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Rating things and Arrow’s Impossibility

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One problem in rating multiple products on multiple criteria is that you can encounter odd paradoxes.

Example:    John rates 3 soaps on 3 criteria: Fragrance, Cushion, and Slickness. From best to worst they rank:

Fragrance: A, B, C
Cushion:    B, C, A
Slickness:  C, A, B

John prefers one soap to another if it ranks higher on 2 or more of the criteria.

Thus he prefers A to B, since A ranks higher than B on Fragrance and Cushion.

He also prefers B to C, since B ranks higher than C on Fragrance and Slickness

And he prefers C to A, since C ranks higher than A on Cushion and Slickness.

So which of the three does he prefer overall?

This is why some of us have a lot of soaps: we prefer them all.🙂


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