[EM] 2018 Chess Candidates Tournament

[Ross Hyman]

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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