Artificial Analysis Intelligence Index

• Artificial Analysis Intelligence Index is a framework that defines and measures AI capabilities through composite, multidimensional indices and mathematical models.
• It employs weighted sums, Choquet integrals, and probabilistic ranking techniques to assess cognitive, economic, and governance dimensions reliably.
• These indices offer actionable insights for policy, investment, and research by benchmarking performance across AI systems, nations, and industries.

An Artificial Analysis Intelligence Index encompasses frameworks, models, and quantitative methodologies developed to assess, analyze, and benchmark AI systems, agents, nations, or economic entities. These indices are designed to address the multidimensional challenges of measuring intelligence, technical development, governance capacity, economic value, and societal impact across AI systems and actors. Approaches range from the formulation of mathematical models representing cognitive capabilities to the construction of composite, multidimensional benchmarking indices suitable for cross-system or cross-country comparison.

1. Theoretical Foundations and Conceptual Models

The development of Artificial Analysis Intelligence Indices is underpinned by formal attempts to define and unify the measurement of intelligence across both artificial and human systems (Liu et al., 2015, Liu et al., 2017). The standard intelligent system model posits four universal capabilities—knowledge acquisition (input), knowledge mastery (storage), knowledge innovation (creation), and knowledge feedback (output)—applicable to both biological and artificial agents. This model is mathematically formalized as an 11-element tuple:

$M = \{K, Ks, KM, KN, Q, QI, QO, I, O, C, N\}$

where $K$ denotes a universal set of knowledge, $KM$ the system’s possessed knowledge, $KN$ innovative knowledge generated by the system, and $I, O, C, N$ are the input, output, control, and innovation functions, respectively (Liu et al., 2015). The intelligence $Q$ of a system $M$ is operationalized as

$$Q = a \cdot f(I) + b \cdot f(O) + c \cdot f(S) + d \cdot f(C), \quad a + b + c + d = 1$$

with $f(I)$, $f(O)$, $f(S)$, $f(C)$ representing the respective functional components and $a,b,c,d$ their weights (Liu et al., 2017).

2. Quantitative Methodologies and Index Construction

Indices in this domain use composite, multidimensional designs informed by multi-criteria decision analysis and robust statistical techniques. Early approaches often relied on weighted sums for composing scores across indicators, but recent advances integrate nonlinear aggregation via the Choquet integral to account for criterion dependencies (Campello et al., 15 Feb 2024). The index score for an entity (nation, system, or company) is thus built as:

• Weighted Sum: $S = \sum_i w_i x_i$, with $w_i$ fixed weights for indicator $x_i$
• Choquet Integral: $$s_{i}^{CI} = \sum_{j=1}^n \left[g_{(j)}(a_i) - g_{(j-1)}(a_i)\right] \mu(\{(j),…,(n)\})$$, where $\mu(\cdot)$ is a fuzzy measure capturing joint importance and redundancy Stochastic Multicriteria Acceptability Analysis (SMAA) is used in tandem to model weight uncertainty, producing probabilistic rankings where $b_i^s$ gives the probability that entity $i$ attains rank $s$ (Campello et al., 15 Feb 2024).

3. Taxonomies and Evaluation Schemes

Multiple schemes exist for index application:

3.1. Intelligence Quotient and Grading

A class of indices uses the Artificial Intelligence IQ (AI IQ) metric to quantify a system’s capability level. This is computed by scoring an agent on a suite of 15 subtests spanning acquisition, mastery, innovation, and output abilities, each with weights determined by expert consensus (Delphi method) (Liu et al., 2015, Liu et al., 2017):

$IQA = \sum_{i=1}^{n} (F_i \times W_i)$

where $F_i$ is the score and $W_i$ the weight on the $i$th subtest. These scores allow for absolute, deviation, and value IQ distinctions and, in some frameworks, are paired with qualitative intelligence grades ($K = 0…6$) reflecting evolutionary stages from inert objects to theoretical superintelligence (Liu et al., 2017, Liu et al., 2017).

3.2. Governance and Policy Indices

Recent indices (AGILE Index (Zeng et al., 21 Feb 2025, Zeng et al., 10 Jul 2025)) assess cross-national AI governance capacity, organizing metrics into layered pillars, dimensions, and indicators. For example, the AGILE Index 2025 uses:

• 4 Pillars: AI Development, Governance Environment, Governance Instruments, Governance Effectiveness
• 17 Dimensions: Ranging from R&D activity and infrastructure to legislative status and inclusivity
• 43 Indicators: E.g., publications/capita, risk incidents/GDP, public trust, legal frameworks Values are normalized with formulas such as:

$$\text{Normalized Score} = 25 \cdot \frac{X-\mu}{\sigma} + 50$$

($X$ = raw score, $\mu$ = mean, $\sigma$ = std. dev.) to preserve cross-country comparability (Zeng et al., 10 Jul 2025).

3.3. Economic and Productivity Benchmarks

Indices such as the AI Productivity Index (APEX) (Vidgen et al., 30 Sep 2025) measure whether AI models can perform economically valuable work, using expert-curated prompts and rubric-based grading of task completion in high-value domains (e.g., law, medicine). The index score is:

$$S = 100 \times \frac{\# \text{passed criteria}}{\# \text{total criteria}}$$

Highlighting the gap between frontier model output and expert human performance is a central feature.

4. Application Domains and Case Studies

Artificial Analysis Intelligence Indices are operationalized at various levels:

• System/Agent Level: Evaluation of AI and human agents for cognitive capacity, as in the AI IQ test of 50 search engines and human subjects, revealing strong performance in knowledge retrieval/mastery but deficits in innovation (Liu et al., 2015).
• Country/National Capability: Composite indices such as AGILE evaluate nations across technological, regulatory, and social metrics (Zeng et al., 21 Feb 2025, Zeng et al., 10 Jul 2025).
• Product/Service Evaluation: Indices such as the three IQs (General, Service, Value) support benchmarking for consumer-facing intelligent devices, incorporating both technical competencies and economic cost (Liu et al., 2017).
• Business and Investment Analysis: Stock indices constructed from natural language processing of corporate filings (e.g., TF–IDF–weighted AI scores in 10-Ks (Ante et al., 3 Jan 2025)) provide data-driven perspectives for financial markets.

5. Limitations, Bias Mitigation, and Future Research

Challenges in index construction include:

• Indicator Correlation: High correlation among criteria can induce redundancy or “double counting;” nonlinear aggregation (Choquet) and unsupervised learning of capacity weights help diminish these effects (Campello et al., 15 Feb 2024).
• Weight Subjectivity: Deterministic weights can reflect subjective bias; stochastic modeling (SMAA) and probabilistic rankings (rank acceptability, Condorcet aggregation) increase robustness to specification choices (Campello et al., 15 Feb 2024).
• Temporal Robustness and Adaptation: Indices are being refined to support longitudinal tracking, dynamic capacity building, and sector-specific adaptation (e.g., time-discounting in stock indices (Ante et al., 3 Jan 2025), region-specific indices for GCC (Albous et al., 5 Sep 2025)).
• Translational Transfer: Frameworks are extendable to other sectors (e.g., healthcare, digital government readiness) and can inform policy, investment, and global cooperation mechanisms.

6. Significance for AI Evaluation and Societal Impact

Artificial Analysis Intelligence Indices are foundational to the scientific and policy discourse around AI capability, safety, and governance. They facilitate:

• Systematic benchmarking of progress in cognitive, economic, and governance domains.
• Objective quantification for informed decision-making by policymakers, researchers, and investors.
• Identification of innovation gaps (e.g., creative reasoning in AI vs. humans (Liu et al., 2015)).
• Guidance for regulatory strategies and resource allocation, particularly as AI becomes embedded across critical domains.

By integrating rigorous mathematical formulations, multi-dimensional structures, and robust aggregation technologies, Artificial Analysis Intelligence Indices provide the analytic infrastructure necessary for responsible monitoring and management of AI development at both micro and macro scales.