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

[Raph Frank]

On Fri, Jan 30, 2009 at 10:09 PM, Juho Laatu <juho4880 at yahoo.co.uk> wrote:
> I don't know what the voter would
> think. Maybe some voters think that
> the two alternatives are equal.
> Maybe most prefer the latter
> alternative.
>
> In any case the first alternative
> may lead sooner to situations where
> the representatives make different
> decisions than the voters would.

I think if the method complies with the proportionality for solid
coalitions criterion, then it would tend to give a PR result.

One option would be to have 2 measures, one measures how PR the method
is and one measures the average utility.

Another option would be to increase the weight for unhappy people when
working out the average.  For example, the most unhappy person would
be given a weighting of 2 and the happiest person would be given a
weighting of 1 (and the rest would be given a weighting  based on the
position of the voter between the 2).  This would make it harder to
offset one group of people against another.

The real problem is how to do it in a way that doesn't tend towards
bias.  At least in a single seat election, summing the utility is a
pretty unbiased method.

PAV uses the rule

1+1/3+1/5+1/7 + ... (i.e. terms = number of approved candidates elected)

However, it doesn't just average the results.  If one of your
candidates are elected, then it counts as full strength, but the 2nd
candidates counts at 1/3 of that strength.  The voter's happiness is 2
units, but it only counts as 1.33 units.  Effectively, that voter's
happiness is deweighted by 33%.

RRV doesn't quite work that way, but it gives the same kind of result
to sequential PAV.

Anyway, maybe the system could be something like

For each possible winning set
- work out the average utility for each voter of all the candidates in
the winning set
- sort the voters in order of their happiness
- give each voter a weight dependent on the position in the ordering
- the happiness for that result is equal to the average happiness
using the above weightings

If the weighting was 1 no matter what, then it wouldn't be a PR method.

I wonder if there is a weighting that would achieve Droop proportionality.

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.