Binary independence condition
Binary independence is a condition in Arrow's theorem. A voting method F satisfies binary independence if and only if the following condition holds; Let A and B be two candidates, and let p1 and p2 be two profiles where each voter's preference for A vs. B in p1 agrees with her A vs. B preference in p2. Then F gives the same A vs. B ranking for both p1 and p2.
The Binary Independence condition requires that in determining the A vs. B outcome, we cannot consider the voter's preferences for B vs. C or C vs. A.