Sometimes known as the Arrow Paradox, after Kenneth J. Arrow
Three candidates are vying for the position of Governor: A
arroll, and Z
eno. In a poll
, 2/3 of the voters
polled prefer Achilles over Carrol, and 2/3 prefer Carroll over Zeno. You would expect
that most voters would therefore prefer Achilles over Zeno. Not necessarily
If the voters ranked their preferences as follows, most preferred to least preferred, each candidate can say he is preferred over another candidate:
1/3: A C Z
1/3: C Z A
1/3: Z A C
This seeming paradox occurs because we expect the problem to obey the mathematical law
. As a problem in Game Theory
, it is not bound by transitivity.
Any situation where at least 3 alternatives are ranked pairwise by at least 3 criteria can give rise to this sort of paradox. For instance, a man choosing between three possible brides may evaluate their respective strengths in sexual skill, economic advantage, and social grace. Assuming each criterion carries equal weight, he may find himself in the predicament of preferring Amy to Bev, Bev to Chrissy, and Chrissy to Amy.
A Blather of Paradoxes