[EM] Weighted PR question

[Vidar Wahlberg]

On Fri, Nov 14, 2014 at 01:39:05AM +0200, Juho Laatu wrote:
> On 14 Nov 2014, at 00:26, Forest Simmons <fsimmons at pcc.edu> wrote:
>> Consider the following approval ballot set:
>> 
>> 40 AB
>> 30 AC
>> 20 C
>> 10 BC
>> 
>> Of the following weighted representations, which would be better?
>> 
>> (I)  A(70), C(20), B(10)
>> 
>> (II) A(70), C(30)
>> 
>> (III) B(50), C(50)
>> 
>> or some other?
> 
> How about
> A 35 = 40 * 1/2 + 30 * 1/2
> B 25 = 40 * 1/2 + 10 * 1/2
> C 40 = 30 * 1/2 + 20 + 10 * 1/2

The "logical" answer to me would be that the result should be between
what Juho wrote and (as he mention later) 70/50/60 (38.9/27.8/33.3),
depending on whether a ballot with multiple candidates should have a
vote strength of 1 in total or 1 per approved candidate.
Although, I don't think a clear and finite answer can be given to the
question, at least not if a goal is to prevent strategic nomination and
tactical voting.
I could throw out another thought for the sake of the discussion:
How about averaging the result of the two approaches?
A = ((40 * 1/2 + 30 * 1/2) + (100 * 70 / 180)) / 2      = 36.9
B = ((40 * 1/2 + 10 * 1/2) + (100 * 50 / 180)) / 2      = 26.4
C = ((30 * 1/2 + 20 + 10 * 1/2) + (100 * 60 / 180)) / 2 = 36.7


-- 
Regards,
Vidar Wahlberg