One consequence of it is the Gibbard-Satterthwaite Theorem, which deals with the concept of non-imposition, or the inclusion of a potential for every result.  
Fishburn proved it false in an infinite case, while Armstrong proved the same result even when profiles are restricted to those which use a Boolean algebra of coalitions. One consequence of it is the Gibbard-Satterthwaite Theorem, which deals with the concept of non-imposition, or the inclusion of a potential for every result.  Underpinning this theory is the concept of unrestricted domain, and excluding the Smith set, some methods can meet all the criteria that it demands.  Amartya Sen famously tried to disprove by using utility analysis.  If it did not hold, a mapping function would have two properties, one of which is monotonicity, or the inability to hurt an option by ranking it higher.  That function would  map individual preferences to societal preferences.  First posited in 1951's Social Choice and Individual Values, FTP, name this theorem, which states that no set of rules for social choice can be achieved that satisfy all reasonable criteria of society, named for a 1972 Nobel Prize-winning economist.
Fishburn proved it false in an infinite case, while Armstrong proved the same result even when profiles are restricted to those which use a Boolean algebra of coalitions.
Arrow's Impossibility Theorem