It is impossible to formulate a social ordering without violating one of the following conditions:

 Unrestricted Domain: Voting must account for all individual preferences.  Non-Dictatorship: The wishes of multiple voters should be taken into consideration.  Pareto Efficiency/Unanimity: Unanimous individual preferences must be respected: If every voter prefers candidate A over candidate B, candidate A should win.  Independence of Irrelevant Alternatives: If a choice is removed, then the others' order should not change: If candidate A ranks ahead of candidate B, candidate A should still be ahead of candidate B, even if a third candidate, candidate C, is removed from participation