<html><head><style type="text/css"><!-- DIV {margin:0px;} --></style></head><body><div style="font-family:times new roman, new york, times, serif;font-size:12pt"><DIV>Brian,</DIV>
<DIV>I am a bit puzzled as to exactly how your IRNR method works.</DIV>
<DIV>From part of your site:</DIV>
<DIV> </DIV>
<DIV>
<H2><A name=IRNR>Instant Runoff Normalized Ratings</A></H2>
<P>Each ballot is normalized so that all ballots have the same magnitude. </P>
<P>The modified ballots are summed, and the choice with the lowest </P>
<P>sumarry rating is disqualified. Each ballot is then normalized again as if </P>
<P>the disqualified choice was not there, redistributing the vote across the </P>
<P>choices in proportion to the original ballot. The new modified ballots </P>
<P>are summed and the process is repeated until there are two choices </P>
<P>remaining and one choice wins over the other. </P>
<P>IRNR slide show: <A href="http://bolson.org/voting/IRNR_explaination.pdf"><FONT color=#0000ff>PDF (219KB)</FONT></A>, <A href="http://bolson.org/voting/IRNR_explaination.mov"><FONT color=#0000ff>QuickTime (2.3MB)</FONT></A></P>
<P> </P>
<P> </P>
<P>Even after looking up the words "normalize" and "magnitude" in the<BR>dictionary, I don't fully understand the first sentence above.</P></DIV>
<DIV> </DIV>
<DIV>As an example you give a ballot that allows the voter to score the</DIV>
<DIV>candidates on a scale of 10 to -10, filled out thus:</DIV>
<DIV> </DIV>
<DIV>A10, B6, C-3, D-10, E4</DIV>
<DIV> </DIV>
<DIV>This you then "normalize" to:</DIV>
<DIV> </DIV>
<DIV>A.62, B.37, C-.19, D-.62, E.25<BR></DIV>
<DIV>For what it's worth, these numbers sum to the not-very-round 0.43.</DIV>
<DIV><BR>How exactly were these numbers derived from the scores on the </DIV>
<DIV>original ballot?<BR></DIV>
<DIV><BR>Chris Benham</DIV>
<DIV><FONT face=Chalkboard color=#ffffff size=7><FONT face=Chalkboard color=#ffffff size=7><FONT face=Chalkboard color=#ffffff size=7>
<P align=left>Example: one vote</P></FONT></FONT></FONT><FONT face=Chalkboard color=#ffffff size=7><FONT face=Chalkboard color=#ffffff size=7><FONT face=Chalkboard color=#ffffff size=7>
<P align=left>To make things fair,</P>
<P align=left>each vote is</P>
<P align=left>normalized to have</P>
<P align=left>the same magnitude</P>
<P align=left>A B C D E</P></FONT></FONT></FONT><FONT face=ArialNarrow color=#ffffff size=6><FONT face=ArialNarrow color=#ffffff size=6><FONT face=ArialNarrow color=#ffffff size=6>
<P align=left>0.62 0.37 -0.19 -0.2 0.25</P></FONT></FONT></FONT><FONT face=Chalkboard color=#ffffff size=7><FONT face=Chalkboard color=#ffffff size=7><FONT face=Chalkboard color=#ffffff size=7>
<P align=left>A B C D E0 6 -3 -10 4</P></FONT></FONT></FONT></DIV></div><br>
<p class="MsoNormal"> </p>
<tbody><tr>
<td style="padding: 0.75pt;">
<div class="MsoNormal" style="text-align: center;" align="center"><font face="Arial" size="3"><span style="font-size: 12pt;">
<hr align="center" size="1" width="100%">
</span></font></div>
<p class="MsoNormal"><img id="_x0000_i1026" src="http://l.yimg.com/au.yimg.com/i/mktg/images/braviasony(25x25).jpg" align="absbottom" border="0" height="25" hspace="4" width="25"><font face="Arial" size="2">Start your day with Yahoo!7 and win a Sony Bravia TV. <span style="font-size: 10pt;"><a href="http://au.rd.yahoo.com/hppromo/mail/tagline2/*http://au.docs.yahoo.com/homepageset/?p1=other&p2=au&p3=tagline
" target="_new"><b><span style="font-weight: bold;" lang="NO-BOK"></span></b><span lang="NO-BOK">Enter Now</span></a>
</span></font><span lang="NO-BOK"><o:p></o:p></span></p></body></html>