[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