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</div><div id="yui_3_16_0_ym19_1_1501712299730_6982">Here is a ratings based Condorcet election method that uses
ratings to determine how much each voter favors one candidate over
another.<span style="mso-spacerun:yes" id="yui_3_16_0_ym19_1_1501712299730_6983"> </span>But it does not use the ratings
to compare candidates across ballots, as their ratings scales might be
different.<span style="mso-spacerun:yes" id="yui_3_16_0_ym19_1_1501712299730_6984"> </span>Perhaps they even used
different ratings ballots.<span style="mso-spacerun:yes" id="yui_3_16_0_ym19_1_1501712299730_6985"> </span>I believe it
is the second simplest way to use a ratings ballot that gives the same results if each
individual ballot undergoes an arbitrary rating shift or rescaling. (The simplist way is direct conversion of ratings to ranks. But this method includes more ratings information.)<span style="mso-spacerun:yes" id="yui_3_16_0_ym19_1_1501712299730_6986"> </span>There is no need to ever shift or rescale any
ballots as this can never change the results.<span style="mso-spacerun:yes" id="yui_3_16_0_ym19_1_1501712299730_6987">
</span>The method uses the Tideman or Schulze method but will not always assign
the same winner as those methods because it uses more ratings information than
a direct conversion of ratings to rankings.<span style="mso-spacerun:yes" id="yui_3_16_0_ym19_1_1501712299730_6988">
</span>The method uses more majority rule information than rankings based
Condorcet.<span style="mso-spacerun:yes" id="yui_3_16_0_ym19_1_1501712299730_6989"> </span></div>
<div style="mso-list:l0 level1 lfo1" id="yui_3_16_0_ym19_1_1501712299730_6990"><span style="mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin" id="yui_3_16_0_ym19_1_1501712299730_6991"><span style="mso-list:Ignore" id="yui_3_16_0_ym19_1_1501712299730_6992">1.<span style="font:7.0pt "Times New Roman"" id="yui_3_16_0_ym19_1_1501712299730_6993">
</span></span></span>Voters rate candidates on ratings ballots of any
type.</div>
<div id="yui_3_16_0_ym19_1_1501712299730_6994">Example:</div>
<div style="margin-left:.25in" id="yui_3_16_0_ym19_1_1501712299730_6995">7<span style="mso-spacerun:yes" id="yui_3_16_0_ym19_1_1501712299730_6996">
</span>A = 1, B = 0.9, C=0</div>
<div style="margin-left:.25in" id="yui_3_16_0_ym19_1_1501712299730_6997">6 B=1,000,000,000<span style="mso-spacerun:yes" id="yui_3_16_0_ym19_1_1501712299730_6998"> </span>C = 400,000,000, A =1</div>
<div style="margin-left:.25in" id="yui_3_16_0_ym19_1_1501712299730_6999">5 C =1, <span style="mso-spacerun:yes" id="yui_3_16_0_ym19_1_1501712299730_7000"> </span>A= - 0.7, B<span style="mso-spacerun:yes" id="yui_3_16_0_ym19_1_1501712299730_7001">
</span>= -1</div>
<div id="yui_3_16_0_ym19_1_1501712299730_7002"> </div>
<div style="mso-list:l0 level1 lfo1" id="yui_3_16_0_ym19_1_1501712299730_7003"><span style="mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin" id="yui_3_16_0_ym19_1_1501712299730_7004"><span style="mso-list:Ignore" id="yui_3_16_0_ym19_1_1501712299730_7005">2.<span style="font:7.0pt "Times New Roman"" id="yui_3_16_0_ym19_1_1501712299730_7006">
</span></span></span>Each ratings ballot is turned into an individual
ranked pair ballot.<span style="mso-spacerun:yes" id="yui_3_16_0_ym19_1_1501712299730_7007"> </span>Each pair A>B is
given the score Rating(A)-Rating(B) on a ballot.<span style="mso-spacerun:yes" id="yui_3_16_0_ym19_1_1501712299730_7008"> </span>The pairs are ranked on each ballot from
largest score to smallest score.<span style="mso-spacerun:yes" id="yui_3_16_0_ym19_1_1501712299730_7009"> </span>From
here on, the ratings ballots are dispensed with and only the ranked pair
ballots are used.</div>
<div id="yui_3_16_0_ym19_1_1501712299730_7010">Example:</div>
<div id="yui_3_16_0_ym19_1_1501712299730_7011">7<span style="mso-spacerun:yes" id="yui_3_16_0_ym19_1_1501712299730_7012">
</span>A>C, B>C, A>B, B>A, C>B, C>A</div>
<div id="yui_3_16_0_ym19_1_1501712299730_7013">6 B>A, B>C, C>A, A>C, C>B,
A>B</div>
<div id="yui_3_16_0_ym19_1_1501712299730_7014">5 C>B, C>A, A>B, B>A, A>C,
B>C</div>
<div id="yui_3_16_0_ym19_1_1501712299730_7015"> </div>
<div style="mso-list:l0 level1 lfo1" id="yui_3_16_0_ym19_1_1501712299730_7016"><span style="mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin" id="yui_3_16_0_ym19_1_1501712299730_7017"><span style="mso-list:Ignore" id="yui_3_16_0_ym19_1_1501712299730_7018">3.<span style="font:7.0pt "Times New Roman"" id="yui_3_16_0_ym19_1_1501712299730_7019">
</span></span></span>For each pair of candidates, A,B if more voters
rank A>B higher than B>A, then B>A is removed from each ballot.<span style="mso-spacerun:yes" id="yui_3_16_0_ym19_1_1501712299730_7020"> </span>Steps 2 and 3 could easily be combined.</div>
<div id="yui_3_16_0_ym19_1_1501712299730_7021">Example:</div>
<div style="margin-left:.25in" id="yui_3_16_0_ym19_1_1501712299730_7022">7<span style="mso-spacerun:yes" id="yui_3_16_0_ym19_1_1501712299730_7023">
</span>B>C, A>B, C>A</div>
<div style="margin-left:.25in" id="yui_3_16_0_ym19_1_1501712299730_7024">6 B>C, C>A, <span style="mso-spacerun:yes" id="yui_3_16_0_ym19_1_1501712299730_7025"> </span>A>B</div>
<div style="margin-left:.25in" id="yui_3_16_0_ym19_1_1501712299730_7026">5 C>A, A>B, B>C</div>
<div style="mso-list:l0 level1 lfo1" id="yui_3_16_0_ym19_1_1501712299730_7027"><span style="mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin" id="yui_3_16_0_ym19_1_1501712299730_7028"><span style="mso-list:Ignore" id="yui_3_16_0_ym19_1_1501712299730_7029">4.<span style="font:7.0pt "Times New Roman"" id="yui_3_16_0_ym19_1_1501712299730_7030">
</span></span></span><span style="mso-spacerun:yes" id="yui_3_16_0_ym19_1_1501712299730_7031"> </span>Now a societal
ranking of pairs of ordered pairs is produced.<span style="mso-spacerun:yes" id="yui_3_16_0_ym19_1_1501712299730_7032">
</span>This is done exactly as is done for Tideman or Schulze, except that the
candidates are ordered pairs of candidates of the form (A>B) so the
societal ordering will include entries like (A>B)>(C>D) if more voters
rank A>B higher than C>D.<span style="mso-spacerun:yes" id="yui_3_16_0_ym19_1_1501712299730_7033"> </span>This is
the step that uses more majority rule information than rankings based
Condorcet.<span style="mso-spacerun:yes" id="yui_3_16_0_ym19_1_1501712299730_7034"> </span></div>
<div id="yui_3_16_0_ym19_1_1501712299730_7035">Example:</div>
<div style="margin-left:.25in" id="yui_3_16_0_ym19_1_1501712299730_7036">(B>C)>(A>B) and (B>C)
> (C>A) tied at 13, 5</div>
<div style="margin-left:.25in" id="yui_3_16_0_ym19_1_1501712299730_7037">(C>A)> (A>B) 11,7</div>
<div id="yui_3_16_0_ym19_1_1501712299730_7038"> </div>
<div style="mso-list:l0 level1 lfo1" id="yui_3_16_0_ym19_1_1501712299730_7039"><span style="mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin" id="yui_3_16_0_ym19_1_1501712299730_7040"><span style="mso-list:Ignore" id="yui_3_16_0_ym19_1_1501712299730_7041">5.<span style="font:7.0pt "Times New Roman"" id="yui_3_16_0_ym19_1_1501712299730_7042">
</span></span></span>Now the Tideman or Schulze method is used to
turn the societal ranking of pairs of ordered pairs into a list of ranked
pairs. </div>
<div id="yui_3_16_0_ym19_1_1501712299730_7043">Example:</div>
<div style="margin-left:.25in" id="yui_3_16_0_ym19_1_1501712299730_7044">B>C</div>
<div style="margin-left:.25in" id="yui_3_16_0_ym19_1_1501712299730_7045">C>A</div>
<div style="margin-left:.25in" id="yui_3_16_0_ym19_1_1501712299730_7046">A>B</div>
<div style="mso-list:l0 level1 lfo1" id="yui_3_16_0_ym19_1_1501712299730_7047"><span style="mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin" id="yui_3_16_0_ym19_1_1501712299730_7048"><span style="mso-list:Ignore" id="yui_3_16_0_ym19_1_1501712299730_7049">6.<span style="font:7.0pt "Times New Roman"" id="yui_3_16_0_ym19_1_1501712299730_7050">
</span></span></span>The Tideman or Schulze method is then used a
second time to turn the ranked pairs list into an ordered list of
candidates.<span style="mso-spacerun:yes" id="yui_3_16_0_ym19_1_1501712299730_7051"> </span></div>
<div id="yui_3_16_0_ym19_1_1501712299730_7052">Example</div>
<div style="margin-left:.25in" id="yui_3_16_0_ym19_1_1501712299730_7053">B</div>
<div style="margin-left:.25in" id="yui_3_16_0_ym19_1_1501712299730_7054">C</div>
<div style="margin-left:.25in" id="yui_3_16_0_ym19_1_1501712299730_7055">A</div>
<div id="yui_3_16_0_ym19_1_1501712299730_7056"> </div>
<div style="mso-list:l0 level1 lfo1" id="yui_3_16_0_ym19_1_1501712299730_7057"><span style="mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin" id="yui_3_16_0_ym19_1_1501712299730_7058"><span style="mso-list:Ignore" id="yui_3_16_0_ym19_1_1501712299730_7059">7.<span style="font:7.0pt "Times New Roman"" id="yui_3_16_0_ym19_1_1501712299730_7060">
</span></span></span>The winner is the highest ranked on the
candidate list.</div>
<div style="margin-left:.25in" id="yui_3_16_0_ym19_1_1501712299730_7061">Example </div>
<div style="margin-left:.25in" id="yui_3_16_0_ym19_1_1501712299730_7062">B wins</div>
<div id="yui_3_16_0_ym19_1_1501712299730_7063"> </div>
<div id="yui_3_16_0_ym19_1_1501712299730_7064">Using a direct conversion of ratings to rankings with just one Tideman/Schulze step, A.</div>
<div style="margin-left:.25in" id="yui_3_16_0_ym19_1_1501712299730_7065"> </div>
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