R9: THE CONDORCET TRIANGLE™

The Condorcet Triangle™

Majority Wisdom Is Not An Opinion

MAEGM™ Thesis Micro-Series · Volume 1 Brent Richardson · CEO & Chief Architect · BWR Group Canada — MyBiz AI Division BrentAI.ca

EGAN PRICE Standard — No ambiguities. No shortcuts. No drift.

In 1794, a French mathematician named the Marquis de Condorcet died in a prison cell. He was fifty years old. He had supported the revolution. He had drafted its constitution. And when the revolution turned on its own, it turned on him.

Nine years earlier, in 1785, he had published a proof that would outlive every person who voted to arrest him. The proof was simple: if each member of a group is more likely to be right than wrong, then the majority of the group is almost certainly right — and the larger the group, the closer to certainty that majority gets. One structural requirement: the group must be odd-numbered. An even group can deadlock. An odd group cannot.

The mathematician was killed by a revolution that could not govern itself. His mathematics survived to govern everything that followed.

The Theorem

If each member of a group has a better than even chance of being correct — if their individual competence exceeds fifty percent — then the probability that the majority reaches the correct decision increases as the group grows. At sufficient scale, the probability approaches certainty.

This is not philosophy. This is not opinion. This is a mathematical proof that has been cited, tested, and applied across governance, voting theory, jury design, and decision science for over two centuries.

The theorem has one structural requirement that most institutions ignore: the group must be odd-numbered. An even-numbered panel can deadlock. An odd-numbered panel cannot.

Consider a jury of seven, each member correct sixty percent of the time. Individually, each juror is barely better than a coin flip. But collectively, the probability that the majority reaches the correct verdict exceeds seventy-seven percent. At nine members with the same competence: over eighty percent. At fifteen: over eighty-seven percent. The mathematics are not aspirational. They are arithmetic. More competent participants, properly governed, produce better decisions — and the guarantee strengthens as the group grows.

The requirement that broke most institutions: the group must be odd. Seven works. Eight deadlocks.

But knowing the mathematics is not the same as building the architecture. The theorem tells you WHAT works. The question is HOW — what forces must be in balance for the mathematics to hold in the real world?

The Triangle

Three forces govern every decision architecture that works.

Evidence — the quality of information entering the system. Without verified evidence, competent individuals produce incompetent outcomes. The governance function degrades. Evidence is the left edge of the triangle. It holds the structure up.

Oversight — the accountability architecture that ensures evidence is not manipulated, suppressed, or ignored. Without oversight, evidence becomes selective. The governance function drifts. Oversight is the right edge. It keeps the structure honest.

Collective Judgement — the base. The foundation. The principle that no single individual — regardless of intelligence, authority, or intention — produces better governance outcomes than a competent group operating under transparent rules with verified evidence and independent oversight.

Consider what happens when any edge breaks. A social media platform with no evidence verification amplifies misinformation at the speed of light — the left edge collapses and the triangle falls. A corporation with no independent oversight hides safety data until people are harmed — the right edge collapses. A government that concentrates decision authority in a single office holder bypasses collective judgement — the base cracks and the structure cannot hold.

Every governance failure in history — from the financial crisis of 2008 to the AI ethics departures of 2020 to the algorithmic failures documented in courts today — traces to a broken triangle. Evidence was suppressed. Oversight was captured. Or collective judgement was replaced by a single voice that believed it knew better.

Condorcet understood this. Five years after publishing his theorem, in 1790, he wrote one of the earliest arguments for women’s suffrage — not as a social opinion but as a mathematical conclusion. If competence exceeds fifty percent, the theorem demands inclusion. Excluding half the population from collective judgement weakens the base of the triangle. The mathematician who proved that groups govern better than individuals also proved that those groups must include everyone capable of contributing.

This is what the Condorcet Jury Theorem proves. Not that groups are always right. That groups governed by competence, evidence, and oversight are mathematically more likely to be right than any individual within them.

The Formula

G(n) = f(?,?,?,?)

Four variables. The governance function. What goes inside the brackets determines whether a system can be trusted.

The question marks are not decorative. They are an invitation. What would YOU put inside a governance function? What four conditions would you require before trusting an AI system with decisions that affect your family, your business, your children?

The thesis series that follows this page answers those questions. Not with opinion. With proof. With evidence from two centuries of film. With heritage documented across two hundred years. With architecture that has been independently verified and has produced zero structural failures.

The Seven

Seven people stand before the triangle in the poster. Not six. Not eight. Seven.

Count the layers of any governance architecture you trust. If the number is even, it can deadlock. If the number is odd, it cannot.

Seven bridge officers on the Enterprise. Seven layers in the architecture that governs this framework. Seven — because a mathematician proved it in 1785 and no one has disproven it since.

The people in the poster are looking at the triangle. They are not inside it yet.

That is the invitation.

Behind every theorem is a laboratory, a conversation, a moment where science met storytelling. The artists were never guessing.

G(n) = f(?,?,?,?)

Condorcet, 1785. Still governing.