This principle, which has become a widely applied strategy in making fishing procedures more efficient, is described in an anonymous Italian manuscript from the 1600s called “Sloan 424”. The principle is employed within an early form of card divination now commonly known as “Out of Sight, Out of Mind”. Lori Pieper's English translation of “Sloan 424” was published in Gibecière, Vol. 5, No. 2, Summer 2010; see p. 155 for this divination trick.
The Principle of Majorities is clearly explained by William Larsen, Sr., in his manuscript, I Won't Play Cards with You, 1931, p. 3. However, the principle doesn't seem to have achieved wider notice until Orville Mayer discussed it in detail in Magic in the Modern Manor, 1949, p. 62. Mayer states the principle is not his origination, but he provided it with a functional name: The Principle of Majorities.