Misinformation Index

• Misinformation Index is a quantitative metric assessing the degree of distortion and factual drift in news, social media, and multi-modal channels.
• It employs claim-tracking, concealment–overstatement, and multi-granularity evidence indices to evaluate how source facts are lost or altered.
• Experimental results demonstrate its use in fact-checking and social network audits with severity measures ranging from factual error to propaganda.

A Misinformation Index is a quantitative metric designed to assess the degree and dynamics of information distortion, factual loss, or manipulation in news articles, social content, or multi-modal communication channels. Recent research formalizes several classes of Misinformation Index, grounded variously in claim-level question answering, surface-level textual statistics, and multi-granularity cross-modal evidence retrieval. These indices serve as reproducible, interpretable tools for simulating, measuring, and mitigating misinformation propagation in both textual and multimodal digital ecosystems (Maurya et al., 13 Nov 2025, Wu et al., 1 Mar 2025, Lee et al., 31 Jul 2024).

1. Formal Definitions of the Misinformation Index

Misinformation Index frameworks are instantiated via distinct computational paradigms:

(A) Claim-Tracking Model

Let $S$ be a fact-checked source article, and $Q = \{q_j\}_{j=1}^{m}$ a set of $m$ curated auditor questions with corresponding gold answers $G = \{g_j\}_{j=1}^m$. For any rewritten or derived text $x$, a binary scoring function

$$s(x, q_j, g_j) = \begin{cases} 1, & \text{if } g_j \text{ is recoverable from } x \ 0, & \text{otherwise} \end{cases}$$

is computed. The auditor output is a binary vector $\mathbf{y}(x)$, where $\mathbf{y}_0 = \mathbf{1}$ for the reference $S$. The core Misinformation Index at node $(b,k)$ after $k$ rewrites on branch $b$ is

$$\mathrm{MI}_{b,k} = d(\mathbf{y}_0, \mathbf{y}_{b,k})$$

where $d$ is normalized Hamming distance. This counts the number of source facts now lost or altered.

A branch-level summary is given by the Misinformation Propagation Rate (MPR):

$$\mathrm{MPR}(b) = \frac{1}{E+1} \sum_{k=0}^{E}\mathrm{MI}_{b,k}$$

with $E$ as branch depth.

(B) Concealment–Overstatement Model

Given two texts—a fact-checked reference (“full story”) with noun set $T_1$ and a candidate article with noun set $T_2$—the metrics are:

Concealment: $C = 1 - \frac{|I|}{|T_1|}, \quad I = T_1 \cap T_2$ Overstatement: $O = 1 - \frac{|I|}{|T_2|}$

A composite scalar index is typically

$M = \frac{C + O}{2}$

or

$M = w_C C + w_O O, \quad w_C + w_O = 1$

or Euclidean distance $(M = \sqrt{C^2 + O^2})$.

(C) Multi-Granularity Evidence Indices

EXCLAIM constructs three separate Faiss-based indices—visual-entity, textual-entity, and event-level—used not for a global score but for structured, fine-grained retrieval and reasoning about cross-modal consistency and integrity. While EXCLAIM does not collapse these into a universal scalar in its core pipeline, a plausible extension is a risk aggregation function:

$$MFI(N_{\text{input}}) = \lambda_1 \cdot \mathrm{mean}\{d_{\text{entity}}\} + \lambda_2 \cdot \mathrm{mean}\{d_{\text{event}}\} + \lambda_3 \cdot \mathrm{mean}\{d_{\text{global}}\}$$

This suggests a vector-valued "Misinformation Index" unifying granular, explainable signals (Wu et al., 1 Mar 2025).

2. Computational Procedures and Implementation

Claim-Tracking Index

Sequential Steps:

1. Select a source $S$; auditor generates $m=10$ QA pairs.
2. For each node $k$ in each of $B$ branches, rewrite via persona-conditioned LLM, audit with $Q$, and calculate $\mathrm{MI}_{b,k}$.
3. Compute branchwise MPR.
4. Assign severity via thresholding: factual error ($\mathrm{MPR} \le 1$), lie ($1 < \mathrm{MPR} \le 3$), propaganda ($\mathrm{MPR} > 3$).

Pseudocode Excerpt:

for b in 1..B: assign_personas(b) X[0] = S MI_sum = 0 for k in 0..E: if k > 0: X[k] = LLM_rewrite(X[k-1], persona[b,k]) ybk = [auditor.answer_binary(X[k], qj) for j in 1..m] MI[b,k] = sum(abs(1 - yjk) for yjk in ybk) MI_sum += MI[b,k] MPR[b] = MI_sum / (E+1)

(Maurya et al., 13 Nov 2025)

Concealment–Overstatement

1. Preprocess: Remove extraneous text, extract all nouns via POS-tagging (e.g., Mecab for Korean).
2. Compute intersection $I$ of $T_1,T_2$; calculate $C$, $O$.
3. Aggregate into final $M$ score.

Multi-Granularity Indices (EXCLAIM)

1. Extract entities and events with YOLOv8 (visual) and spaCy NER (text).
2. Encode and index visual/text/event embeddings in Faiss.
3. At runtime, for each query extract, retrieve top-$k$ neighbors from each index.
4. Multi-agent pipeline reasons over retrieved evidence:
   • Retrieval Agent: Coarse consistency checks.
   • Detective Agent: Fine-grained fact contradiction detection.
   • Analyst Agent: Synthesis and explanation.

No single scalar is used during EXCLAIM’s judgment, but the retrieved evidence and contradictions could be pooled into a structured index (Wu et al., 1 Mar 2025).

3. Experimental Findings and Severity Taxonomy

Misinformation Propagation in Rewriting Networks

• In homogeneous LLM-branch experiments (fixed persona per branch), $\mathrm{MPR}$ ranged $0$–$10$ with:
  • Factual error: $22.4\,\%$
  • Lie: $46.2\,\%$
  • Propaganda: $31.4\,\%$
  • “Identity” personas (e.g., Young Parent, Religious Leader) accelerated factual drift; expert/neutral resisted it (avg $\mathrm{MPR} < 2$).
• Heterogeneous (random personas per node) led to $85.2\,\%$ propaganda severity, with multiple domains $100\%$ propaganda.
• No formal $p$-values, but the qualitative domain/persona effects were stark (Maurya et al., 13 Nov 2025).

Indexes Based on Concealment–Overstatement

• In Korean news, fake articles showed higher Concealment ($C$) and Overstatement ($O$) than real articles.
• Logistic regression/QDA classifiers on $(O,C)$ achieved $0.92$ accuracy distinguishing real vs. false.
• Politics articles had the highest overstatement tendency.
• Both metrics separated real vs. fake news (Mann–Whitney $z_{C},z_{O}$ both highly significant) (Lee et al., 31 Jul 2024).

Multi-Granularity Cross-Modal Evaluation

• EXCLAIM achieved $92.7\%$ accuracy (test) for out-of-context misinformation detection, $+4.3\%$ over prior state-of-the-art.
• Ablation of any index or agent led to lower performance, confirming each component’s necessity (Wu et al., 1 Mar 2025).

Severity Taxonomy

Severity bucket definitions (per-branch average): | Severity | $\mathrm{MPR}(b)$ Range | Interpretation | |-----------------|------------------------|--------------------------------------------| | Factual error | $\leq 1$ | Minor informational drift | | Lie | $1 < \mathrm{MPR} \leq 3$ | Systematic distortion (2–3 claims lost) | | Propaganda | $> 3$ | Wholesale collapse (>3 claims lost) |

These map to fabrication/manipulation/propaganda typologies in misinformation studies (Tandoc et al. 2018) (Maurya et al., 13 Nov 2025).

4. Theoretical and Taxonomic Context

• The MI, MPR, and concealment/overstatement indices correspond to specific theoretical strands:
  • Quantifying "drift" connects to studies of cognitive bias and motivated reasoning (Vosoughi et al. 2018; Pennycook & Rand 2019).
  • Severity bins align with typologies of fabrication, manipulation, and propaganda.
  • Persona-based drift replicates echo-chamber and reinforcement phenomena in network theory (Conte et al. 2012).
• Expert/neutral personas function as corrective priors, suppressing misinformation diffusion (Lewandowsky et al. 2012).

5. Practical Applications, Strengths, and Limitations

Application Area	Implementation Mode	Limitation
Fact-checking	Concealment/overstatement	Requires full story reference
Social network audit	MI/MPR via LLM agents	Fixed-depth, non-interactive topology
Image-text detection	Multi-granularity index	No scalar risk score in core EXCLAIM pipeline

• Misinformation indices provide directives for journalists (article self-audit), fact-checkers (triage by $M$), and readers (browser “M-meter”).
• Concealment/overstatement do not require heavy neural models or feature engineering but do depend on suitable reference articles and noun-level content matching.
• The claim-tracking approach in LLM rewrites enables claim-level auditing with interpretable output but conflates "lost" and "inverted" facts, lacking graded nuance.
• EXCLAIM’s design achieves explainability and modular generalization at the cost of integrating rather than collapsing index signals into one dimension (Lee et al., 31 Jul 2024, Maurya et al., 13 Nov 2025, Wu et al., 1 Mar 2025).

6. Extensions and Open Problems

Current research highlights several open avenues:

• For claim-tracking indices, potential improvements include introducing partial-credit or confidence-weighted QA scoring, belief-updating in agents, embedding branches in complex graphs, and adding statistical significance testing.
• Concealment/overstatement can be extended beyond nouns, with cross-domain and cross-lingual generalization requiring validation.
• Multi-modal indices like EXCLAIM may be extended to video, audio, and non-standard modalities by defining appropriate extractors and adapting the multi-agent pipeline. Aggregating fine-grained distances with learnable weights could yield a scalable scalar misinformation risk index for high-throughput screening (Maurya et al., 13 Nov 2025, Wu et al., 1 Mar 2025, Lee et al., 31 Jul 2024).