morethanhalf

Morethanhalf is a term used in mathematics, probability, and social choice theory to describe a quantity or threshold that exceeds one half of a defined whole. It represents the simplest form of a majority criterion and is frequently used to determine winners, signals of support, or thresholds for decision-making.

Formally, for a finite set with n elements, morethanhalf refers to a count or subset with size k such that k > n/2. When n is odd, the smallest more-than-half size is (n+1)/2; when n is even, it is n/2 + 1. In probability terms, an event is said to occur with more than half the probability if its probability p satisfies p > 1/2.

Applications of morethanhalf include voting and governance, where it commonly defines a simple majority. It contrasts with supermajorities, which require more than a fixed fraction above 1/2 (for example, two-thirds), and with plurality rules, which require the most votes but not necessarily a majority. In digital logic, the majority function outputs 1 when more than half of its inputs are 1, and in computing and distributed systems, many consensus and fault-tolerance protocols rely on a more-than-half condition to guarantee agreement.

See also: majority, simple majority, absolute majority, supermajority, threshold, voting theory.