[Election-Methods] RE : Corrected "strategy inCondorcet" section

[Dave Ketchum]

Paul's words are tempting, for this exchange has little to do with 
desirability of Condorcet, or of margins vs WV.

Looking closer, the votes are:
      1000 A>B>C=D
      1000 C>D>A=B
         1 D>B>A=C

2000 voters rate A vs C as a tie, only agreed that B and D should lose.

The one vote agrees to the A vs C tie, but mostly muddies the water.

So, a not believable election tally gets debated for weeks.  True that 
margins vs WV is an important topic, but each can offer believable 
examples in their favor - serious thought would be based on more 
believable examples than debated here.

DWK

On Tue, 14 Aug 2007 17:25:57 -0500 Paul Kislanko wrote:
> This is enough to convince me that approval is an appropriate method.
> 
> ------------------------------------------------------------------------
> From: election-methods-bounces at lists.electorama.com 
> [mailto:election-methods-bounces at lists.electorama.com] On Behalf Of 
> Chris Benham
> Sent: Tuesday, August 14, 2007 5:11 PM
> To: Juho
> Cc: Forest W Simmons; Election Methods Mailing List
> Subject: Re: [Election-Methods] RE : Corrected "strategy inCondorcet" 
> section
> 
> 
> 
> 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
-- 
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  Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
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