Ideometric Index of Human Progress

• IIHP is defined as a formal index that quantifies the quality of idea processes through its core components: generation (G), evaluation (E), prioritization (P), and implementation effectiveness (Iₑ).
• The multiplicative structure of IIHP highlights its sensitivity to underperformance, where a near-zero score in any component significantly undermines overall progress.
• Integration with outcome monitoring and the temporal framework of ProgressGym allows IIHP to validate present-time evaluations against future realized values.

The Ideometric Index of Human Progress (IIHP) is a formal index for measuring human progress in ideometrics terms as improvement in the ability of individuals and societies to generate, evaluate, prioritise, and implement ideas under scarcity and uncertainty, such that prioritised ideas increasingly align with those that truly lead to preferred future states (Rudan et al., 29 May 2026). In its core formulation, IIHP is a present-time process-quality measure rather than a downstream outcome measure: it quantifies the quality of the idea life cycle through the components $G$, $E$, $P$, and $I_e$, while future-time outcome monitoring $O$ is used to validate whether perceived future value was aligned with true realised future value (Rudan et al., 29 May 2026). A complementary line of work shows that IIHP can be grounded, designed, and validated using ProgressGym’s temporal alignment framework, historical corpus, historical LLMs, and benchmarks for tracking, predicting, and coevolving values across centuries (Qiu et al., 2024).

1. Definition and conceptual scope

IIHP is defined within ideometrics as a measure of the quality of the process by which ideas are handled across their life cycle. The underlying definition of human progress is a measurable improvement in the ability of individuals and societies to generate, evaluate, prioritise, and implement ideas—under scarcity of human capacity, energy, time, and resources—in a way that increasingly aligns the prioritised ideas with those that truly lead to preferred future states, given available information and uncertainty (Rudan et al., 29 May 2026). This framing shifts attention from static outcomes such as wealth, health, or technological advancement to the quality of the upstream processes that shape future states.

The paper formalises the “idea life cycle” as generation, evaluation, prioritisation, implementation, and monitoring. IIHP captures the present-time quality of the first four stages, while outcome monitoring $O$ is assessed at future times $t$ to validate the alignment between perceived and realised values (Rudan et al., 29 May 2026). A preferred future state is defined as one assigned higher expected value by a conscious observer—individual or collective—given values, goals, and available information. The framework remains agnostic to the content of preferences and instead focuses on the quality of the process that selects and implements ideas (Rudan et al., 29 May 2026).

ProgressGym provides a related but distinct conceptual grounding by treating moral progress as the expansion and refinement of human moral beliefs and practices across time and cultures. In that framework, progress alignment is formulated as learning the mechanics of human moral progress from history in order to mitigate moral lock-in, defined as the entrenchment of outdated or harmful values by AI systems trained on contemporary biases (Qiu et al., 2024). Within that synthesis, IIHP functions as an ideational index that aggregates descriptive measurement, predictive modeling, and coevolutionary analysis of value change.

2. Formal structure of the index

The canonical IIHP formulation is multiplicative. The process-quality subindex is defined as

$Q_i \;=\; G \times E \times P.$

Implementation effectiveness is initially proxied by

$I_e \;=\; \frac{I(t)}{S(t_0)}.$

The full index is then

$$\mathrm{IIHP} \;=\; (G \times E \times P) \times I_e \;=\; Q_i \times I_e.$$

Here, $E$0 denotes the set of ideas prioritised at completion time $E$1, and $E$2 denotes the number of those ideas successfully executed by future time $E$3 (Rudan et al., 29 May 2026). The worked example in the paper treats components as proportions in $E$4, so that $E$5 under appropriate normalisation.

The multiplicative form is explicitly chosen to encode fragility across the stages of the idea cycle. If any component is near zero, IIHP collapses, which models the “chain is only as strong as its weakest link” principle (Rudan et al., 29 May 2026). The paper notes that weighted or unweighted means “could” be considered, but does not adopt them as canonical. Instead, it chooses the product form to show that failing in any element of the idea cycle affects the entire progress process.

The decision-theoretic interpretation is given in terms of states, outcomes, and utilities. Let $E$6 be the set of states of the world and $E$7 the set of outcomes. An idea is a map $E$8. Let $E$9 denote the true state of the world, and let $P$0 denote the true utility of outcome $P$1 assessed at time $P$2. Then the true realised future value of an idea $P$3 at time $P$4 is

$P$5

Given uncertainty over states represented by a probability distribution $P$6 and an estimated utility function $P$7, the perceived future value at present time is

$P$8

Outcome monitoring is defined as

$P$9

A sufficient condition for progress is that estimation error declines over time across ideas:

$I_e$0

This condition formalises improving alignment between perceived and true realised future value (Rudan et al., 29 May 2026).

3. Components and operational measurement

The four core components of IIHP correspond to the main stages of the idea process. $I_e$1 denotes the quality of idea generation and captures completeness, diversity, and novelty of the initial set of candidate ideas relative to the relevant idea space for the problem under consideration. $I_e$2 denotes the accuracy of idea evaluation under uncertainty and captures how well the evaluation process estimates future realised value given present information. $I_e$3 denotes the efficiency of idea prioritisation under scarcity and captures how closely selection for implementation follows the evaluation ranking while resisting undue influences and incorporating uncertainty and portfolio constraints. $I_e$4 denotes the effectiveness of implementation and captures how many prioritised ideas are implemented and how well implementation changes reality toward preferred states (Rudan et al., 29 May 2026).

The paper outlines concrete measurement strategies for each component. For $I_e$5, completeness and diversity of the initial idea set can be assessed using structured frameworks such as “4D in health: description, delivery, development, discovery,” while AI or LLMs can generate large idea sets whose semantic diversity, saturation, and semantic distance to existing knowledge are measured and then normalised to $I_e$6 (Rudan et al., 29 May 2026). For $I_e$7, the recommended approach is multi-criteria evaluation with weights that reflect contextual importance, ideally informed by data such as PCA, and supported by large expert panels for replicability; agreement and uncertainty are quantified, and AI evaluations can be compared with expert processes such as CHNRI (Rudan et al., 29 May 2026).

For $I_e$8, the operational focus is rank adherence, bias diagnostics, and portfolio optimisation under budget constraints. The implemented set is compared with the top-ranked evaluated ideas, and integrity of the prioritisation process is assessed through inter-scorer agreement and bias detection tools (Rudan et al., 29 May 2026). For $I_e$9, the initial proxy is the fraction $O$0, with suggested refinements for delays, fidelity, cost overruns, and achieved impact. The PLANET tool—Planning, Monitoring and Evaluation—is identified as a support tool for implementation tracking and effectiveness assessment (Rudan et al., 29 May 2026).

A concise summary of the canonical components is as follows:

Component	Meaning	Measurement emphasis
$O$1	quality of idea generation	completeness, diversity, novelty
$O$2	accuracy of idea evaluation under uncertainty	criteria, weights, expertise, uncertainty
$O$3	efficiency of idea prioritisation under scarcity	rank adherence, integrity, portfolio optimisation
$O$4	effectiveness of implementation	execution, fidelity, timeliness, impact

The paper also provides a sample numeric calculation. With $O$5, $O$6, $O$7, and $O$8, the resulting value is

$O$9

This example is illustrative and is used to show how multiplicative aggregation penalises weakness in any stage (Rudan et al., 29 May 2026).

4. Outcome monitoring, validation, and regress

IIHP is paired with future-time validation through $O$0 and alignment diagnostics. The index itself measures present-time process quality, while realised future value is established only later, when implemented ideas can be observed in the world (Rudan et al., 29 May 2026). This separation is central to the framework: evaluation $O$1 is necessarily a present-time proxy for future value, whereas $O$2 provides empirical validation after outcomes have materialised.

The paper lists domain-specific proxies for realised future value. These include financial returns for stock portfolios, earnings or profits for start-ups, publications, patents, and citations for research grants, macro indicators such as GDP trends for policy portfolios, and documented outcomes for personal goals (Rudan et al., 29 May 2026). Validation proceeds by computing IIHP at time $O$3, tracking $O$4 and the alignment error $O$5 at later times, and examining whether higher IIHP predicts higher $O$6 and faster decline in alignment error relative to benchmarks.

The framework also provides a formal definition of human progress $O$7 at the realised-outcome level. Let $O$8 be the set of all theoretically possible ideas and $O$9 the set prioritised at $t$0. Then human progress at time $t$1 is proportional to the difference between the average realised value of prioritised ideas and the average realised value of all possible ideas:

$t$2

If this difference is positive, prioritisation outperforms random selection; if negative, it implies “relative regress” (Rudan et al., 29 May 2026). Regress can also be represented procedurally as declining IIHP over time,

$t$3

or as increasing misalignment,

$t$4

This design makes the framework explicitly testable, but it also highlights the measurement difficulty that true value is unknowable at present, outcomes are noisy and delayed, and counterfactuals for unselected ideas are difficult to establish (Rudan et al., 29 May 2026).

5. Historical and temporal grounding through ProgressGym

A later synthesis proposes that IIHP can be grounded, designed, and validated using ProgressGym’s temporal alignment framework. ProgressGym formulates alignment as a temporal POMDP with a human value state $t$5 that evolves over time, actions $t$6 representing AI prompts or outputs, observations $t$7 as human responses, and a utility $t$8 that rewards alignment to evolving or future moral states (Qiu et al., 2024). This framework is designed to address moral lock-in and to learn the mechanics of historical moral progress from data.

The empirical substrate consists of a 38GB public-domain historical corpus spanning 1221–2022 across books, legal texts, newspapers, and speeches, totaling approximately $t$9 million documents, together with 18 historical LLMs derived by temporally segmented continued pretraining and instruction tuning of Llama3-8B and Llama3-70B for the 13th through 21st centuries (Qiu et al., 2024). These models function as human proxies aligned to era-specific value distributions. ProgressGym also defines a 19-dimensional values representation $Q_i \;=\; G \times E \times P.$0, built from 5104 evaluation questions spanning basic morality, social morality, values, and worldviews and sourced from MoralChoice, the World Values Survey, and the Integrated Worldview Framework. Cosine similarity in this space measures proximity between value states across time (Qiu et al., 2024).

Within this temporal framework, IIHP can be instantiated as a time-indexed ideational index. The proposed value extraction takes the form

$Q_i \;=\; G \times E \times P.$1

where $Q_i \;=\; G \times E \times P.$2 collects historical text features and historical LLM outputs for time $Q_i \;=\; G \times E \times P.$3, $Q_i \;=\; G \times E \times P.$4 is a task-specific estimator, and robust normalization uses long-run statistics $Q_i \;=\; G \times E \times P.$5 with cross-temporal trimming or Huberization (Qiu et al., 2024). Text-derived indicators include stance detection, topic prevalence, and supervised regression on sentence embeddings to measure proxies such as religious centrality, democracy, liberalism, expectation for progress, and uncertainty avoidance. Model-derived indicators come from applying the 19-dimension evaluation framework to historical LLMs calibrated to each century.

ProgressGym’s three core tasks then become measurement and modeling primitives for IIHP. PG-Follow tracks evolving values by maximising cosine similarity between an agent and the relevant historical human proxy. PG-Predict aligns toward future proxies and is used to build predictive components of IIHP. PG-Coevolve simulates feedback loops in which the human proxy evolves under both endogenous temporal forces and AI outputs, allowing IIHP to assess whether interventions avoid lock-in or backsliding (Qiu et al., 2024). A plausible implication is that these tasks extend IIHP from a static process index into a temporally explicit system for tracking, forecasting, and governing ideational change.

6. Aggregation, governance, limitations, and extension

In the ideometrics paper, the canonical IIHP is multiplicative and process-centric. In the ProgressGym-based design, IIHP is additionally expressed as an aggregate over a normalized value vector $Q_i \;=\; G \times E \times P.$6, with multiple possible weighting schemes:

$Q_i \;=\; G \times E \times P.$7

The proposed weighting options include normative anchors, PCA-based or entropy weighting, and weights learned from historical milestones such as abolition, suffrage, civil rights enactments, and decriminalization of inhumane punishments (Qiu et al., 2024). This does not replace the canonical multiplicative definition in ideometrics; rather, it provides a way to aggregate historically calibrated value dimensions when IIHP is implemented as a temporal index over texts and historical LLMs.

The temporal design also introduces smoothing, uncertainty, predictive, and coevolutionary components:

$Q_i \;=\; G \times E \times P.$8

and

$Q_i \;=\; G \times E \times P.$9

$I_e \;=\; \frac{I(t)}{S(t_0)}.$0

For coevolution, the value dynamics are written as

$I_e \;=\; \frac{I(t)}{S(t_0)}.$1

where $I_e \;=\; \frac{I(t)}{S(t_0)}.$2 are AI actions and $I_e \;=\; \frac{I(t)}{S(t_0)}.$3 are exogenous shocks (Qiu et al., 2024). Guardrails are proposed to detect regressions through negative $I_e \;=\; \frac{I(t)}{S(t_0)}.$4 beyond tolerance and to trigger damped responses rather than reinforcement.

Governance recommendations in the ProgressGym synthesis include pluralistic weighting, publication of multiple IIHP variants, uncertainty reporting, regression audits through PG-Coevolve monitors, anti-lock-in constraints, open leaderboard tracks for IIHP construction, red-teaming, periodic re-estimation with new texts and models, and deliberate inclusion of underrepresented cultures as data expands (Qiu et al., 2024). These recommendations address a central limitation shared by both frameworks: weight choices, criteria, and preferences are value-laden and culturally contingent.

The main limitations are explicit. The ideometrics paper notes the need for empirical justification of multiplicative aggregation, refinement of $I_e \;=\; \frac{I(t)}{S(t_0)}.$5, robust normalisation, broader validation across domains, and better portfolio optimisation methods under budget constraints (Rudan et al., 29 May 2026). The ProgressGym-based synthesis adds data coverage gaps due to predominantly English corpora, difficulties of cultural comparability across genres and contexts, path dependence and model bias in historical LLMs, and the possibility that data-driven trends may miss conceptual breakthroughs (Qiu et al., 2024). The same synthesis therefore suggests combining ProgressGym with reasoning-driven approaches, including AI-assisted moral philosophy, to surface new dimensions and update $I_e \;=\; \frac{I(t)}{S(t_0)}.$6.

The framework also extends beyond present-time human progress to historical accumulation. The Ideometric Index of Civilisational Progress (IICP) is defined by adding documentation $I_e \;=\; \frac{I(t)}{S(t_0)}.$7 and intergenerational transmission $I_e \;=\; \frac{I(t)}{S(t_0)}.$8 and integrating over time:

$I_e \;=\; \frac{I(t)}{S(t_0)}.$9

Here, $$\mathrm{IIHP} \;=\; (G \times E \times P) \times I_e \;=\; Q_i \times I_e.$$0 is an appropriately transformed outcome value compatible with multiplicative aggregation (Rudan et al., 29 May 2026). This extension preserves the same fragility logic as IIHP: near-zero performance in any component can stall or reverse progress across historical time.

In summary, IIHP is a formal and testable framework for measuring human progress as the quality of idea processes under uncertainty and scarcity. In its canonical ideometric form, it is the product $$\mathrm{IIHP} \;=\; (G \times E \times P) \times I_e \;=\; Q_i \times I_e.$$1, validated by future outcome monitoring $$\mathrm{IIHP} \;=\; (G \times E \times P) \times I_e \;=\; Q_i \times I_e.$$2 and by declining misalignment between perceived and realised future value (Rudan et al., 29 May 2026). In its temporally extended implementation, ProgressGym supplies historical corpora, historical LLMs, value embeddings, alignment tasks, and governance mechanisms that can convert IIHP into a time-indexed, uncertainty-aware, and coevolution-sensitive measure of ideational and moral progress (Qiu et al., 2024).