Quantifying the Blockchain Trilemma: A Comparative Study of Algorand and Ethereum 2.0

Overview

This project aims to provide a comprehensive analysis of blockchain technologies, focusing on their efficiency, security, and decentralization aspects. It includes comparative studies of systems like Algorand and Beaconchain, offering insights into the blockchain trilemma.

Features

• Comparative analysis of blockchain systems
• Quantitative measurements of decentralization, efficiency, and security
• Data-driven insights into blockchain technologies

Data

Data preparation

Acquire Algorand data from Bitquery, and acquire Beacon data from Beacon Explorer by using SIPDER framework.

The data was stored in the Algorand_data and Beacon_chain_data

Data dictionary

We evaluate the decentralization in two layers, the consensus layer and the transaction layer.

For the consensus layer, we use proposer/validator data to represent the staking or voting process.

Proposer data (Algorand)

Column Name	Discription
date	The specific date for which the data is recorded, formatted as "YYYY-MM-DD".
proposer_count	The number of proposers that participated in the block proposal process on the given date.
reward	The Reward for block proposal per day.

Validator data (Beacon)

Column Name	Discription
date	The specific date for which the data is recorded, formatted as "YYYY-MM-DD".
Value	Average account balance of validators per day.

For the transaction layer, we use the number of daily transaction data to quantify the decentralization.

Beacon transaction data

Column Name	Discription
Timestamp	The timestamp when the transactions were recorded
daily_transaction	The daily transaction on Beacon (USD).

Algorand transaction data

Column Name	Discription
time	The timestamp when the transactions were recorded
count	Transaction count per day.
fees	Tokens used for transaction.

Methodologies to quantify on-chain decentralization

Shannon Entropy

A higher value indicates more chaos in authority distribution while a lower value refers to a more centralized system. We define the indice $H(v)$ as: $$H(v) = \prod \limits_{i=1}^N P(v_i)^{-P(v_i)}$$ where the $v_i$ refers to the unit data for each layer and the $P(v_i)$ refers to the weight of the unit data in respect to the overall dataset: $$P(v_i) = \frac{v_i}{\sum_{i=1}^N v_i}$$

Gini Coefficient

$$G = 1 - \sum_{i=1}^N P_i^2$$

Nakaoto Coefficient

$$ N = min{k \in [1,...,K] : \sum_{i=1}^K P_i > 0.51}$$

Herfindahl Hirschman Index

$$HHI = \sum_{i=1}^N P_i^2$$

Usage

To execute the Jupyter Notebook and perform the analysis:

1. Navigate to the directory where you cloned the repository.
2. Start the Jupyter Notebook server by running jupyter notebook in your command line.
3. Open the experiment.ipynb file from the Jupyter Notebook interface in your browser.
4. Execute the notebook cells in sequence to conduct the analysis.

Contributing

We welcome contributions from the community. If you wish to contribute to the project, please follow these guidelines:

• Fork the repository and create a feature branch.
• Make your changes and ensure that your code adheres to the existing style.
• Submit a pull request with a clear description of your improvements or bug fixes.

License

This project is licensed under [MIT License]. For more details, see the LICENSE file in the repository.

Contact

For any inquiries or potential collaborations, please reach out to the project maintainers at [[email protected]]. We are open to feedback and interested in hearing about how you may want to use or improve the project.