[EM] [Election-Methods] Clarke taxes and group strategies

[raphfrk at netscape.net]

 Jobst Heitzig wrote:
> Now, I have the impression that a slight modification of the tax formula may reduce this incentive considerably. Consider this tax:
>
>?? sum { R(W,k) - R(W(i),k)
>?? + sum { ( R(W(i),k) - R(W(i,j),k) ) / 2
>?? : j different from i and k }
>?? : k different from i }
>
> where W(i,j) is the winner after removal of both i and j. If I'm right, this formula makes it ineffective to misrepresent ratings for both individual voters and pairs of voters.
>
> Please check this!
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This is a 2-d sum, so people could pay way more than they thought.
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The outer loop just calculates the Clarke tax and the inner loop is
an adder.
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Anyway, in simple terms, the system is (I think)
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- count up the totals excluding your ballot
- If the result is different from the actual result
? pay to change it to the actual winner
? (i.e. the amount the actual winner lost by)
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Your system adds
- If the result is further changed by removal of another ballot
?in addition to yours, pay half the cost to switch it to
?the winner that would result with just the removal of your ballot
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The 2nd cost gets added for every other potential pair that your ballot
can match with.? In a large election the tax could be massive.
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For example, if lots of people cast
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A) 10
B) 0
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and A defeated B by 15,
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then the payment would be huge.
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The removal of any one voter's ballot would have no effect, A would still
win by 5.? However, the removal of any 2 would cause B to win.
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If there were 1000 voters of that type, then each of them would have to pay
999 times 2.5 in the tax (A loses by 5 999 times and they pay half each
time).

My preference for a solution here is to limit the size that people may bid.
For example, the highest 10% of ratings are assumed to be equal to
the lowest of them.

I.e. where (Rmax-Rmin) on a ballot is greater than the 90th percentile,
rescale the ballot by 
(90th percentile)/(Rmax-Rmin)


 
This means that bidding a really large number will just be ignored and your
ballot rescaled.

This does break the optimal utility effect though.



Raphfrk


 


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