  The Condorcet Jury Theorem or the Miracle of Aggregation are frequently
invoked to ensure the competence of some aggregate decision-making processes.
In this article we explore an estimation of the prior probability of the thesis
predicted by the theorem (if there are enough voters, majority rule is a
competent decision procedure). We use tools from measure theory to conclude
that, prima facie, it will fail almost surely. To update this prior either more
evidence in favor of competence would be needed or a modification of the
decision rule. Following the latter, we investigate how to obtain an almost
sure competent information aggregation mechanism for almost any evidence on
voter competence (including the less favorable ones). To do so, we substitute
simple majority rule by weighted majority rule based on some weights correlated
with epistemic rationality such that every voter is guaranteed a minimal weight
equal to one.
