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# ''Independence of irrelevant alternatives'' (known jocularly as the ''Nader corollary''). This condition means that a third-party candidate (such as [[Ralph Nader]] in the 2000 primaries) should not be able to "swing" the election to one side or another. In particular, a third party should be unable to draw votes away from the primary candidates, as Nader did to [[Al Gore]] in 2000, or as [[Pat Buchanan]] did to [[George W. Bush|Bush]]. This condition is perhaps the most relevant to the state of elections in the [[United States]] today.

# ''Independence of irrelevant alternatives'' (known jocularly as the ''Nader corollary''). This condition means that a third-party candidate (such as [[Ralph Nader]] in the 2000 primaries) should not be able to "swing" the election to one side or another. In particular, a third party should be unable to draw votes away from the primary candidates, as Nader did to [[Al Gore]] in 2000, or as [[Pat Buchanan]] did to [[George W. Bush|Bush]]. This condition is perhaps the most relevant to the state of elections in the [[United States]] today.

In 1951, Kenneth Arrow proved that no system of voting, however so fair, can possibily satisfy all five of these constraints. For example, the [[Electoral College]] system used in the United States satisfies all of them except the last two (and in fact even the first, unrestricted domain, is questionable, since [[federal judge]]s are not elected by the people, but rather ''appointed'' by the bench).

In 1951, Kenneth Arrow proved that no system of voting, however so fair, can possibly satisfy all five of these constraints. For example, the [[Electoral College]] system used in the United States satisfies all of them except the last two (and in fact even the first, unrestricted domain, is questionable, since [[federal judge]]s are not elected by the people, but rather ''appointed'' by the bench).

The 1952 Presidential election demonstrated beyond doubt the correctness of Arrow's vision; incumbent [[Dwight D. Eisenhower]] beat his "egghead" Democratic challenger [[Adlai Stevenson]] in the largest landslide in human history. Nevertheless, the [[West Virginia]] Democratic primary was won by [[Averell Harriman]], who had never before held any elected office. This abnomaly led to closer investigation of Arrow's results. For his work on modern voting metholodgy, Arrow was awarded the 1972 [[Nobel Prize]] in [[Economics]].

The 1952 Presidential election demonstrated beyond doubt the correctness of Arrow's vision; incumbent [[Dwight D. Eisenhower]] beat his "egghead" Democratic challenger [[Adlai Stevenson]] in the largest landslide in human history. Nevertheless, the [[West Virginia]] Democratic primary was won by [[Averell Harriman]], who had never before held any elected office. This abnomaly led to closer investigation of Arrow's results. For his work on modern voting metholodgy, Arrow was awarded the 1972 [[Nobel Prize]] in [[Economics]].

[[Category:Mathematics]]

[[Category:Mathematics]]