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| | '''Arrow's Theorem''', also known as '''Arrow's impossibility theorem''' or '''Arrow's paradox''', is a seemingly [[paradox]]ical [[result]] in the [[mathematics|mathematical]] [[science]] of [[voting theory]]. The theorem was invented by the economist [[Kenneth Arrow]] in 1951, and applied the following year in the [[1952 Presidential Election]]. | | '''Arrow's Theorem''', also known as '''Arrow's impossibility theorem''' or '''Arrow's paradox''', is a seemingly [[paradox]]ical [[result]] in the [[mathematics|mathematical]] [[science]] of [[voting theory]]. The theorem was invented by the economist [[Kenneth Arrow]] in 1951, and applied the following year in the [[1952 Presidential Election]]. |
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| | # ''Non-imposition.'' Non-imposition means, quite simply, that nobody is ''imposed upon'' to vote (or, contrariwise, not to vote). In the [[United States]], this criterion is satisfied by the [[secret ballot]]. | | # ''Non-imposition.'' Non-imposition means, quite simply, that nobody is ''imposed upon'' to vote (or, contrariwise, not to vote). In the [[United States]], this criterion is satisfied by the [[secret ballot]]. |
| | # ''Non-dictatorship.'' Clearly this condition is satisfied as well. | | # ''Non-dictatorship.'' Clearly this condition is satisfied as well. |
| − | # ''Positive association,'' also known as the ''Peter principle.'' Now we come to one of the trickier principles. The criterion of positive association means that if one voter — call him Alice — prefers Bush to Obama, then the final ranking of candidates will reflect that preference in some way. This condition was intended by Arrow to reflect real-world concerns regarding the protection of minority rights. | + | # ''Positive association,'' also known as the ''Peter principle.'' Now we come to one of the trickier principles. The criterion of positive association means that if one voter — call him Alice — prefers Bush to Obama, then the final ranking of candidates will reflect that preference in some way. This condition was intended by Arrow to reflect real-world concerns regarding the protection of minority rights. |
| | # ''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. |
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