Social choice theory

Condorcet jury theorem and collective accuracy

The Condorcet jury theorem gives a hopeful result. If voters are independently more likely than not to choose the correct option, majority decisions can become more accurate as the group grows.

Nicolas mechanism signals

These concepts follow the mathematical contract used by the app.

Convex cost

cost = c * sum a_ij^2

Voice budget

sum a_ij^2 <= B

Outcome rule

shifted softmax over support

What the theorem says

In its classic form, the theorem assumes a binary choice with a correct answer, where each voter independently has a probability greater than one half of choosing correctly.

Under those assumptions, the probability that the majority chooses correctly rises as the number of voters grows.

Why the assumptions matter

The result depends on competence, independence, and a decision with a meaningful correct answer. Many political, workplace, and governance choices fall outside it because they are value tradeoffs rather than factual questions.

Correlated errors, shared misinformation, or unequal expertise can weaken the theorem's relevance.

Where Nicolas fits

Nicolas is useful when the group needs to compare alternatives and measure how strongly participants care, rather than when it needs an accuracy theorem tool.

Delegation can help route influence toward trusted expertise, but it does not by itself guarantee independence or correctness.

Use cases

Where this decision model helps

Competence assumptions

Ask whether participants are independently more likely than not to identify the stronger option.

Expertise routing

Use delegation carefully when knowledge is unevenly distributed.

Value tradeoffs

Recognize when a decision is about preference intensity rather than objective correctness.

FAQ

Does the theorem apply to every group vote?

No. It is most relevant when there is a correct answer and voters make sufficiently independent judgments.

Does delegation guarantee stronger decisions?

No. Delegation can route influence toward trusted expertise, but it does not guarantee competence, independence, or accuracy.

Why include it near Nicolas?

It helps explain when group size and voting can improve accuracy, and where Nicolas' preference-intensity model solves a different problem.