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

[Juho]

If the ballots are considered to hold both approval and ranking  
information (maybe even giving higher weight to approval) then also I  
have some sympathy towards D. But if we compare this kind of combined  
ballots to pure ranking ballots then probably also the votes would be  
different.

I mean e.g. that since the 1000 A>B voters seemed to have a uniform  
and therefore maybe strong opinion A>B that might mean that if they  
were told to give votes where also approval would be counted then the  
vote could have been closer to (but maybe not all the way) 1000 A,  
1000 B, 1 D>B.

I read you comments so that winning votes was not very good.  
Combining approval and margins would be better. And pure margins  
would be worse than approval + margins. I assumed also that D would  
be a good winner with approval + margins but I'm not sure you stated  
anything on if D should win if the ballots were purely ranking based  
(1000 A>B>C=D>E, 1000 C>D>A=B>E, 1 D>B>A=C>E to "fool" your method :-).

The comparison is of course a bit tricky since approval + margins has  
more data available, although it also limits the expressiveness  
somewhat since the approval cutoff is at a fixed position. A free  
cutoff location would allow the voter to express also preferences  
between the non-approved candidates. Maybe you didn't allow that for  
some strategy resistance reasons (as usual :-).

Juho



On Aug 15, 2007, at 1:10 , Chris Benham wrote:

>
>
> 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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