# [LMB] OT: Adventures in grading II

**Jim Parish
**
jparish at siue.edu

*Sun, 01 Dec 2002 05:00:47 -0600*

At 11:54 PM 11/30/2002, Mark A. Mandel wrote:
<snip calculations>
And a virtual brownie (sans points) to MAM!
The easiest way to do it is to consider rankings. If 1/3 of the time
A>B>C, and 1/3 of the time B>C>A, and 1/3 of the time C>A>B, then 2/3
of the time A>B, 2/3 of the time B>C, and 2/3 of the time C>A.
The connection with psephology (theory of voting) is that this is a
disguised form of Condorcet's Voting Paradox: in a race with three
candidates, it is possible that candidate A would defeat candidate B
head-to-head, candidate B would defeat candidate C, and yet candidate C
would defeat candidate A. This was noticed by the Marquis de Condorcet
in the late 18th century.
Jim Parish