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

[Juho Laatu]

--- On Sat, 31/1/09, Raph Frank <raphfrk at gmail.com> wrote:

> <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 scenario that I was thinking is one
where there are n seats and n groups of
clone voters that each vote for one
candidate from their own group (=> quite
perfect proportionality, all groupings
are solid coalitions). There could be n
candidates that achieve better average
utility than the n clone candidates
(=good compromise candidates than
everyone likes quite a lot).

It is however quite easy to generate
scenarios where a majority opinion
among the clone representatives would
change to a reverse majority opinion
among the compromise candidates. The
clone representatives would (in theory)
always make same decisions as the
voters would.

> 
> 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.

I see these alternatives as a different
philosophies towards decision making in
a democracy. Should the system maximize
the average utility among the citizens
or the worst utility among the citizens.
I guess in most democracies the truth
(or the target ideal) lies somewhere
between these two extremes. Well, maybe
also decisions that favour some group
(e.g. the most influential people)
on matters where they are in a good
position already before the decision
are sometimes made :-).

> 
> 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.

I think most multi-winner methods are
also quite unbiased. Arranging a balance
between maximizing average and worst
utilities may be trickier, or maybe it
is just tricky to state what kind of a
balance one actually would like to have.

Juho



> 
> 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.