When Centuries Compete: Condorcet's 18th Century Collective Reasoning and Modern AI Agent Competition

Abstract

This thesis explores how principles from 18th century probabilistic reasoning can be combined with modern autonomous agent systems to improve artificial intelligence validation and reliability.

The Condorcet Jury Theorem, formulated by the Marquis de Condorcet in 1785, demonstrated mathematically that collective judgement can outperform individual decision making when participants independently possess a probability greater than random chance of being correct.

However, modern AI systems such as large language models violate the independence assumption underlying the theorem. Shared training data and architectural similarities produce correlated reasoning errors, meaning multiple models often fail in the same way.

To address this limitation, a second mechanism is introduced: a competitive adversarial testing system in which autonomous agents interact with software through Playwright, competing to discover reproducible defects while being penalised for incorrect reports.

The combination of Enlightenment era probabilistic reasoning and modern agent competition produces a framework designed to improve AI reliability through empirical verification rather than consensus.

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The Central Idea

The thesis is built on two core methods.

Method One: The Condorcet Jury Theorem (1785)

Condorcet demonstrated that if each member of a group is more likely than not to make a correct decision, then the probability that the majority decision is correct increases as the group grows larger.

This principle established the mathematical foundation of collective intelligence.

If each juror has a probability p > 0.5 of being correct, and jurors vote independently, then as the number of jurors n approaches infinity, the probability that the majority vote is correct approaches 1.

— Marquis de Condorcet, Essai sur l'application de l'analyse (1785)

Method Two: Competitive Autonomous Agent Testing

Instead of relying on agreement between agents, autonomous systems compete to discover errors.

Eight agents interact with an application using Playwright and attempt to find software defects through simulated user behaviour.

The scoring rules are deliberately asymmetric:

Outcome	Points	Condition
Real bug discovered	+1 point	Reproducible defect confirmed
False positive submission	-3 points	Three other agents must confirm it is a false positive

The competition continues until an agent reaches twenty points.

This 3:1 penalty ratio is critical. It creates a strong economic disincentive against speculative reporting. An agent submitting one false positive must discover three genuine bugs just to return to its previous score. This forces agents toward high-confidence, evidence-backed submissions.

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Why These Two Centuries Matter

The Enlightenment produced structured reasoning systems designed to analyse uncertainty through probability and explicit assumptions.

Modern AI systems operate through probabilistic prediction and autonomous decision making.

The surprising insight is that 18th century reasoning structures align extremely well with the requirements of modern AI architectures.

• Condorcet provides the conceptual framework for collective reasoning under uncertainty
• Competitive agent testing introduces adversarial incentives and empirical verification

Together they produce a system designed to improve AI accuracy through structured competition and reproducible evidence.

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The Independence Problem

Condorcet's theorem requires that voters make independent judgements. This is where modern AI systems introduce a fundamental challenge.

Large language models share training data, architectural patterns, and optimisation techniques. When GPT-4 and Claude are asked the same question, their errors are often correlated rather than independent. They tend to fail in similar ways because they learned from similar sources.

This means that simply having multiple AI models vote on an answer does not satisfy Condorcet's independence requirement. Five models agreeing on a wrong answer provides far less signal than five independent human experts reaching the same conclusion.

The competitive testing framework addresses this directly. Rather than asking agents to agree on answers, it asks them to find evidence of failures. The adversarial structure and penalty system mean that agents are incentivised to explore different testing paths rather than converge on the same approach.

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How This Improves AI

This approach improves AI systems in several distinct ways:

1. Replaces consensus-based validation with empirical verification — Instead of asking whether models agree, the system asks whether defects can be reproduced. Agreement without evidence is worthless; evidence without agreement is still valuable.
2. Discourages speculative reasoning through asymmetric penalties — The -3 penalty for false positives forces agents to operate with high confidence thresholds before reporting. This mirrors how senior engineers approach bug reports: they verify before escalating.
3. Introduces adversarial peer review among agents — When an agent submits a bug report, other agents have an incentive to challenge it. If they can prove it is a false positive, the submitting agent loses three points. This creates a self-policing quality mechanism.
4. Creates a competitive discovery environment — Competition drives agents to explore different areas of the application rather than clustering around obvious failures. The first agent to discover a bug claims the point, incentivising broader exploration.

Instead of multiple models agreeing on answers, agents must produce evidence that a defect exists.

This shift from agreement to evidence significantly improves reliability.

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Practical Implementation

The framework operates through a straightforward architecture:

1. Target Application — A web application deployed and accessible via browser
2. Agent Pool — Eight autonomous agents, each with Playwright browser access
3. Scoring Engine — Central system tracking points, validating submissions, and managing the competition lifecycle
4. Validation Panel — Three randomly selected agents review each submission for false positive determination
5. Evidence Repository — All bug reports include reproduction steps, screenshots, and network traces

Each agent operates independently, choosing its own testing strategy. Some may focus on form validation, others on navigation flows, and others on edge cases in data handling. The competitive structure naturally produces diverse testing coverage without explicit coordination.

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Conclusion

When viewed together, the Condorcet Jury Theorem and competitive autonomous agent testing represent two centuries of reasoning about collective intelligence.

The Enlightenment provided the mathematical foundations for understanding how groups reason under uncertainty.

Modern AI systems provide the tools to operationalise these ideas through autonomous agents capable of interacting with complex software environments.

By combining probabilistic collective reasoning with competitive empirical validation, this framework proposes a new method for improving artificial intelligence systems — one that values evidence over agreement, competition over consensus, and reproducibility over speculation.