More votes help only under the right errors¶
Cross-Domain EchoesShared pattern · Aggregation
A model ensemble combines predictions from several trained models. An idealized jury model combines binary judgments by majority vote. In both, the usefulness of the group depends on how individual errors combine, not just on how many opinions are collected. Condorcet’s model makes this unusually clear: independent, equally competent voters improve the majority only when each is better than chance. Real machine-learning ensembles may use dependent training and learned weights instead. The shared diagram separates contributors, combination rule, and result, so the conditions behind “more is better” cannot hide inside the group’s size.
Choose a role to see its counterpart in both examples. The diagrams show relationships, not measured quantities.
Machine learning
Combine model predictions
Read Ensemble learningDomain-specific abstraction
Multiple models contribute predictions under a fixed or learned aggregation rule.
In this example: Training dependence and out-of-sample validation matter; extra models alone are not a guarantee.
Collective judgment
An idealized odd-numbered jury
Read Condorcet's Jury TheoremDomain-specific abstraction
A majority combines independent, equally competent binary judgments in a mathematical model.
In this example: The pictured contributors stand for an odd panel; they are not a literal two-person majority.
Contributors supply separate outputs; the relation between their errors determines how much new information is added.
Written comparison
What is combined
Machine learning
Predictions from multiple trained models
Collective judgment
Judgments from an idealized odd panel
Contributors supply separate outputs; the relation between their errors determines how much new information is added.
The combining rule
Machine learning
Voting, weighting, or a learned combiner
Collective judgment
Unweighted simple majority
The rule is a substantive modeling choice, not an invisible bookkeeping step.
The aggregate result
Machine learning
One prediction evaluated on unseen data
Collective judgment
One binary group answer
A group result requires its own performance argument. Condorcet supplies one under narrow assumptions; an arbitrary ensemble needs validation.
What carries across
Before adding more contributors, inspect the quality and dependence of their errors and the combining rule. A larger aggregate can amplify a shared mistake.
Where the comparison stops
Condorcet’s guarantee requires independent, equal-quality, better-than-chance binary judgments and an odd simple majority. Most trained ensembles do not automatically satisfy these conditions.
- The jury is a mathematical illustration, not an empirical claim about courts or elections. Learned weights, boosting, and shared training data can produce different dependencies.
Conditions for this comparison
- The task has a defined target against which output quality can be assessed.
- Competence, dependence, and aggregation rule are checked before claiming a benefit from extra members.
Source entries
Shared pattern
Aggregation
Prime
Core Idea
Aggregation collapses many items into a unified form that retains chosen features while suppressing granular detail, formalized in classical statistics as the reduction of a sample to a summary statistic (Fisher, 1925).
Machine learning
Ensemble learning
Domain-specific abstraction
Core Idea
Bagging, random forests, boosting, stacking and voting differ in dependence, training sequence and combiner; leakage-free validation and diversity matter more than model count alone.
Collective judgment
Condorcet's Jury Theorem
Domain-specific abstraction
Core Idea
If their correctness events are independent and have the same probability \(p\), a simple majority is more reliable as the odd group grows when \(p>1/2\), and its accuracy approaches one in the idealized unlimited-size limit.