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

[Juho]

July 29th I drafted also one example that was intended to be more  
realistic than the 1000 1000 1 scenario.

Juho


--excerpt---
Here's another version of the example - longer, but now the numbers  
could be from real life. There seems to be a consensus (within both  
of the two parties, "AB" and "CD") that A is better than B and C is  
better than D. Some voters (32%) truncate the candidates of the other  
party but all rank their own candidates. One additional vote (e.g.  
B>D) can lift B and/or D to the same level with A and C. The point is  
that this threat exists also when votes are more balanced than in the  
first (extreme but easy to catch) scenario. This may quite well  
happen in real life elections.

10 A>B
12 A>B>C
9  A>B>D
6  B>A
8  B>A>C
5  B>A>D
10 C>D
12 C>D>A
9  C>D>B
6  D>C
8  D>C>A
5  D>C>B
--end of excerpt---


On Aug 17, 2007, at 19:41 , Dave Ketchum wrote:

> 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
> -- 
>  davek at clarityconnect.com    people.clarityconnect.com/webpages3/davek
>  Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
>            Do to no one what you would not want done to you.
>                  If you want peace, work for justice.
>
>
>


		
___________________________________________________________ 
Try the all-new Yahoo! Mail. "The New Version is radically easier to use" – The Wall Street Journal 
http://uk.docs.yahoo.com/nowyoucan.html