In Boolean logic, the majority function (also called the median operator) is the Boolean function that evaluates to false when half or more arguments are false and true otherwise, i.e. the value of the function equals the value of the majority of the inputs.

A majority gate is a logical gate used in circuit complexity and other applications of Boolean circuits. A majority gate returns true if and only if more than 50% of its inputs are true.

For instance, in a full adder, the carry output is found by applying a majority function to the three inputs, although frequently this part of the adder is broken down into several simpler logical gates.

Many systems have triple modular redundancy; they use the majority function for majority logic decoding to implement error correction.

A major result in circuit complexity asserts that the majority function cannot be computed by AC0 circuits of subexponential size.

For any x, y, and z, the ternary median operator ⟨x, y, z⟩ satisfies the following equations.

An abstract system satisfying these as axioms is a median algebra.

Other useful properties of the ternary median operator function include: