<html><head></head><body><div style="color:#000; background-color:#fff; font-family:Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:13px"><div id="yui_3_16_0_ym19_1_1522180788344_3331" dir="ltr">The 2018 double round robin chess candidates tournament just ended. The matrix for the tournament is available here:</div><div id="yui_3_16_0_ym19_1_1522180788344_33718" dir="ltr"><a href="https://en.wikipedia.org/wiki/Candidates_Tournament_2018" class="" id="yui_3_16_0_ym19_1_1522180788344_36720">https://en.wikipedia.org/wiki/Candidates_Tournament_2018</a></div><div dir="ltr" id="yui_3_16_0_ym19_1_1522180788344_36761"><br></div><div id="yui_3_16_0_ym19_1_1522180788344_147173" dir="ltr">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.)<br></div><div dir="ltr" id="yui_3_16_0_ym19_1_1522180788344_213747"><br></div><div dir="ltr" id="yui_3_16_0_ym19_1_1522180788344_207708">The rank ordering using points:(using the name abbreviations from the Wikipedia martrix) :</div><div id="yui_3_16_0_ym19_1_1522180788344_162483">CAR > (MAM = KAR)> DIN > (KRA = GRI) > SO > ARO<br></div><div id="yui_3_16_0_ym19_1_1522180788344_165495"><br></div><div id="yui_3_16_0_ym19_1_1522180788344_97191" dir="ltr">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.<br></div><div id="yui_3_16_0_ym19_1_1522180788344_112320"><br></div><div id="yui_3_16_0_ym19_1_1522180788344_118292">DIN>MAM>KAR>CAR>KRA>GRI>SO>ARO.</div><div id="yui_3_16_0_ym19_1_1522180788344_124320"><br></div><div id="yui_3_16_0_ym19_1_1522180788344_191001" dir="ltr">which makes Din Laren come in first and Caruna come in fourth. <br></div><div dir="ltr" id="yui_3_16_0_ym19_1_1522180788344_247017"><br></div><br><div id="yui_3_16_0_ym19_1_1522180788344_109242"><br></div><div id="yui_3_16_0_ym19_1_1522180788344_112319"><br></div><div id="yui_3_16_0_ym19_1_1522180788344_106291"><br></div><div id="yui_3_16_0_ym19_1_1522180788344_106290"><br></div></div></body></html>