<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns="http://www.w3.org/TR/REC-html40">
<head>
<meta http-equiv=Content-Type content="text/html; charset=us-ascii">
<meta name=Generator content="Microsoft Word 11 (filtered medium)">
<!--[if !mso]>
<style>
v\:* {behavior:url(#default#VML);}
o\:* {behavior:url(#default#VML);}
w\:* {behavior:url(#default#VML);}
.shape {behavior:url(#default#VML);}
</style>
<![endif]-->
<style>
<!--
/* Font Definitions */
@font-face
{font-family:Tahoma;
panose-1:2 11 6 4 3 5 4 4 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0in;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Times New Roman";}
a:link, span.MsoHyperlink
{color:blue;
text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
{color:purple;
text-decoration:underline;}
span.EmailStyle17
{mso-style-type:personal-reply;
font-family:Arial;
color:navy;}
@page Section1
{size:8.5in 11.0in;
margin:1.0in 1.25in 1.0in 1.25in;}
div.Section1
{page:Section1;}
-->
</style>
</head>
<body lang=EN-US link=blue vlink=purple>
<div class=Section1>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>“</span></font>But I do NOT believe
that an individual can have such preferences. Or, more accurately, an
individual may have such preferences, but I do not consider them logical, and I
have absolutely no interest in factoring such preferences into a social choice
algorithm.”<o:p></o:p></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>If you do not believe an individual should be allowed to think, you
should not be worried about voting methods. I gave an example of how an
individual might sincerely have different pariwise rankins that cannot be
inferred from a single ranked ballot.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>Now PROVE that an individual’s pairwise preferences can be
inferred from a ranked ballot. And “I don’t understand it” is
not a proof. </span></font><font size=2 color=navy face=Arial><span
style='font-size:10.0pt;font-family:Arial;color:navy'><o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
<div>
<div class=MsoNormal align=center style='text-align:center'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'>
<hr size=2 width="100%" align=center tabindex=-1>
</span></font></div>
<p class=MsoNormal><b><font size=2 face=Tahoma><span style='font-size:10.0pt;
font-family:Tahoma;font-weight:bold'>From:</span></font></b><font size=2
face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma'> election-methods-electorama.com-bounces@electorama.com
[mailto:election-methods-electorama.com-bounces@electorama.com] <b><span
style='font-weight:bold'>On Behalf Of </span></b>Adam Tarr<br>
<b><span style='font-weight:bold'>Sent:</span></b> Monday, September 06, 2004
1:06 PM<br>
<b><span style='font-weight:bold'>To:</span></b>
election-methods@electorama.com<br>
<b><span style='font-weight:bold'>Subject:</span></b> Re: [EM] Cycles in
sincere individual preferences andapplication to vote-collection </span></font><o:p></o:p></p>
</div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>Paul Kislanko wrote:<br>
<br>
<br>
<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Suppose I were a staunch pro-life believer, so anti-abortion
is my most important criterion. There are 5 candidates in the race, and A &
E are both anti-abortion, but have opposite views on gun control (A for, E
against) and capital punishment (A against, E for). B, C, and D are all
pro-choice, and either pro gun control or anti-capital punishment or both. When
asked to rank all 5 I give A>B>C>D>E.<br>
</span></font><br>
<font size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>If you
ask me to compare B, C or D to E I d rank E>any.</span></font><o:p></o:p></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><br>
Then... why on earth would you rank E behind them all? That runs contrary
to all three pairwise preferences you purport to have.<br>
<br>
<br>
<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> If you ask me to compare B, C or D pairwise to each
other, the abortion issue isn t a factor, and my sincere preference might be
D>either B or C because of fiscal policy and a virtual tie on the other
pro-life issues.</span></font><o:p></o:p></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><br>
Then... why do you rank D behind B and C? Your preferences appear to be
completely transitive as A>E>D>B?C.<br>
<br>
<br>
<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>To suggest that you can infer my sincere pairwise preference
between any two alternatives who are not my first choice among many is
unwarranted. </span></font><o:p></o:p></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><br>
Only because you appear to have picked your ranked order arbitrarily, aside
from the first choice.<br>
<br>
<br>
<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>To prove that construction of a pairwise matrix from ranked
ballots is always possible, I think you d need to show inductively that all
orderings by any voter of N candidates will always be the same for those as
those obtained by asking each voter to order N+1 candidates (with respect to
the N original candidates). </span></font><o:p></o:p></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><br>
I agree with all of that, more or less.<br>
<br>
<br>
<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>I believe a logical consequence of such a proof would be
contrary to Arrow s theorem, and therefore is impossible. (Just substitute
issue for individual and ranked ballot for group and the same logic applies).</span></font><o:p></o:p></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><br>
(I think you mean, substitute issue AND individual WITH ranked ballot AND
group?)<br>
<br>
And therein lies my objection. I don't think you can simply substitute
individual for group. A group can have cyclic preferences, and on that
fact rests Condorcet's paradox and Arrow's theorem.<br>
<br>
But I do NOT believe that an individual can have such preferences. Or,
more accurately, an individual may have such preferences, but I do not consider
them logical, and I have absolutely no interest in factoring such preferences
into a social choice algorithm.<br>
<br>
I guess this makes me a "transitive preference elitist" of
sorts. I'm comfortable with that.<br>
<br>
-Adam<o:p></o:p></span></font></p>
</div>
</body>
</html>