Theory of majority decision elements

Abstract

A decision-making organization whose output is either 1 or 0 according to which of the numbers, 1 or 0, is predominant in its inputs, is defined as the majority decision element. A Boolean function represented by such an element is called a majority decision function. Elements of this sort play a significant role in the computer field. The present paper deals with various problems concerned with a single element of this sort: that is, in Section 3, the algebraic properties, and a necessary condition for realizability of a given function; in Section 4, the types of functions realizable by a single element; in Section 5, the determination of the structure of the element for a given function by means of linear programming; and in Section 6, properties of the functions of a small number of variables realizable by a single element. © 1961.