Multi-Scientist Consensus

THE CLASSICAL RESULT. Condorcet's jury theorem (1785), in its standard elementary form: for a BINARY question with a correct answer, decided by sincere majority vote among an odd number of voters whose votes are CONDITIONALLY INDEPENDENT given the truth and who each have the same probability p above one half of being right, the probability the majority is correct rises toward one as the group grows. It is the formal case for aggregating judgements, and it is the reason 'the desks agree' feels like strong evidence.

NOW READ THE CONDITIONS, because both are load-bearing and neither holds cleanly here.

• CONDITIONAL INDEPENDENCE. The scientists read overlapping data - largely the same prices, the same news corpus, the same universe and window - so their errors are correlated and the elementary theorem simply does not apply. That does not mechanically erase every benefit of aggregating; the effect depends on the dependence structure, and sufficiently persistent positive correlation is what prevents accuracy converging to one. Correlated voters reading one dataset can agree confidently and be wrong together.
• BETTER THAN CHANCE. Under the same assumptions, if EVERY voter has p below one half, majority accuracy falls toward zero as the group grows. The theorem is a lever that works in both directions, and nothing in a consensus score establishes which side of one half the voters sit on.

SO WHAT IS THE HONEST READING? A consensus is a summary of what the desks said, weighted by a convention we chose. It is not a probability that the read is correct, and its confidence should not rise with the number of agreeing scientists in the way the theorem would license.

DISSENT FLAGS ARE THE MOST VALUABLE OUTPUT HERE, and it is worth saying why rather than treating them as a nicety. Correlation reduces the incremental information carried by agreement, which makes DISSENT worth investigating - it may reveal genuinely different inputs or methods. Do not overstate it into a rule: dissent can equally reflect noise, misspecification or an unstable model, and agreement among correlated analysts is not worthless. Surfacing dissent explicitly, rather than averaging it away, is what distinguishes a synthesis from a smoothing operation - an average of correlated opinions with the outliers removed is the least informative object you can build from a set of analyses.

MISSING INPUTS LOWERING COVERAGE RATHER THAN FAILING THE RUN is the right design, and note what it implies for reading: a consensus formed over three scientists and one formed over ten are not the same measurement, so coverage should be read before the score.