One of its conditions is an independence of irrelevant alternatives, which states that the social welfare function must provide the same set of rankings in a subset of choices as it would for the whole set.  
It is analogous to May's theorem, which replaces one of the conditions with anonymity and considers only the case of two options.  The Gibbert- Satterthwaite theorem is a special case of this result, and Amartya Sen extended upon it to create the Liberal Paradox.  One of its conditions is an independence of irrelevant alternatives, which states that the social welfare function must provide the same set of rankings in a subset of choices as it would for the whole set.  First stated in 1951's Social Choice and Individual Values, FTP, name this theorem that says that no non-dictatorial voting system based on ranked preferences of three options can take everyone's choices into account.
It is analogous to May's theorem, which replaces one of the conditions with anonymity and considers only the case of two options.  
{Arrow’s Impossibility} Theorem