Introduction

This document examines conditions for fair and reliable distribution of rewards in a decentralised data availability (DA) network, where $N$ nodes independently sample peers to judge their performance. Our focus is on three core properties:

Ensuring coverage. We show that even when each node samples only a small number of peers per round, across $T$ rounds, the probability that every node gets observed is very high when $N<T$.
Stability of peer sampling. By treating the collection of all peer samples as a random graph, we demonstrate that each node's number of observations remains tightly clustered around the average. This ensures the mechanism stays predictable and robust.
Robust opinion aggregation. We consider a simple majority-vote rule for combining all (binary) reports of nodes into a single consensus judgment and prove that this rule tolerates the maximum number of inconsistent or malicious reports without breaking.

Throughout, we support our theoretical claims with simulations and numerical experiments, showing that the proposed sampling rates, observation windows, and voting thresholds create an efficient, scalable reward system that is both reliable and resilient against failures or adversarial behavior.

Key Findings

Small sampling rates achieve network coverage exponentially with block count.
Node connectivity follows predictable binomial distribution.
The $N/2$ threshold maximises disagreement tolerance while recovering true opinions.
System tolerates up to $\lfloor N/2 \rfloor$ disagreements in odd-sized networks and $N/2 -1$ disagreements in even-sized networks.

This analysis provides theoretical foundations for a robust decentralised reward system resistant to failures and adversarial behaviour.

Overview

This document examines conditions for fair and reliable reward distribution in a decentralized data availability network with independent peer sampling.

We present a comprehensive mathematical model and theoretical framework supporting the reward distribution system. The framework consists of:

Assumptions: Exploration of network structure, participant interaction patterns, and underlying sampling mechanisms.
Efficiency of Sampling: Probability analysis backed by simulations and statistical validation.
Analysis of DA Sampling: Protocol specifications, implementation considerations, and network connectivity assessment.