Detailed Plan

<u>Overview</u>

The Photrek and West Africa Decentralized Alliance (WADA) teams will collaborate to design and simulate a detailed voting and funding system that enables balancing of influence across a diverse decentralized autonomous organization and flexibility in the allocation of funds. While the focus will be a system for the Cardano Catalyst and Voltaire governance, the results will be applicable to the broader Cardano community developing DAOs. Key features of the system will be the ability to detect correlation in voting preference across wallets, use of the correlation measure to form virtual cliques of mutual interest, and use of power-law weightings, such as quadratic voting, to ensure that dominant cliques and/or individuals do not gain oligarchic control of decision making.

<u>Proposed Outcomes</u>

(1) To model agent-based opinion, voting, and funding dynamics within the framework of the complex network;

(2) To use computer simulations for the time evolution of interaction network in the opinion, voting, and funding process;

(3) To analyze power-law voting designs and their generalizations for their ability to balance the voting influence, including the role of correlated cohorts of voters.

(4) To design and analyze methods of providing flexible funding levels so that well-supported projects are not eliminated by marginal differences between proposed and available funds.

(5) To design a voting and funding protocol, such as square-root voting across correlated cohorts, for implementation by Cardano Catalyst and other DOAs in the Cardano ecosystem.

<u>Methodology and Impact</u>

To investigate Cardano voting systems Photrek will employ Agent-based Models & Simulations, Voting & Funding Design, and Power-law Statistical Analysis. The outcome will be an evidence-based recommendation for a Diversified Voting & Flexible Funding System.

Agent-based Models & Simulationsconsist of a computational model that simulates the actions and interactions of multiple agents or individuals to re-create or predict the appearance of complex phenomena, where "the whole is greater than the sum of its parts". It represents the natural choice for our computational simulation scenario for uncovering the natural laws of voting and expressing opinions. On the other hand, the complex network framework ensures the substantial and non-trivial geometrical features representing the interaction between agents in voting assemblies. The key aspect of the complex network approach relies on the patterns of connection between their elements that are neither purely regular nor purely random, as the real-world networks of people are structured.

The Monte Carlo method is a statistical method that uses a sequence of random numbers to simulate the evolution of a physical system, especially useful for modeling social voting dynamics. The process is applied to a series of replicas of the same experiment (samples) to determine averaged configurational quantities as a physical result. The Monte Carlo method is exceptionally efficient for the simulation of systems with many local interactions, such as in problems of disordered materials, voting dynamics, consensus formation, disease spreading, and others.

Voting Design & Modelling. From our previous investigation (Cardano Catalyst Fund 4: Diversify Voting Influence), we identified the following power-law voting mechanics worthy of further investigation: Square Root Voting and Quadratic Voting and their generalizations with different powers. These designs empower us to build more effective and balanced voting mechanics for the Cardano ecosystem and to specify flexibility in the funding level of awarded projects. First, we can compose a voting power for each individual that depends on the size of their wallet and the selected power-law weighting. Secondly, the literature indicates that it is important that the voting influence be treated as a budget that the voter allocates across proposals as pseudo investments. This allows voters to concentrate their influence on proposals about which they have strong preferences rather than trying to evaluate all the proposals. Finally, the "voting investment" received by a proposal will be used to both rank and specify a degree of flexibility in the funding level awarded. The result is a Voting & Funding Design that balances influence and provides flexibility in assuring broadly supported proposals are awarded an appropriate funding level.

Power-law Statistical Analysis. The output of the voting design, modeling, and simulation will produce a rich collection of information from which we will extract valuable knowledge, noteworthy conclusions, and evidence to support diversified decision-making for the Cardano Catalyst Community. The evidence, conclusions, and knowledge will be formed using careful statistical analysis including statistical moments, such as the second moment and kurtosis. Additionally, because power-law systems have undefined or infinite moments, we will also utilize the innovations of Nonlinear Statistical Coupling, which was developed by Dr. Nelson for the purpose of estimating, generating, and analyzing the statistics of complex systems.

Diversified Voting & Flexible Funding System. In this stage, we share with the community the crucial points of our design and research regarding the implementation of an efficient, mathematically refined, and diversified voting and flexible funding mechanics for the Cardano Catalyst and other DOAs in the Cardano ecosystem.

<u>Milestones, Schedule, and Budget</u>

November 2021: Prototyping of Agent-Based Model and Simulation

Lead Staff: Andre Vilela

Support Staff: Computer Scientists, Hess & Nelson

Staff Budget: $14,833

Computer Supply Budget: $1834

December 2021: Complete Voting & Funding Design

Lead Staff: Megan Hess

Support Staff: Social Scientist, Vilela, and Nelson

Staff Budget: $16,300

Survey Supply Budget: $367

January 2022: Analysis of the Power-law Statistics of Design

Lead: Kenric Nelson

Support: Vilela for analysis; Hess for dissemination

Staff Budget: $16,666

Six Month Milestone: Propose and oversee Fund 7 challenge to prototype diversified voting and flexible funding system

Twelve Month Milestone: Collaborate with IOG Voltaire team to implement diversified voting and flexible funding system

<u>References</u>

Square-Root Voting

Werner Kirsch, On Penrose's Square-Root Law and Beyond, in Power, Voting, and Voting Power: 30 Years After, Heidelberg: Springer, 2013.

K. Życzkowski and W. Słomczyński, "Square Root Voting System, Optimal Threshold and π," in Power, Voting, and Voting Power: 30 Years After, Berlin, Heidelberg: Springer Berlin Heidelberg, 2013, pp. 573–592.

W. Kirsch and J. Langner, "The Fate of the Square Root Law for Correlated Voting," Springer, Cham, 2014, pp. 147–158.

• Considers the effect of both Strong Opinions or equivalently a common societal belief system and the influence of neighbors as modeled by spin dynamics.

L. S. Penrose, "The Elementary Statistics of Majority Voting," J. R. Stat. Soc., vol. 109, no. 1, p. 53, 1946.

W. Slomczynski and K. Zyczkowski, "Penrose voting system and optimal quota," Oct. 2006.

Quadratic Voting

Eric A. Posner and E. Glen Weyl. "Quadratic Voting as Efficient Corporate Governance", Coase-Sandor Working Paper Series in Law and Economics, University of Chicago Law School Chicago Unbound, 2013.

Steven P. Lalley and Glen Weyl. "Quadratic Voting: How Mechanism Design Can Radicalize Democracy", Aea Papers and Proceedings, Vol. 108, 2018.

Eric Posner and E. Glen Weyl. "Quadratic Voting and the Public Good: Introduction", 172 Public Choice 1, 2017.

Vitalik Buterin, Zoë Hitzig and E. Glen Weyl. "Liberal Radicalism: A Flexible Design For Philanthropic Matching Funds", Arxiv preprint, 2020.

M. J. Holler and H. Nurmi, Eds., "Power, Voting, and Voting Power: 30 Years After." Heidelberg: Springer, 2013.

Correlation and Complex Systems

S.Braun. "Correlation Functions", Encyclopedia of Vibration, Elsevier, 2001.

K. P. Nelson, S. R. Umarov, and M. A. Kon, "On the average uncertainty for systems with nonlinear coupling," Phys. A Stat. Mech. its Appl., vol. 468, no. 15 Feb, pp. 30–43, Feb. 2015.

K. P. Nelson and S. Umarov, "Nonlinear statistical coupling," Phys. A Stat. Mech. its Appl., vol. 389, no. 11, pp. 2157–2163, Jun. 2010.

Governance Theory

André L. M. Vilela and H. Eugene Stanley. "Effect of Strong Opinions on the Dynamics of the Majority-Vote Model", Scientific Reports, Nature, 2018.

• In this work, we investigate how the presence of individuals with strong voting opinions affects a network of social interactions based on the majority-vote model. We find that such a weighted voting mechanism weakens the consensus of the network, imposing a fragile social-ordered regime, where opposing voting states dominate.
• key insights: voting interactions, weighted voting, consensus robustness.

André L. M. Vilela; Chao Wang; Kenric P. Nelson; H. Eugene Stanley. "Majority-vote model for financial markets", Physica A - Statistical Mechanics and its Applications, Elsevier, 2018.

• In this work, we propose a heterogeneous agent-based two-state sociophysics model to simulate the opinion dynamics on financial markets. Focusing on stock market trader dynamics, we propose a model with two kinds of individuals in which local and global interactions govern the dynamics of buying and selling investors. Despite its simplicity, our model presents such stylized facts of real financial markets and provides us insights regarding the voting dynamics influence on the stock market prices.
• key insights: voting interactions, voting strategies, market opinion dynamics.

M. J. Holler and H. Nurmi, Eds., Power, Voting, and Voting Power: 30 Years After. Heidelberg: Springer, 2013.

Werner Kirsch, On Penrose's Square-Root Law and Beyond, in Power, Voting, and Voting Power: 30 Years After, Heidelberg: Springer, 2013.

A. Laruelle and F. Valenciano, "Voting and Power," in Power, Voting, and Voting Power: 30 Years After, Berlin, Heidelberg: Springer Berlin Heidelberg, 2013, pp. 137–149.

• Provides valuable insights about the shortcomings and difficulties of theoretical analysis of voting. Distinguishes between egalitarian and utilitarian balances of influence. Nevertheless, also derives square-root voting as a weighting mechanism for several important cases.

<u>Photrek and WADA Team</u>

Dr. Kenric Nelson is President and Founder of Photrek, which is developing novel approaches to Complex Decision Systems, including the dynamics of cryptocurrency protocols, sensor systems for ecological studies, and robust machine learning methods. His recent experience includes Research Professor with Boston University's Department of Electrical & Computer Engineering and Sr. Principal Systems Engineer with Raytheon Company. He has pioneered novel approaches to measuring and fusing information, which have been applied to improving the accuracy and robustness of radar signal processing, sensor fusion, and machine learning algorithms. His education in electrical engineering includes completing a B.S. degree summa cum laude from Tulane University, an M.S. degree from Rensselaer Polytechnic Institute, and a Ph.D. degree from Boston University. His professional education includes an Executive Certificate from MIT Sloan and a certification with the Program Management Institute.

Dr. André L. M. Vilela has investigated the dynamics of interacting agent-based models in statistical mechanics, combining phase transitions, critical phenomena, and finite-size scaling analysis with sociophysics, econophysics, and complex network theory. His research focuses on unveiling the underlying mathematical mechanisms that drive the behavior of agents in groups within social networks and financial markets, and how their decisions promote active collective phenomena. He is a Distinguished Visiting Scientist at Boston University, a full Professor at the University of Pernambuco, and Coordinator of the Materials Physics undergraduate program. His education in Physics includes completing a B.S. degree With High Honors Award, an MSc. degree with Distinction Award, and a Ph.D. degree from the Federal University of Pernambuco.

Nelson and Vilela are currently analyzing candidates for the diversified voting influence with an award from Cardano Catalyst Fund 4. They have collaborated together on complex opinion dynamics for 4 years, publishing scientific advances and completing engineering analysis for cryptocurrency platforms such as IOTA. They have experience running mining and stakepool operations.

Megan Hess is joining in this initiative from WADA (West Africa Decentralized Alliance) to assist with communication and collaboration with the wider Cardano ecosystem. Megan is acting as the Sub-Regional coordination lead with WADA for Central Africa, Francophone liaison, and Cameroon Team Lead. She has a Bachelor's degree in Physics from the University of Denver and has taught both Math and Physics at the middle to high school levels. She will be an invaluable addition to this initiative given that she is well versed in explaining complicated mathematical algorithms and concepts which will be crucial in getting the whole community involved in this process. She has been vocal in the community already about some ways in which the voting and decision making process could be improved and is passionate about improving our voting system to make it both fair and understandable.

Cardano Developers and Social Scientists for Voting Systems Photrek will employ a Cardano Developers and Social Scientists focused on designing the specifications for a diversified voting system. The team is currently working closely with the IOG Voltaire team to organize the Catalyst Voting data for analysis. The team is actively participating in the Cardano Catalyst and Catalyst Swarm communities via Discord and Townhalls. Through these discussions and meetings, the team has spoken Robert O'Brien, who has strong expertise in DAO governance. We will work with IOG, Catalyst Swarm, O'Brien and his research colleagues to identify a strong candidate for the position of Cardano Developer for Voting Systems.