pi-\mathsf{EU}_\sigma)$$8: the share of estimator variance not explained by the moments, arising from misspecification channels, Jacobian variation, or weight-matrix estimation (Yu et al., 29 Jun 2026).

These formalisms differ in object and scale, but they share a structure: informativeness is not equated with mere availability of a signal. It is the effective contribution of that signal to valid inference, accurate knowledge, or decision value.

4. Measurement designs in applied systems

One important family of measurement designs defines the gap relative to an ideal answer. In gap-focused question generation, the complete text $$\mathsf{IG}(\pi,\sigma)=\sup_{(A,u)\in\mathcal{U}}(\mathsf{EU}_\pi-\mathsf{EU}_\sigma)$$9 and the incomplete text $$\Delta_k=\frac{\sigma_{\theta_k g}\sigma_{gg}^{-1}\sigma_{g\theta_k}}{\sigma_{\theta_k\theta_k}}$$0 are partitioned into common ground and uncommon ground, and the gap is operationalized as the teacher-only region: information present in $$\Delta_k=\frac{\sigma_{\theta_k g}\sigma_{gg}^{-1}\sigma_{g\theta_k}}{\sigma_{\theta_k\theta_k}}$$1 but absent from $$\Delta_k=\frac{\sigma_{\theta_k g}\sigma_{gg}^{-1}\sigma_{g\theta_k}}{\sigma_{\theta_k\theta_k}}$$2 (Rabin et al., 2023). Gap-focused questions are then questions answerable from $$\Delta_k=\frac{\sigma_{\theta_k g}\sigma_{gg}^{-1}\sigma_{g\theta_k}}{\sigma_{\theta_k\theta_k}}$$3 but not from $$\Delta_k=\frac{\sigma_{\theta_k g}\sigma_{gg}^{-1}\sigma_{g\theta_k}}{\sigma_{\theta_k\theta_k}}$$4, with an additional preference for phrasing that does not reveal the missing content in the question itself. A closely related framework uses a hypothetical LLM-generated comprehensive answer $$\Delta_k=\frac{\sigma_{\theta_k g}\sigma_{gg}^{-1}\sigma_{g\theta_k}}{\sigma_{\theta_k\theta_k}}$$5 and defines missing information as the aspects in $$\Delta_k=\frac{\sigma_{\theta_k g}\sigma_{gg}^{-1}\sigma_{g\theta_k}}{\sigma_{\theta_k\theta_k}}$$6 but not in an initial answer $$\Delta_k=\frac{\sigma_{\theta_k g}\sigma_{gg}^{-1}\sigma_{g\theta_k}}{\sigma_{\theta_k\theta_k}}$$7; a follow-up question is informative when it is answerable by $$\Delta_k=\frac{\sigma_{\theta_k g}\sigma_{gg}^{-1}\sigma_{g\theta_k}}{\sigma_{\theta_k\theta_k}}$$8 but unanswerable from $$\Delta_k=\frac{\sigma_{\theta_k g}\sigma_{gg}^{-1}\sigma_{g\theta_k}}{\sigma_{\theta_k\theta_k}}$$9 (Liu et al., 24 Feb 2025). In both cases, the informativeness gap is a reference–response difference.

A second family defines the gap between a full corpus and a consumed subset. In search, the full result set for a query is represented by a corpus vector $G_n=1-I_{\text{completeness},n}$0, and cumulative information completeness after viewing the top $G_n=1-I_{\text{completeness},n}$1 results is

$G_n=1-I_{\text{completeness},n}$2

The corresponding gap is

$G_n=1-I_{\text{completeness},n}$3

This metric was validated on 6.5 trillion search results extracted from daily search trends across 48 nations for one year, and a randomized intervention showed that awareness of information completeness reduced fact resistance and increased exploration of lower-ranked results (Khanna, 12 Oct 2025).

A third family measures informational coverage in generated text. EVA-Score evaluates long-form summaries by extracting atomic facts and document-level relations from both reference and candidate summaries, validating candidate facts against reference facts with an LLM, and computing precision, recall, and F1 over information units (Fan et al., 2024). In child-directed text, contextual informativeness is operationalized through a modified cloze task: human annotators guess masked target words from story context, and the gold informativeness score is the average cosine similarity between the guesses and the target word in ConceptNet Numberbatch space (Valentini et al., 2024). These approaches differ methodologically, but both treat informativeness as recoverable semantic content rather than lexical resemblance.

5. Mechanisms that create the gap

Several papers identify recurrent mechanisms that widen informativeness gaps. One is overreliance on a proxy objective. In VLM-as-a-Judge systems, the proxy is informativeness itself: judges often favor the more informative answer even when it conflicts with the image (Zou et al., 20 Apr 2026). The paper quantifies this with an Informativeness Bias

$G_n=1-I_{\text{completeness},n}$4

where the IDS subset contains cases in which the preferred answer is also the more informative one, and the CDS subset contains cases in which correctness requires preferring the less informative answer. The same study shows that judges often pay limited attention to the image, as measured by an Image Reliance Score, and proposes BIRCH, which first corrects inconsistencies in candidate answers against the image and then compares the answers against a merged truthful anchor. BIRCH reduces informativeness bias by up to 17% and yields performance gains of up to 9.8% (Zou et al., 20 Apr 2026).

A second mechanism is misallocation of annotation or attention toward low-informative instances. In educational dialogue act classification, Data Maps show that most annotated sentences are “Easy”: high confidence, low variability, high correctness, and therefore low informativeness for further classifier learning (Tan et al., 2023). The resulting mismatch between what gets labeled and what would most improve generalization is itself framed as an informativeness gap. A diversity-aware active learning method, CoreMSE, narrows that gap and reaches roughly the same performance with 600 labeled samples that Random, Least Confidence, and Maximum Entropy reach only at about 900 samples, corresponding to about 30% annotation savings (Tan et al., 2023).

A third mechanism is optimization for local plausibility rather than global salience. In open-domain keyphrase extraction, prior neural models favor phraseness—short, entity-style n-grams—over globally informative phrases that better capture document-level topics (Sun et al., 2020). JointKPE addresses this by combining local chunking with a global ranking objective over phrase informativeness in the document. The paper describes the original failure mode as a bias toward locally coherent but less globally informative phrases, which is another domain-specific manifestation of an informativeness gap (Sun et al., 2020).

Across these examples, the gap is produced when the system’s operative objective—verbosity, uncertainty, local phraseness, or frequency—deviates from the target notion of epistemic usefulness.

6. Methodological limits and research directions

The literature also shows that informativeness gaps are highly measurement-dependent. In reasoning evaluation, informativeness depends on the model family used to instantiate V-information, on step segmentation, and on whether one measures model-informative or human-informative content (Prasad et al., 2023). In search, completeness depends on embedding quality and on how the “full corpus” is defined, especially under personalization and filtering (Khanna, 12 Oct 2025). In gap-focused question generation, the method assumes an available complete reference $G_n=1-I_{\text{completeness},n}$5 and models omissions rather than misconceptions; it is therefore less suited to open-ended settings without a clear ideal answer (Rabin et al., 2023). In GMM, simpler weights preserve informativeness that optimal weights can lose, which introduces an explicit trade-off between classical efficiency and informativeness (Yu et al., 29 Jun 2026).

A second methodological issue is that the phrase “informativeness gap” is not a single native term across the literature. In some papers it is explicit, as with predictors (Feng et al., 16 Jul 2025). In others it is a direct reinterpretation of an existing construct, such as the “generative AI knowledge gap” (Morisco, 25 Mar 2026) or the discrepancy between correctness and pvi-based contribution (Prasad et al., 2023). This suggests that the concept is best treated as a unifying analytic lens rather than as a settled technical primitive with one canonical definition.

The forward-looking research agenda is correspondingly plural. In the generative-AI inequality framework, the next steps are group comparisons by education, measurement of critical AI literacy, longitudinal designs, domain-specific studies, and interventions that teach critical engagement (Morisco, 25 Mar 2026). In search, the next steps include extensions beyond search to social feeds, alternative definitions of the corpus, and cluster-based measures of completeness (Khanna, 12 Oct 2025). In question-generation settings, natural extensions include handling misconceptions, planning multi-turn question policies, and coupling gap detection with uncertainty or information gain (Rabin et al., 2023). In statistical estimation, informativeness diagnostics invite systematic comparison of weight matrices and estimation routines under misspecification (Yu et al., 29 Jun 2026).

Taken together, the literature suggests a general principle: informativeness is rarely exhausted by access, lexical similarity, or output length. It is a structured relation between available evidence and what agents, evaluators, or estimators can validly extract from it. The informativeness gap names the residual distance between those two.