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Abd ul-Rahman Lomax wrote:
<blockquote cite="mid7.0.0.16.0.20061106235205.014b1050@lomaxdesign.com"
type="cite"><br>
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<pre wrap="">No, Range does this. If we assume that voters
express their expected value for the various
candidates, the expected value for the voters,
collectively, is the sum of the individual expectations.
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<pre wrap="">Sure, but I don't see how this assumption can be taken for granted.
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<pre wrap=""><!---->
No election method can extract information from the voters and use it
to determine the winner if the voters do not express the information.
The assumption cannot be taken for granted, which is exactly why I
expressed it as an assumption. However, what is being said is that if
people use Range sincerely and honestly, Range will maximize expected
value, summed over all the voters.
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Yes, but how many of "the people"?<br>
<br>
90: A9>B1 (sincere is A9>B1)<br>
10: B99>A0 (sincere is B5>A3)<br>
<br>
All the voters have a sincere low opinion of both candidates, but 90%
think that A is 900%<br>
better than B and yet B wins (with only 10% of the voters not being
"sincere and honest").<br>
<blockquote cite="mid7.0.0.16.0.20061106235205.014b1050@lomaxdesign.com"
type="cite">
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Consider a diagnostic tool, a questionnaire to be filled out to
determine health status and medical treatment. If people lie on the
questionnaire, the results will be suboptimum.
Now, the question then becomes, will people lie? Some will, depends
on the definition of "lie."
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The definition is fuzzy because the voters are not even being asked a
clear unambiguous<br>
question.<br>
<blockquote cite="mid7.0.0.16.0.20061106235205.014b1050@lomaxdesign.com"
type="cite">
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Here is the paradox: if voters care little about whether or not A or
B wins, but want A to win, they can distort the rating of B. For the
condition to be true, the voters must simultaneously "care little"
and care enough to lie about their true preferences.
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That rests on the false assumption that it is (significantly) more
bother to lie than to tell the truth.<br>
In fact it seems to me to be less bother. I can well imagine being sure
that I prefer A to B but<br>
not sure exactly what my honest rating of each is, so I'd find it
easier to vote A max. and B min.<br>
<blockquote cite="mid7.0.0.16.0.20061106235205.014b1050@lomaxdesign.com"
type="cite">
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My real point is that we don't know, very well, how voters will
actually behave. We very much need real-world examples, theory will
only take us so far.
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<pre wrap="">If we can't make this assumption then there is no guarantee that Range
will outperform a majoritarian method in terms of expected value.
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We can certainly be sure majoritarian methods will outperform Range in
the worst-case scenarios.<br>
<br>
<br>
Chris Benham<br>
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