what is arrow s impossibility theorem 
arrow s impossibility theorem is a social choice paradox illustrating the flaws of ranked voting systems it states that a clear order of preferences cannot be determined while adhering to mandatory principles of fair voting procedures arrow s impossibility theorem named after economist kenneth j arrow is also known as the general impossibility theorem understanding arrow s impossibility theoremdemocracy depends on people s voices being heard for example when it is time for a new government to be formed an election is called and people head to the polls to vote millions of voting slips are then counted to determine who is the most popular candidate and the next elected official according to arrow s impossibility theorem in all cases where preferences are ranked it is impossible to formulate a social ordering without violating one of the following conditions arrow s impossibility theorem part of social choice theory an economic theory that considers whether a society can be ordered in a way that reflects individual preferences it was lauded as a major breakthrough and went on to be widely used for analyzing problems in welfare economics 1example of arrow s impossibility theoremlet s look at an example illustrating the type of problems highlighted by arrow s impossibility theorem consider the following example where voters are asked to rank their preference among three projects a b and c this country has 99 voters who are each asked to rank the order from best to worst for which of the three projects should receive the annual funding in this scenario 66 voters prefer a over b 66 voters prefer b over c and 66 voters prefer c over a this represents a paradoxical result as a two thirds majority of voters prefer a over b b over c and c over a arrow s theorem posits that it is impossible to formulate a social ordering on a problem such as indicated in this example without violating one of the above conditions 1arrow s impossibility theorem is also applicable when voters are asked to rank political candidates however there are other popular voting methods such as approval voting or plurality voting that do not use this framework history of arrow s impossibility theoremthe theorem is named after economist kenneth j arrow arrow who had a long teaching career at harvard university and stanford university introduced the theorem in his doctoral thesis and later popularized it in his 1951 book social choice and individual values the original paper titled a difficulty in the concept of social welfare earned him the nobel memorial prize in economic sciences in 1972 12arrow s research has also explored the social choice theory endogenous growth theory collective decision making the economics of information and the economics of racial discrimination among other topics 