Majority function

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.

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

For n = 3 the ternary median operator can be expressed using conjunction and disjunction as xy + yz + zx.

For an arbitrary n there exists a monotone formula for majority of size O(n5.3).

[3] Approaches exist for an explicit formula for majority of polynomial size: Media related to Majority functions at Wikimedia Commons