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<div>The ratio R(X) should be ...</div>
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<div>... the smallest pairwise support for X divided by the greatest pairwise opposition to X.</div>
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<div>In the sports context that would be the ratio of X's smallest score to the greatest score against it.</div>
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<div>In terms of the pairwise matrix ... it is the smallest entry in X's row divided by the largest entry in X's column.</div>
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<div>The entry in row i of column j is simply the number of points team i scored in the game against team j.</div>
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<div>In the election context it is the number of ballots on which candidate i was strictly preferred over candidate j ... plus the number on which they were both voted equal Top and half the number on which they were voted equal but not Top or Bottom.</div>
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<div>I hope everybody gets this corrected definition of the ratio R.</div>
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<div dir="auto" style="font-size:85%; color:#575757">Sent from my MetroPCS 4G LTE Android Device</div>
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<div>-------- Mensaje original --------</div>
<div>De: Susan Simmons <suzerainsimmons@outlook.com> </div>
<div>Fecha: 4/8/21 11:30 a. m. (GMT-08:00) </div>
<div>A: election-methods@lists.electorama.com </div>
<div>Asunto: Re: Round Robin Tournament Showings </div>
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<div>Note if we replace A(X) approval of X with </div>
<div>Log R(X), where R(X) is the ratio of X's best pairwise score to X's worst pairwise score, then ASM and RSM are the same</div>
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<div id="composer_signature">
<div dir="auto" style="font-size:85%; color:#575757">Sent from my MetroPCS 4G LTE Android Device</div>
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<div>-------- Mensaje original --------</div>
<div>De: Susan Simmons <suzerainsimmons@outlook.com> </div>
<div>Fecha: 4/8/21 10:31 a. m. (GMT-08:00) </div>
<div>A: election-methods@lists.electorama.com </div>
<div>Asunto: Round Robin Tournament Showings </div>
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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 dir="auto" style="font-size:85%; color:#575757">Sent from my MetroPCS 4G LTE Android Device</div>
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