tag:blogger.com,1999:blog-264226589944705290.post7996000376834868136..comments2021-12-14T05:53:12.175-08:00Comments on God Plays Dice: The Olympic posetMichael Lugohttp://www.blogger.com/profile/15671307315028242949noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-264226589944705290.post-80191123289484243672008-09-07T12:20:00.000-07:002008-09-07T12:20:00.000-07:00... and it is equivalent to the orders proposed fo...... and it is equivalent to the orders proposed for the Olympics and other 'graded' event categories, like medical side effects (<A> CSS 2003 </A>), Tour-de-France jerseys (<A> JSE 2006 </A>, <A> 2007 </A> ) and many more (see <A> JQAS 2008 </A>).Unknownhttps://www.blogger.com/profile/05641813314226545427noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-1382892881832386452008-09-06T04:47:00.000-07:002008-09-06T04:47:00.000-07:00"This seems like it's equivalent to Tatham's order..."This seems like it's equivalent to Tatham's order, but I haven't thought that hard about it."<BR/><BR/>I have :-) It is.<BR/><BR/>Under any scoring system of the type you describe, a country's total score is xG+yS+zB, which can also be written as (x-y)G + (y-z)(G+S) + z(G+S+B), which is now helpfully written in terms of exactly the three quantities which are product-ordered by my order relation - and each of those quantities is being multiplied by one of the non-negative quantities (x-y),(y-z),z. Hence, if country A has all of G, G+S and G+S+B at least as good as country B, then its score as calculated above must be greater than that of country B.<BR/><BR/>Conversely, suppose country B has at least one of G, G+S and G+S+B better than A. If it has higher G, then it beats A under the scoring system x=1,y=z=0; if it has higher G+S then it beats A under the system x=y=1,z=0; if it has higher G+S+B then it wins under the system x=y=z=1.<BR/><BR/>Hence, exactly as you say, my partial order ranks country A as strictly better-or-equal to B if and only if A's score under any scoring system of the above type would be at least B's score.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-12586665614717473812008-09-03T13:03:00.000-07:002008-09-03T13:03:00.000-07:00Hi Simon,I like your graph a lot! A bit more on co...Hi Simon,<BR/><BR/>I like your graph a lot! A bit more on computational aspects of this approach is available in a recent publication "U-Scores for Multivariate Data in Sports" http://www.bepress.com/jqas/topdownloads.html, see also http://newswire.rockefeller.edu/<BR/><BR/>KnutAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-68262919103634495312008-09-01T11:02:00.000-07:002008-09-01T11:02:00.000-07:00Thank you for your link to that visualisation of t...Thank you for your link to that visualisation of the Olympic medal table. It roused me to write about a <A HREF="http://joningram.org/blog/2008/09/exploring-euclids-elements/" REL="nofollow">visualisation of the first book of Euclid's Elements</A> which I created using the same piece of software (Graphviz) a while back.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-62652451813263097952008-09-01T04:29:00.000-07:002008-09-01T04:29:00.000-07:00I second John's idea. I'd like to see every nation...I second John's idea. I'd like to see every nation given a "fitness" distribution, and then use order statistics and medal results estimate results.<BR/><BR/>Of course, I wouldn't want to do such things myself...Davidhttps://www.blogger.com/profile/01334886702580555715noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-66048196648583849742008-08-30T06:13:00.000-07:002008-08-30T06:13:00.000-07:00Yay, majorization!Yay, majorization!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-89751353987300309052008-08-29T14:08:00.000-07:002008-08-29T14:08:00.000-07:00I will leave aside the question of whether to adj...I will leave aside the question of <I>whether</I> to adjust medal counts for population or popularity, but here's a post that suggests a start for <A HREF="http://www.johndcook.com/blog/2008/08/12/variation-in-male-and-female-olympic-performance-ii/" REL="nofollow">how</A> you might do so. The post was written to examine what you would expect if men and women had equal ability but differing levels of interest in some sport, but the same analysis would apply to any two populations with equal ability distributions but differing sizes.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-43338119357654758992008-08-29T14:05:00.000-07:002008-08-29T14:05:00.000-07:00What is the point of meta-accolades anyway?What is the point of meta-accolades anyway?Anonymousnoreply@blogger.com