cleve callison’s blog

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)