Nostr Revolution: Possible Solutions to the Mathematical Impossibilities of Voting Systems

Democracy, a system that ideally reflects the will of the people, faces significant mathematical challenges, particularly in the way votes are cast and counted. One of the most prominent issues lies within the first-past-the-post (FPTP) voting system, a method that has been in use for centuries. This system allows voters to select only one candidate, which can lead to scenarios where a party secures power without obtaining a majority of the votes. Such outcomes raise questions about the true representation of voter preferences and the overall health of democratic processes.

The Flaws of First-Past-The-Post

The FPTP system has been illustrated through historical examples, such as the British Parliament and the contentious 2000 U.S. presidential election. In these instances, the so-called “spoiler effect” emerged, where third-party candidates siphoned votes from major candidates, ultimately skewing the results. Voters often feel that their preferences are not accurately represented, leading to disillusionment with the electoral process. This discontent underscores the need for a more representative voting system.

Introducing Ranked-Choice Voting

To address the shortcomings of FPTP, ranked-choice voting (RCV), also known as instant runoff voting, has been proposed. In this system, voters rank candidates in order of preference, allowing for a more nuanced reflection of voter sentiment. RCV not only captures a broader spectrum of voter preferences but also encourages candidates to engage in more civil discourse. For example, in the 2013 Minneapolis mayoral race, candidates exhibited a camaraderie that is often absent in traditional campaigns, as they sought to appeal to voters for second and third choices.

However, the implementation of RCV is not without its challenges. Concerns arise about the potential for a candidate performing poorly to inadvertently assist in the election of another candidate. A hypothetical scenario involving three candidates—Einstein, C, and Bore—illustrates this point. The elimination of candidates based on voter preferences can lead to unexpected outcomes, complicating the electoral landscape.

Historical Context and Mathematical Foundations

The discussion of voting systems is enriched by historical context, particularly through the lens of French mathematician Marie Jean Antoine Nicolas de Caritat, the Marquis de Condorcet. Condorcet advocated for a fair voting method that required candidates to win head-to-head matchups. His method, which involves ranking preferences, introduces a potential issue known as Condorcet’s Paradox. This paradox occurs when cyclical preferences prevent a clear winner from emerging, highlighting the complexities of voter choice.

Various mathematicians, including Lewis Carroll, have sought to develop fair election systems but encountered similar challenges. In 1951, economist Kenneth Arrow proposed five conditions that a voting system should meet to ensure fairness: decisiveness, unrestricted domain, transitivity, independence of irrelevant alternatives, and stability of group preferences. These conditions serve as a benchmark for evaluating the effectiveness of different voting systems.

Arrow’s Impossibility Theorem

A significant aspect of the discussion revolves around Arrow’s impossibility theorem, which posits that it is impossible to create a ranked voting system that satisfies all five of Arrow’s conditions when there are three or more candidates. This theorem can be illustrated through a thought experiment involving three candidates (A, B, and C) and various voter rankings. The proof demonstrates that if a candidate is unanimously ranked first or last by voters, society must reflect that ranking. However, the theorem also reveals scenarios where a pivotal voter can dictate the overall ranking, effectively acting as a “dictator” in determining societal preferences.

This leads to a sobering conclusion: according to Arrow’s theorem, a truly democratic voting system is unattainable when dealing with multiple candidates. Yet, there is a more optimistic perspective introduced by mathematician Duncan Black, suggesting that alternative methods may exist to better represent voter preferences.

The Dynamics of Voter Preferences

The dynamics of voter preferences along a political spectrum, from liberal to conservative, further complicate the electoral process. The choice of the median voter often determines election outcomes, aligning with the majority’s decision and helping to avoid the paradoxes identified by Arrow’s theorem. This discussion introduces rated voting systems, particularly approval voting, where voters indicate approval for candidates without ranking them.

Research indicates that approval voting can increase voter turnout, reduce negative campaigning, and mitigate the spoiler effect. Despite its historical use in electing popes and the Secretary General of the United Nations, approval voting has not been widely adopted in large-scale elections, suggesting a need for further real-world testing and evaluation.

The Importance of Political Engagement

While traditional voting methods like FPTP have significant flaws, the importance of political engagement and the necessity of striving for a more representative electoral process cannot be overstated. The complexities of voting systems and the historical evolution of these methods highlight the ongoing struggle for fairness in elections.

As democracy continues to evolve, enhancing knowledge and critical thinking skills about voting systems will be crucial in advocating for reforms that better reflect the will of the people. Understanding the mathematical underpinnings of these systems is essential for promoting a more equitable and representative democratic process.

The mathematical challenges of democracy, particularly in the context of voting systems, reveal significant flaws in traditional methods like first-past-the-post. The exploration of ranked-choice voting and other alternatives offers a glimpse into potential solutions that could enhance voter representation and engagement. As society navigates the complexities of democratic processes, it is essential to remain informed and proactive in advocating for systems that truly reflect the diverse preferences of the electorate.

Proposed Solution: Leveraging the Nostr Protocol

To further enhance the democratic process and address the challenges of traditional voting systems, we can consider utilizing the Nostr protocol. Nostr is a decentralized protocol that allows for open, self-verifiable, anonymous communication and data sharing, making it an ideal candidate for implementing a modern voting system. There have been other attempts at voting via nostr, this is my concept and contribution. View the code below.

Key Features of Using Nostr for Voting

1. Decentralization: By leveraging Nostr’s decentralized architecture, we can eliminate single points of failure and reduce the risk of manipulation or censorship in the voting process.
2. Public-Private Key Cryptography: Each voter can generate a unique public npub and private nsec key pair. The npub public key serves as their identity, while the nsec private key is used to sign votes, ensuring authenticity and integrity.
3. Anonymity and Privacy: Voter identities can remain anonymous, as only their public keys are visible. This protects against coercion and ensures that voters can express their preferences freely.
4. Secure Vote Submission: Voters can submit their ranked choices or preferences as signed encrypted messages through Nostr and its relays. This ensures that votes are tamper-proof and verifiable.
5. Real-Time Results and Transparency: The distributed nature of Nostr allows for real-time updates on the voting process, providing transparency and enabling independent verification of results.
6. Mitigating the Spoiler Effect: By implementing ranked-choice voting through Nostr, we can capture a broader spectrum of voter preferences and reduce the impact of third-party candidates acting as spoilers (hopefully).
7. Public Auditing: The system can provide an audit trail of all votes cast, allowing for independent verification and fostering trust in the electoral process.

By integrating the Nostr protocol into the voting process, we can create a more secure, transparent, and representative electoral system, particularly at the local level. This approach not only addresses the mathematical challenges of traditional voting methods but also empowers voters and enhances engagement in the democratic process.

I am new and inexperienced in programming, but I have wrote a bit of code with the help of general purpose AI’s. Please review and improve and/or comment as best you can below👇

Code on Github

Thank you for supporting my work with zaps ⚡ supermax@minibits.cash

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I would like to implement a test at some point when the code is running stable. A distributed vote, if you will. Thank you for your support.

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