Cherry pie
[Update 7/15/10: here’s an analysis of on The Arithmetic of Voting, related to the material below. Not a surprise that approval voting is the way to go.]
From Martin Gardner. Not really a paradox, but it is entirely possible to have:
- two-thirds of the people prefer apple pie to blueberry;
- two thirds prefer blueberry to cherry; and
- two thirds prefer cherry to apple.
Imagine that you have 99 pie-eaters. . .
- the 33 Albigensians prefer apple, blueberry and cherry, in that order
- the 33 Bulgars prefer blueberry, cherry and apple, in that order
- the 33 Cathars prefer cherry, apple and blueberry, in that order
So we have:
- 2/3rds (66) prefer apple to blueberry (the Albigensians and the Cathars)
- 2/3rds prefer blueberry to cherry (Albigensians and Bulgars)
- 2/3rds prefer cherry to apple (Bulgars and Cathars)
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