[EM] RE : Re: RE : Majority Criterion, hidden contradictions
Chris Benham
chrisjbenham at optusnet.com.au
Mon Nov 6 22:30:52 PST 2006
Abd ul-Rahman Lomax wrote:
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>>>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.
>>>
>>>
>>Sure, but I don't see how this assumption can be taken for granted.
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>No election method can extract information from the voters and use it
>to determine the winner if the voters do not express the information.
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>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"?
90: A9>B1 (sincere is A9>B1)
10: B99>A0 (sincere is B5>A3)
All the voters have a sincere low opinion of both candidates, but 90%
think that A is 900%
better than B and yet B wins (with only 10% of the voters not being
"sincere and honest").
>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.
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>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
question.
>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.
In fact it seems to me to be less bother. I can well imagine being sure
that I prefer A to B but
not sure exactly what my honest rating of each is, so I'd find it easier
to vote A max. and B min.
>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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>>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.
Chris Benham
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