In this note we show the consistency of majority decisions under preference conditions that are more general than Single-Peaked Preferences (Arrow [1], Black [2]), Single-Caved Preferences (Inada [5]), Preferences separable into Two Groups (Inada [5]), and Latin-Square-less Preferences (Ward [12]). In the first part of the note, the underlying concepts and approach are introduced; in the second part the theorem is stated and proved; and in the third part its relationship with other sufficiency conditions is discussed.