[EM] Thread on rec.sport.table-tennis

[Rob Lanphier]

Hi all,

There's currently a thread going on on the rec.sport.table-tennis Usenet 
newsgroup:

http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&safe=off&threadm=U_2cneATzah6cTujXTWcqg%40comcast.com&rnum=3&prev=/groups%3Fq%3D%2522kenneth%2Barrow%2522%2BOR%2B%2522arrow%27s%2Btheorem%2522%26hl%3Den%26lr%3D%26ie%3DUTF-8%26safe%3Doff%26scoring%3Dd%26selm%3DU_2cneATzah6cTujXTWcqg%2540comcast.com%26rnum%3D3

The gist is that they are trying to figure out how to fix the way 
rankings are done.  I haven't followed it fully, but figured that there 
would be people here who might be interested.

Rob

----
From: Larry Bavly 
<http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&safe=off&q=author:bavly%40rci.rutgers.edu+> 
(bavly at rci.rutgers.edu <mailto:bavly%40rci.rutgers.edu>)
Subject: Re: Ratings

 
View this article only 
<http://groups.google.com/groups?q=g:thl4282187313d&dq=&hl=en&lr=&ie=UTF-8&safe=off&selm=3EA6D79A.3060403%40rci.rutgers.edu> 


Newsgroups: rec.sport.table-tennis 
<http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&safe=off&group=rec.sport.table-tennis>
Date: 2003-04-23 11:11:26 PST

rickchartrand wrote:

>Finally: no rating system will ever be perfect.  There's actually a
>mathematical theorem related to this (Arrow's Theorem, in the context of
>elections; no election system can always reflect the will of the people). 
>
Interesting. I've also given some thought on how Arrow's Theorem is 
related to our ratings system.
 From one perspective it seems inappropriate to compare the USATT 
ratings to Arrow's theorem because the "players" in Arrow's theorem are 
rated, or ranked, according to voters' preferences. If members of the 
USATT were given ballots to rank the top players, then the conditions 
for Arrow's Theorem would be met perfectly. Kenneth Arrow didn't prove 
anything about ranking based on performance.
 From another perspective, however, it does seem to be an appropriate 
comparison. Arrow came up with a set of fairness criteria and proved 
they could not simultaneously be satisfied. So, analogous to Arrow's 
Theorem, there must exist a set of fairness criteria (obviously 
different from Arrow's) that no rating system can satisfy.
I've come up with one very similar to Arrow's monotonicity criterion. If 
player A is rating higher than player B before a tournament and A's 
results (opponents' ratings along with wins and losses) are identical to 
B's, then A should be rated higher than B after the tournament. This 
criterion is obviously not satisfied by our current system. For example, 
A is 1600 and beats ten 1600 players, +8 each, and comes out 1680. B is 
1500 and beats ten 1600 players, +20 each, and comes out 1700