Strict Majority (COMSOC)

Definition

Strict Majority ( COMSOC)

A strict majority is support from more than half of the voters being counted. For $k$ supporters among $n\ge 1$ voters,

$$k>\frac{n}{2}⟺k\ge \lfloor \frac{n}{2}\rfloor +1.$$

In a head-to-head contest with complete, strict rankings, $x$ defeats $y$ by strict majority exactly when

$$N_R(x,y)>n/2,$$

where $N_R$ is the pairwise support function. Exactly half is insufficient: a tie is not a victory.