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<div><font face="sans-serif">After a Round RobinTournament concludes its pairwise contests how should we decide the finishing order (1st place, 2nd place, 3rd place, etc.) of the participating teams?</font></div>
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<div><font face="sans-serif">Here's a solution that's reminiscent of Approval Sorted Margins:</font></div>
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<div>Since there is no precise analogue for a team's approval in this context we use the ratio R of its best score to its worst score to determine a tentative list order.</div>
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<div>Then as long as some adjacent pair of teams is out of order pairwise, among such pairs transpose the one whose members' R ratios are closest, i.e. with the smallest absolute value of log(R1/R2).</div>
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<div>The CW and CL (when they exist) will appear at opposite ends of the sorted list.</div>
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<div>And there is the same kind of reverse symmetry that ASM provides in the context of elections.</div>
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<div>In fact, we could call this method RSM or Ratio Sorted Margins, where the margins are the absolute differences of form</div>
<div> |log R1 - log R2| </div>
<div>in analogy to the approval margins of form |A1 - A2|.</div>
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<div>People that are uncomfortable with approval cutoffs can use RSM instead of ASM ... no approval necessary ... ranked preference style ballots are perfectly adequate ...in fact, since it is a tournament method, the pairwise vote matrix is adequate by itself.</div>
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<div>No more excuses for clone dependent, intractable Kemeny-Young: just use RSM!</div>
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<div style="font-size:85%;color:#575757" dir="auto">Sent from my MetroPCS 4G LTE Android Device</div>
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