Arrow's impossibility theorem: Difference between revisions
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The theorem’s content, somewhat simplified, is as follows. |
The theorem’s content, somewhat simplified, is as follows. |
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A society needs to agree on a [[preference]] order among several different options. Each individual in the society has a particular personal preference order. The problem is to find a general mechanism, called a ''social choice function,'' which transforms the set of preference orders, one for each individual, into a global societal preference order. This social choice function should have several desirable (“fair”) properties: |
A society needs to agree on a [[preference]] order among several different options. Each individual in the society has a particular personal preference order. The problem is to find a general mechanism, called a ''social choice function,'' which transforms the set of preference orders, one for each individual, into a global societal preference order. This social choice function should have several desirable (“fair”) properties: |
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* '''unrestricted domain''' or the [[universality criterion]]: the social choice function should create a deterministic, complete societal preference order from every possible set of individual preference orders. (The vote must have a result that ranks all possible choices relative to one another, the voting mechanism must be able to process all possible sets of voter preferences, and it should always give the same result for the same votes, without random selection.) |
* '''unrestricted domain''' or the '''[[universality criterion]]''': the social choice function should create a deterministic, complete societal preference order from every possible set of individual preference orders. (The vote must have a result that ranks all possible choices relative to one another, the voting mechanism must be able to process all possible sets of voter preferences, and it should always give the same result for the same votes, without random selection.) |
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* '''non-imposition''' or '''citizen sovereignty''': every possible societal preference order should be achievable by some set of individual preference orders. (Every result must be achievable somehow.) |
* '''non-imposition''' or '''citizen sovereignty''': every possible societal preference order should be achievable by some set of individual preference orders. (Every result must be achievable somehow.) |
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* '''non-dictatorship''': the social choice function should not simply follow the preference order of a single individual while ignoring all others. |
* '''non-dictatorship''': the social choice function should not simply follow the preference order of a single individual while ignoring all others. |
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