<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html>
<head>
<meta http-equiv="Content-Type" content="text/html;charset=ISO-8859-1">
<title></title>
</head>
<body>
Adam,<br>
<pre>This is from my Tues.Mar.2 post:
"To my mind, Approval does NOT satisfy Independence of Irrelevant Alternatives (IIA), or even
the much weaker Independence of Clones.
For my demonstration, I am assuming that the voters know nothing but their own sincere ratings
of all the candidates on the ballot, and that in that situation they all use the best "strategy"
of approving all the candidates they rate above average, and no others.
Initial two candidate election (with ratings out of ten).
01: A(9)>>B(1)
99: B(8)>>A(7)
B wins 99 to 1. Now we add a third candidate X, which all the voters rank adjacently to A, and who
therfore meets the Blake Cretney definition of a clone of A.
Same voters and initial 2 candidates, but with a third candidate added.
01:A(9)>>X(2)>B(1)
99:B(8)>A(7)>>X(1)
A wins 100 to 99. So adding a clone of A, which ALL the voters ranked last, changed A from a
1/100 loser to the winner."
In reply to this you asked (Sun.Jun.6):
<blockquote type="cite"><pre>Why would the B faction vote for A in the second example? There's nothing
"dishonest" about them only voting for B, which is exactly what they
should, and almost certainly would, do.
</pre></blockquote>This is the bit you (and Bill Clark) apparently did't read:
<blockquote type="cite"><pre>For my demonstration, I am assuming that the voters know nothing but their own sincere ratings
of all the candidates on the ballot, and that in that situation they all use the best "strategy"
of approving all the candidates they rate above average, and no others.</pre></blockquote></pre>
The B faction vote for A in the second example because their average sincere
rating of the three candidates is 5.333 and they rate<br>
A as 7.<br>
<br>
Bill Clark asked me why not:<br>
<blockquote type="cite">
<pre>01:A(9)>X(2)>>B(1)
99:B(8)>>A(7)>X(1)
Also, if A and X are supposed to be clones, I find it somewhat odd that
the voters rate them so differently.
Is the Blake Cretney definition only meant for rank methods? A and X
don't seem to satisfy the "spirit" of what it means to be a clone, since
they basically have nothing in common -- not even whether they're voted
the same way by even a single voter.
><i> A wins 100 to 99. So adding a clone of A, which ALL the voters
</i>><i> ranked last, changed A from a 1/100 loser to the winner.
</i>
The A-voter doesn't rank X last (not that it really matters.)</pre>
</blockquote>
Bill,<br>
Regarding your example, the A faction's average sincere rating of the candidates
is 4/10 and they rate X below that (2/10) so they<br>
don't approve X. As explained above, the B faction rate A as above average
in the field.<br>
Clones do not have a "spirit", only a definition.<br>
Regarding your last sentence, oops! you are right. If the A voter had ranked
X last, then X would not be a true clone of A.<br>
But if we swap the A voter's sincere rating and ranking of X and B, then
the point would be that the method doesn't meet Independence<br>
of Pareto-Dominated Alternatives (IPDA) and the method can be manipulated
by nominations.<br>
<br>
Chris Benham<br>
</body>
</html>