The 1785 Proof That Three Judges Beat One — Condorcet and the Mathematics of Panel Composition

In 1785, the Marquis de Condorcet proved mathematically what common sense had always suggested: that a group of independently competent decision-makers, each more likely than not to be right, will collectively reach the correct answer with a probability that increases toward certainty as the group grows. It is one of the few results in social choice theory that genuinely deserves the label "theorem." Two hundred and thirty-nine years later, the Joint Presidential Guidance on panel composition arrived on every Employment Tribunal judge's desk — asserting, without quite explaining, that lay members "add significant value" to the process of adjudication.

The Guidance and the theorem are making the same argument. Only one of them shows its working.

The October 2024 Guidance

The Joint Presidential Guidance on Panel Composition, issued by Judge Barry Clarke and Judge Susan Walker on 29 October 2024, implements the most significant structural change to Employment Tribunal proceedings in recent years. Under the accompanying Practice Direction, judges now decide case by case — having regard to "the interests of justice and the overriding objective" — whether a tribunal should consist of a judge sitting alone or a judge with two non-legal members.

The Guidance lists the relevant factors at paragraph 8: the views of the parties (not determinative); whether the issues require "an understanding of contemporary workplace norms, practices and challenges, to which members can contribute their experience"; and the practical availability of members. Non-legal members are described as bringing "experience of the workplace" so that "any decisions to which they contribute are made with an understanding of the realities of the modern workplace and current industrial practices." In the Senior President's words, their involvement is "an indispensable part of the style and culture of tribunals justice."

What the Guidance does not do is explain why that additional experience improves outcomes. It asserts the value. It does not identify the mechanism.

Condorcet's Jury Theorem

Condorcet's Jury Theorem, published in his Essai sur l'application de l'analyse à la probabilité des décisions rendues à la pluralité des voix (1785), provides exactly that mechanism. The theorem is straightforward: if each member of a decision-making body is more likely than not to reach the correct answer on a given question, the probability that the majority will be correct increases with the size of the body — and converges toward certainty as it grows.

Two conditions matter. Each decision-maker must be independently competent — bringing distinct information or judgment, not merely duplicated reasoning. And the question must admit of a better and a worse answer.

Employment Tribunal lay members satisfy both conditions in a way worth pausing over. An employer member who has spent decades managing workforces and an employee member who has served as a trade union representative bring cognitive inputs that are genuinely independent of the Employment Judge's legal training. When the tribunal asks whether an employer's decision fell within the range of reasonable responses, or whether unwanted conduct had the effect of violating a person's dignity, the lay members are not duplicating the judge's analysis. They are supplementing it with something the judge, by training and professional formation, may not possess: lived experience of how workplaces actually function.

The Condorcetian implication is precise. The more a determination depends on an assessment of workplace norms — the more that "reasonableness" is doing the real work in the legal test — the greater the expected accuracy gain from a full panel. Paragraph 9 of the Guidance intuitively reflects this: its examples of cases where members add value are overwhelmingly those involving assessments of reasonableness. But it reaches the destination without mapping the route.

I should concede that the analogy is imperfect. Condorcet assumed binary choices and independent voting. Tribunal deliberations are richer: members can persuade one another, revise their positions, and engage in genuine deliberation rather than simultaneous polling. But this is an objection that strengthens rather than weakens the case for panels. Deliberation between independently informed decision-makers is at least as powerful a mechanism for improving accuracy as independent voting — and arguably more so.

Jury Equity: What Panels Are Not

There is a second, older tradition of lay participation in English justice that illuminates the Employment Tribunal position by contrast.

In Bushell's Case (1670), Vaughan CJ established the principle that jurors cannot be punished for their verdicts. Edward Bushell was one of two jurors fined and imprisoned for acquitting William Penn and William Mead of unlawful assembly — a prosecution so transparently political that the jury's refusal to convict became the foundation of modern jury independence. As the Court of Appeal recently put it in R v Webster & Ors [2026] EWCA Crim 9, at paragraph 52, Bushell's Case "may be best understood as recognising an immunity from punishment in respect of their decision as to what verdict to return, rather than a right to return verdicts in defiance of the evidence."

From that immunity grows the doctrine of jury equity: the unreviewable power of a jury to acquit according to conscience. Saini J adopted what the Court of Appeal called "a rather more expansive approach" to this doctrine in HM Solicitor General v Warner [2024] EWHC 918 (KB), holding that jury equity was "a principle of our law" and "an established feature of our constitutional landscape." The Court of Appeal in Webster, while not doubting that the freedom exists, pointedly declined to follow Warner, observing that the rule against mentioning jury equity in court "does not resolve this tension, it hides it."

The constitutional settlement around jury equity is, to put it charitably, productive rather than elegant. Jurors possess the power to nullify. But nobody in court may tell them so. Employment Tribunal lay members occupy a fundamentally different position. They have no power to nullify. They cannot override the legal framework or return a verdict of conscience. They sit with the judge, not in opposition to the judge.

Their contribution is epistemic, not equitable: they improve the quality of fact-finding by bringing information the judge lacks. The lay member who has spent thirty years in HR or on a shop floor sees something the judge does not — not a reason to override the law, but a reason to apply it differently to the facts.

Practical Implications

The Guidance's factors, read through this lens, acquire sharper edges. Practitioners should press for a full panel wherever the central issue turns on workplace norms that a judge sitting alone might assess differently from those who have inhabited the relevant environment: the "range of reasonable responses" in unfair dismissal; whether conduct was "unwanted" in harassment claims; the reasonableness of an employer's failure to make adjustments; whether a belief was "reasonable" in whistleblowing.

Conversely, where the hearing is genuinely confined to legal questions — jurisdiction, time limits, the construction of contractual terms — the Condorcetian case for members weakens, and the proportionality concerns at paragraph 8.3 of the Guidance (member availability, delay, cost) become more significant.

Ireland v University College London [2024] EAT 68, cited at footnote 17 of the Guidance, is a reminder that panel composition decisions are not merely administrative. They are case management orders capable of grounding a challenge on appeal. Practitioners who fail to engage with the panel composition question on the ET1 and ET3 forms, or at the preliminary hearing where the question is typically decided, are leaving a structural issue unaddressed that may matter more than any individual witness.

The Presidential Guidance tells practitioners that lay members are valuable. Condorcet explains why — and by extension, when. Jury equity, the older and more dramatic tradition of lay participation, clarifies what Employment Tribunal panels are not: a conscience-based check on judicial power. They are something both narrower and, for the practitioner advising a client at a case management hearing, more useful: a mechanism for reducing the risk — with mathematical confidence in the result — that the law will be applied correctly to facts that nobody in the room has the experience to assess. That last scenario is not a crisis. It is merely a worse decision, reached more efficiently.

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