Condorcet's 1785 result that if voters choose independently between two options and each is more likely than not to be right, a majority's chance of being right rises with group size and approaches certainty.
In more detail
The theorem cuts both ways: if average competence is below one half, larger groups are almost certainly wrong. Later results relax the assumption of equal competence (Grofman, Owen and Feld, 1983) and extend it to more than two options (List and Goodin, 2001). The most demanding assumption is independence: voters who rely on the same sources or leaders make correlated errors, which weakens the effect. The theorem is central to epistemic arguments for democracy and to debates about juries, committees and crowds.