Re: [Election-Methods] Is rangevoting.org down? (plus some questions on converting Range to Approval)

[raphfrk]

 From: Juho <[EMAIL PROTECTED]>


> On Mar 29, 2008, at 23:35 , Michael Rouse wrote:

> > has
> > someone proposed a method to convert Range votes to maximal strategy
> > Approval votes? I was just wondering what the properties of such a
> > system might be (including cool-looking graphs, if available), and any
> > paradoxes or problems that might arise.
> >
> > For example, would it be possible to convert Range ballots into the
> > equivalent of Approval ballots where every voter has the equivalent of
> > perfectly accurate polling data?
>
> It may be possible to create some interesting algorithms. The first  
> problem to solve is that the optimal strategy is not stable since the  
> best strategy of one voter depends on the decisions of other voters.  
> That means that you maybe need to force the voters to use some  
> strategy that is equally good for all but not optimal.

There was a suggestion to use the standard approval strategy

"Approve your favourite of the top 2 and everyone you prefer to that candidate"

It doesn't converge if there is a condorcet loop.

E.g.

Voter 1 (A>B>C>D)
A: 10
B: 7
C: 3
D: 0

Voter 2 (B>C>D>A)
A: 0
B: 10
C: 7
D: 3

Voter 3 (C>D>A>B)
A: 3
B: 0
C: 10
D: 7

Voter 4 (D>A>B>C)
A: 7
B: 3
C: 0
D: 10

Assume, top 2 is A,B.

Voter 1 approves A
Voter 2 approves B
Voter 3 approves A, C, D
Voter 4 approves A, D

A: 3
B: 1
C: 1
D: 2

New top 2 is A,D

Voter 1 approves A
Voter 2 approves B, C, D
Voter 3 approves D, C
Voter 4 approves D

A: 1
B: 1
C: 2
D: 3

New top 2 is C,D

If you repeat the process it goes

A,B
D,A
C,D
B,C
A,B

and loops (following the condorcet loop)

This also happens (I assume) with the strategy

"approve your favourite of the top 2 and everyone you prefer to the expected 
winner"

or

"approve everyone who you rate higher than the expected utility of the election"

In the above example, it is a perfect tie, but there might be a way to get it 
to converge.

Also, it doesn't use ratings at all and only considers the rankings.  The last 
strategy would use ratings though. 



Raphfrk

Interesting site
"what if anyone could modify the laws"

www.wikocracy.com

 





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Re: [Election-Methods] Is rangevoting.org down? (plus some questions on converting Range to Approval)

[Juho]

On Mar 29, 2008, at 23:35 , Michael Rouse wrote:

> has
> someone proposed a method to convert Range votes to maximal strategy
> Approval votes? I was just wondering what the properties of such a
> system might be (including cool-looking graphs, if available), and any
> paradoxes or problems that might arise.
>
> For example, would it be possible to convert Range ballots into the
> equivalent of Approval ballots where every voter has the equivalent of
> perfectly accurate polling data?

It may be possible to create some interesting algorithms. The first  
problem to solve is that the optimal strategy is not stable since the  
best strategy of one voter depends on the decisions of other voters.  
That means that you maybe need to force the voters to use some  
strategy that is equally good for all but not optimal.

> Are there weird
> Approval cycles -- like you have with Condorcet "rock-paper-scissors"
> ties -- or areas where the strategy is indeterminate?

Yes. The opinion cycles are not really Condorcet specific but they  
occur in the preferences of a group irrespective of the election  
method. Condorcet just records them and then tries to make decisions  
including also the cyclic preferences in the decision making process.  
If you record the opinions of the voters using Range style ballots  
you will record the cycles too.

(Also normal Approval has this problem. If the preferences are  
A>B>C>A then the applied strategy (who approves whom) determines the  
winner. It is just that the voters themselves have to guess and  
decide on the election day what might be the best strategy for them.)

Juho









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