# Implementing Generalized Impact Evaluators Through Network-Based Attribution

### **Overview**

We define a generalized, modular framework for retrospective impact attribution in multi-agent systems using a typed, weighted, heterogeneous graph. The system operationalizes the Generalized Impact Evaluator (GIE) model through iterative graph-based score propagation, supporting fine-grained configurability over edges, node types, and individual node identifiers.

This architecture is suitable for contexts where attribution, trust, and reward distribution are core concerns—e.g., decentralized governance, open science, environmental tracking, or reputation-based incentive mechanisms.

### **1. Data Model**

We model the system state as a graph $G = (V, E, \tau, \omega, \mu)$, where:

* $V$: set of nodes representing entities (actors, artifacts, evaluators, signals, ...)
* $E \subseteq V \times V$: directed edges representing evaluative, contributive, or metric relationships
* $\tau: V \cup E \rightarrow \text{Type}$: node and edge type annotations
* $\omega: E \rightarrow \mathbb{R}_{\geq 0}$: edge weights (configurable per edge type)
* $\mu: V \cup E \rightarrow \text{Metadata}$: optional attributes (e.g., timestamps, confidence, attestations)

This structure supports arbitrary source data: blockchain events, Ethereum attestations (EAS), Hypercert claims, application telemetry, or academic impact metrics.

### **2. Scope Function $S$**

A scope function $S: G \rightarrow G_S$ extracts a **temporal and semantic subgraph** $G_S \subseteq G$, constrained by:

* Time interval $T_i$
* Action types (e.g., `created`, `validated`, `measured`)
* Node or edge attribute filters (e.g., domain-specific)

This enables interval-bounded evaluation consistent with the MER (Measure-Evaluate-Reward) loop.

### **3. Measurement Function $m$**

The measurement phase extracts a subset of **relevant indicators** from $G_S$, defined as structured interactions:

* Edges representing actions (e.g., contribution, endorsement)
* Edges linking external metrics (signals) to artifacts
* Node metadata such as attestations or credit splits

Indicators may be filtered, normalized, or aggregated depending on the application domain.

### **4. Evaluation Function $e$: Centrality-Based Score Propagation**

Impact is computed via a recursive score propagation algorithm over the indicator subgraph:

#### **Propagation Equation**

For each node $n \in V$, its impact score $s_n$ is updated as:

$$
s_n = \sum_{e = (u \rightarrow n)} s_u \cdot \omega(e) \cdot \alpha(u)
$$

Where:

* $\omega(e)$: edge weight (based on edge type)
* $\alpha(u)$: authority weight of node $u$, defined as:

$$
\alpha(u) = \theta_{\tau(u)} \cdot \psi(u)
$$

* $\theta_{\tau(u)}$: type-based weight
* $\psi(u)$: per-node override (by ID), if specified

This supports hybrid weighting:

* **Edge-type weighting**: E.g., validation edges count more than endorsements
* **Node-type weighting**: DAOs > individuals > bots
* **Node-ID weighting**: Explicit priors on trusted evaluators (e.g., `verifier-1` gets $\alpha = 1.2$)

The propagation algorithm generalizes PageRank, eigenvector centrality, or custom authority flow models.

### **5. Reward Function $r$**

A configurable reward function maps scores $s_n$ into incentives:

$$
R_n = r(s_n, \Theta)
$$

Where $\Theta$ includes:

* Reward pool (fixed, dynamic, zero-sum, positive-sum)
* Scoring curve (linear, superlinear, capped, sigmoid)
* Eligibility constraints (e.g., minimum score threshold)

This supports economic incentive mechanisms, reputation assignment, or credential issuance.

### **6. Memory Mechanism**

Each evaluation interval concludes by writing computed rewards or impact scores back into the graph as:

* Node attributes (e.g., `past_score`, `total_rewards`)
* New edges (e.g., `rewarded_by(system)`)

This enables temporal continuity, longitudinal reputation accumulation, and recursive influence (i.e., prior rounds affect future evaluations).

### **7. Configuration Interface**

The system is parameterized via a configuration object:

config = {
  scopeCriteria: { timeWindow, nodeFilters, edgeFilters },
  edgeWeights: { contribution: 1.0, validation: 0.8, signal: 0.6 },
  nodeWeights: { DAO: 1.5, Community: 1.0, Signal: 0.7 },
  nodeWeightsById: { 'verifier-1': 1.2, 'expert-42': 1.4 },
  rewardFunction: (score) => curve(score),
  rewardPool: 1000
}

This allows domain-specific instantiations without modifying core mechanics.

Could be governed by DAO governance.

### **8. System Properties**

* **Modular**: Supports plug-and-play data sources and scoring strategies
* **Transparent**: All outputs traceable through graph paths and weights
* **Auditable**: Impact claims are inspectable and re-computable
* **Incentive-Compatible**: Can be tuned to discourage gaming and promote verifiable impact
* **Domain-Agnostic**: Applies to blockchain ecosystems, research funding, education, public goods, and more

### **Conclusion**

This system offers a general-purpose, graph-native architecture for evaluating and rewarding impact in complex systems. By leveraging score propagation algorithms and multi-layered weighting, it provides a scalable, interpretable, and incentive-aligned mechanism for impact attribution across diverse domains.

It represents a unification of structural graph theory, distributed trust models, and programmable incentives into a cohesive impact evaluation framework.