[EM] Strategies for RRV/RSV and BR for multi-member constituencies

[Raph Frank]

On Tue, Feb 3, 2009 at 10:25 PM, Kristofer Munsterhjelm
<km-elmet at broadpark.no> wrote:
> I would guess that PAV, being based on a divisor method (Sainte-Laguë in the
> case above), must fail Droop proportionality to some extent, just like
> Webster's method must fail quota.

There is also a version for d'Hondt, i.e

1+1/2+1/3+...

>> If a group of voters were to vote max for 1 candidate, and min for all
>> the rest, I wonder is there a weighting function that will guarantee
>> that that candidate will be in the best winning circle.
>
> For PAV, that would be bullet voting. What do you mean by the "best winning
> circle" - the Smith set?

I meant the set of winners that maximises the total score.

The d'Hondt version of the PAV formula probably does it.

However, my question was if there was a way to do it where the weight
to each voter depends on the position of the voter when they are
ordered according to happiness with the result.

This would make the result independent if an offset is added to all
the voter's utilities.

With PAV, the zero point matters, and with utility, the zero point
shouldn't matter.

Also, using the PAV formula with range ballots is not entirely straight forward.

If a voters approves candidates A and B, and they are both in the
winning circle, then the voter's happiness with the result is

1+1/2 = 1.5

However, if the voter rated them as

A: 100 (of 100)
B: 75 (of 100)

It isn't entirely clear how to convert that to a happiness rating.

The voter's happiness is 1.75 before conversion.  That isn't quite the
same as 2 approved candidates elected, but is more than 1 approved
candidate elected.

One option would be to split each candidate out, i.e.

1/1 + 0.75/2 = 1.375

Another option is

ln( (total)/max + (offset) )

The offset changes slowly.  It would need to be set so that for
integer totals, the formula matches desired the PAV formula.