[EM] 2018 Chess Candidates Tournament

[Ross Hyman]

I think hcess is an example where Borda is preferable to Condorcet.  Grand masters are criticized for excessively drawing.  If the winner was chosen by Condorcet, this would exasperate the problem by further incentivizing draws.  Ding Liren is the Condorcet winner because he did not loose a single game.  But he drew 13 times out of 14 games.   

    On Tuesday, March 27, 2018 3:36 PM, Ross Hyman <rahyman at sbcglobal.net> wrote:
 

 The 2018 double round robin chess candidates tournament just ended. The matrix for the tournament is available here:https://en.wikipedia.org/wiki/Candidates_Tournament_2018
Each of the 8 players plays every other player twice (once as white, once as black.)  A player get one point for a win, 1/2 point for a draw, and 0 points for a loss.  The winner, (Fabiano Caruna, who wins the right to play Magnus Carlson for the world championship, the first time a U.S. player will compete for the championship since Bobby Fischer) is the player with the most points. (This is effectively Borda, I think.)

The rank ordering using points:(using the name abbreviations from the Wikipedia martrix) :CAR > (MAM = KAR)> DIN > (KRA = GRI) > SO > ARO

It is interesting to apply Condorcet to this matrix. I kept only those matrix elements with a decisive victory ( one victory and one draw or two victories), dropping everything else.  This produced a very sparse matrix with no cycles and the following Condorcet ranking.

DIN>MAM>KAR>CAR>KRA>GRI>SO>ARO.
which makes Din Laren come in first and Caruna come in fourth. 








   
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