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<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
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<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>Alex Small<br>
<b><span style='font-weight:bold'>Sent:</span></b> Monday, September 06, 2004
7:46 PM<br>
<b><span style='font-weight:bold'>To:</span></b> election-methods-electorama.com@electorama.com<br>
<b><span style='font-weight:bold'>Subject:</span></b> [EM] Re: Election-methods
Digest, Vol 3, Issue 18</span></font><o:p></o:p></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>Paul Kislanko wrote:<o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>>Prove that you can infer my pair-wise choices from my ranked
ballot, if you<br>
>want to use my ranked ballot to populate a pair-wise matrix.<br>
><br>
>It can't be done. So just allow the voters to explicitly input their pair-wise
preferences.<br>
><o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>>This is not rocket science.<o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>Um, OK.<o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>Let's that your particular preference order amonst N
candidates happens to be:<o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>C_1>C_2>...>C_N-1>C_N<o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>where I have conveniently assigned the candidates names (well, numbers)
derived from your preference order, just to keep the notation simple.<o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>I can infer that in a contest between candidates C_i and C_j you prefer
candidate C_i if i<j, and you prefer candidate j if i>j.<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>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>===== you are not allowed to infer that
======= <o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>Now, let's suppose that you indicated indifference between some
candidates (i.e. you ranked them equally), so that some of the ">"
signs above should be changed to "=" signs. Well, I think we
can all see how you'd vote in those pairwise contests: You'd abstain.<o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>This isn't rocket science.<o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>Now, you might say "Oh, but my ranked ballot doesn't
represent my true preferences. In truth my preferences are cyclic."<o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>OK, well, let's sit down and chat. I say to you "Paul, which
candidate do you most want to win?" You ponder it and then you give
me an answer. If you don't then you haven't made up your mind and you
won't be voting in this election. Or at least I assume you won't be
voting, because you don't seem sure whom you want.<o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>Anyway, you give me an answer. You say "I'll take candidate
C_1, please."<br>
<br>
Then I turn to you and say "OK, but what if candidate C_1 dropped out
of the race after tearfully admitting to being the governor of <st1:State
w:st="on"><st1:place w:st="on">New Jersey</st1:place></st1:State>? Whom
do you want then?" And you deliberate over it, but in the end you
admit that you would take candidate C_2.<o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>Well, we now know 2 entries in your preference order.
C_1>C_2>all others.<o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>So then we come up with some reason why C_2 will drop out as
well. And I ask whom you want instead. You say C_3. So now we
know that your preference is C_1>C_2>C_3>all others. We continue
this for all N candidates and get a preference order.<o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
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<p class=MsoNormal style='border:none;padding:0in'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'>You can say what you want
about cyclic preferences, but I maintain that I've just described a procedure
for elucidating your preferences, and I've described a procedure for
elucidating your pairwise preferences from your ordinal preferences.<o:p></o:p></span></font></p>
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<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>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>Correct, but now we don’t get to sit
down and have that chat. <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>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>Infer from my original ballot what I would
have said if we did get to discuss it after my first choice is eliminated
WITHOUT asking me. You can’t.<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>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>The question was not “who did I want
to win”, it was “what is my ranked ballot”, and obviously who
I wanted to win was my first choice. The assumption that my second choice for
first would be the second on my ranked ballot IF I HAD KNOWN THAT MY FIRST
CHOICE WASN’T AVAILABLE is not warranted, because just as you said, if
you’d asked me a second time I might’ve given an answer that was
different from C_2 on my first ballot.<o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <font color=navy><span style='color:navy'>That’s all I (and
Jobst) have been trying to say. The ranked ballot does not necessarily reflect
an individual’s pair-wise preferences. If we had that little chat, and
you told my first choice was unavailable and asked me who my choice was given
that, I’d integrate issues over remaining candidates and come up with an
answer, but there is no particular reason to assume that it would be the same
answer as the one listed in position 2 on my original ranked ballot. </span></font><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>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>Now, if the vote-counting is IRV, I would
know to fill out the ranked ballot as if we’d had that chat. But if the vote-counting
is a Condorcet-based system that depends upon pair-wise comparisons, I have to
know a lot more than who my 2<sup>nd</sup>-favorite choice is. In IRV, I would
be happy with A>B>C>D>E because that integrates all my issues over
all candidates’ positions exactly. But in a Condorcet-based system I’d
be less than happy with the B>E inference on at least one issue.<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>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>I don’t see how it creates a problem
for any method that depends upon pair-wise comparisons to count the votes to
allow voters to explicitly state pair-wise preferences. To just say voters are
stupid and must conform to the method to make the method easier to analyze just
strikes me as academic arrogance.<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>
<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>
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