[EM] RE : Re: RE : Majority Criterion, hidden contradictions

[Chris Benham]

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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