Arrow Impossibility Theorem

 

The theorem in economics, due to Kenneth Arrow, which says that you can't construct a "social preference function" (ranking the desirability of varius social arrangements) out of individual preferences, while retaining a particular set of features ("nondictatorship" - the social preference function can't be just one person's individual preferences; consistency - the social preference function can't rank A above B, B above C, and C above A; "positive relation" between individual and social preference - if the social preference function ranks A above B, and some person's individual preference changes from "B above A" to "A above B", that shouldn't cause the social preference to switch to "B above A"; and an "irrelevance" assumption which I don't quite remember, but is something like this, that if an individual changes their mind about the relative worth of C and D, it shouldn't affect the social preference standings of A and B.)

Source

The theorem in economics, due to Kenneth Arrow, which says that you can't construct a "social preference function" (ranking the desirability of various social arrangements) out of individual preferences, while retaining a particular set of features ("nondictatorship" - the social preference function can't be just one person's individual preferences; consistency - the social preference function can't rank A above B, B above C, and C above A; "positive relation" between individual and social preference - if the social preference function ranks A above B, and some person's individual preference changes from "B above A" to "A above B", that shouldn't cause the social preference to switch to "B above A"; and an "irrelevance" assumption which I don't quite remember, but is something like this, that if an individual changes their mind about the relative worth of C and D, it shouldn't affect the social preference standings of A and B.)

Source


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