[Election-Methods] RE : Corrected "strategy in Condorcet" section

[Chris Benham]

Juho wrote:

>On Aug 2, 2007, at 6:44 , Kevin Venzke wrote:
>
>  
>
>>>1000 A>B, 1000 C>D, 1 D>B
>>>      
>>>
>
>  
>
>>Yes, I do think D is the proper winner.
>>
>Do you have a verbal (natural language) explanation why D is better  
>than A and C. This scenario could be an election in a school. One  
>class has voted A>B (A and B are pupils of that class), another class  
>has voted C>D, the teacher has voted D>B. What should the teacher  
>tell the C>D voting class when they ask "didn't you count our votes"?  
>Maybe this is clear to you. Unfortunately not as clear to me. The  
>teacher vote seemed to be heavier than the pupils votes :-).
>  
>

I  agree with Kevin that D is the proper winner, but Winning Votes isn't 
my favourite algorithm.
If we are sticking with Condorcet  "immune" methods and so are only 
focussing on how to compare
(measure) defeat strengths, then I like Approval Margins (Ranking) if we 
are using plain ranking ballots.

So interpreting ranking (above bottom or equal-bottom) as approval, we 
get these approval scores:
D1001,   B1001,   A1000,  C1000

All the candidates have at least one pairwise defeat, and by AM  the 
weakest is D's single defeat, C>D
by an AM of -1.
I also like  Approval-Sorted Margins(Ranking), which  is probably 
equivalent to AM.

The initial approval order is  D=B>A=C.  The smallest approval gaps 
(zero) are between D and B, and A
and C.  A pairwise ties with C but D pairwise beats B, so our first 
modification of the order is D>B>A=C.
A pairwise beats B, so the second modification is  D>A>B=C.  B pairwise 
beats C, so the third modified
order is D>A>B>C.  This order accords with the pairwise comparisons so 
is the final order and D wins.

I also like eliminating (and dropping from the ballots) the candidate 
lowest in this order and then repeating
the whole process until one remains. In this case that would give the 
same winner, with the elimination order
just being the reverse of  the ASM(R) order.

The only candidate with any sort of claim versus D is C, and  C is 
pairwise beaten by a more approved
candidate (B) so C is outside the "Definite Majority (Ranking)" set.

Chris Benham





-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20070815/a23b89d7/attachment-0003.htm>