[EM] PRfavoringracialminorities

[Raph Frank]

On 8/26/08, Kristofer Munsterhjelm <km-elmet at broadpark.no> wrote:
>  No, it uses logarithmic and exponential functions to find the divisor
>  that corrects the bias that arises with certain assumptions about the
>  distribution of voters. See
> http://rangevoting.org/NewAppo.html . Warren
>  refers to states and total population, but it works for parties as well
>  - the "state population" is the number of voters that voted for the
>  party in question, and the "total population" is the total number of
>  voters -- or for scored single-winner methods, the score for the party
>  and the total score, respectively.

Ahh, I think I had read that page before.

Anyway, his conclusion is that his parameter should be set to
d=0.495211255149063832...

Webster's sets d to 0.5, so I think that would be easier to use that.

The difference is thus pretty slight and thus the benefit (if any) is
also pretty low.

>  Yes. In the same vein, for single-winner methods, a NOTA that actually
>  does something is preferrable to one that has no influence apart from
>  showing that people dislike all the candidates.

Yeah.  It could be argued that it is a leave the seat vacant/hold
another election vote.

With IRV, it could even be a ranked option.

You can rank NOTA as your lowest option.

In the last round, if the winner doesn't have a majority including
NOTA votes, then the election is declared to have failed and a new one
called or the office left vacant.

>  If we can fix the adjustment for multiple seats, it could be used with
> methods that don't reduce to IRV or other nonmonotonic single-winner
> methods. Reweighted Range Voting is monotonic, as are all additively
> reweighted methods based on monotonic single-winner methods. However, these
> don't do very well in my simulation - the best one is "reweighted
> plurality", which is just plurality, or in other words, SNTV.

RRV still would need the local constituencies to announce a complex
list of results.  To work out the winner, you need to know how many
voters voted A, B, C ... and also A+B, A+C, A+D, B+C ... and so on
(and that is assuming everyone votes approval style).

Actually, it is even more complex, I think for RRV you might need the
individual ballot list.

The only way to get transfers to work would be if there was a very
simple way to handle them.

I really don't like PR-SNTV, but it would work.

Another, possibly better option, would be party lists in the constituency.

Each voter would vote one candidate and his vote would be interpreted
as a vote for that party.   (or a vote for the 'non-party' party if he
votes for an independent).

The central office would be informed how many votes each party
received in each constituency.

It could then work out the appropriate number of seats for each party
nationwide.

It would be a simple calculation to determine how many seats each
party gets in each constituency after it recalculates the multipliers.

Once it has completed, it would announce the multipliers (so anyone
can check them) and also how many seats each party gets in each
constituency (with Webster's).

The local constituencies would then work out which candidates from
each party wins using any method they like.

In principle, voters could submit a ranked ballots ranking the local
party candidates and PR-STV could be used if the party gets 2+ seats.
In practice, they would probably just use open lists.

> I've also
> found a quota method based on Bucklin; I think that method is monotonic, but
> I'm not certain, as its elimination mechanics may make it nonmonotonic for
> more than one winner. Is CPO-STV monotonic?

Not sure.  It would probably depend on the condorcet completion method used.
>  What FMV does is that it increases the strength of parties that should have
> more seats. In other words, it displaces rival party members from the
> constituency vote until proportionality is achieved. The analogous thing to
> do with independents is to displace *them*, but no more than is required to
> retain proportionality.

Sounds reasonable.  What it is in effect doing is assigning all
independents into an 'non-party' party.

Maybe the rule would be that independents are encouraged to form
'loose alliances' and if they don't, they are placed into the general
independent's virtual party.

>  However one may set it up, with only three parties, and parties of unequal
> power, two of them could exclude the other unless the third has a majority.
> That's what I mean by breaking the assumption that power is directly
> proportional to the number of seats given.

That assumes that parties are cohesive blocks.  That depends on
political culture and to a certain extent on election law.  In New
Zealand, leaving a party means that you have to give up your seat.
This means that parties are potentially very cohesive.

>  Another problem, as was hinted to below, is that presumably any worthwhile
> method would assign Center a nonzero score. That would be unfortunate in
> cases with small even-size districts, at least if the score is sufficiently
> larger than Left and Right so that the Center gets  seats in small
> districts. The effect disappears for larger sizes.

Right, that was why I suggested a 5 seater with 4 PR-STV seats and 1
condorcet seat.

>  If we try to model it as parties approximating the opinion spectrum of the
> voters, then for small sizes, rounding effects come into play. For size 1,
> we're dealing with a single-winner method. Since I think Condorcet is a good
> idea, the centrist should be elected here, since it reaches to both sides of
> the spectrum. For size 2, the situation is the opposite: if Center and Left
> is elected, then there's an overlap on the left-center area of the spectrum,
> but if Left and Right are elected, then they (presumably) have wings that
> converge toward the middle at the same rate. For size 3, if we clone all
> three candidates, electing two of either Left and Right would create an
> overlap, but Left-Center-Right would cover it somewhat evenly.

Right, you want the positions as

n/(S+1)

S = seats and n = 1 to S

E.g.

S=1 => 1/2
S=2 => 1/3 and 2/3
S=3 => 1/4, 1/2 and 3/4

and so on

Assuming voters are uniformly distributed, this minimises the distance
from a voter to his representative (and possibly average distance
too).

>  That model assumes all preference distances are about equally apart, i.e.
> no Left >> Center > Right. But we can't infer differences in preference
> distances using ranked ballots, anyhow, so that's as good an assumption as
> any other, if not better because it doesn't assume any particular
> difference.

This could be seen because the point where voters switch from

L>C>R

to

C>L>R

would be shifted rightwards.

>  Here's an example that shows the Left-Right-Center problem with Droop
> proportionality, adapted from one of my messages about RRV:
>
>  52: Left > Center > Right
>  50: Right > Center > Left
>  13: Center > Right = Left
>
>  For size 2, Left and Right have a Droop quota each, and so should be
> elected. But a Condorcetian single-winner method would pick Center first,
> leaving room for only one of Left or Right. In score terms, it would have
> Center > Left > Right, meaning that no matter the divisor, Center would get
> elected first.
>
>  Thus, no score-scaled single-winner method that elects Center in the
> single-winner case can pass Droop proportionality.
>

I am still not getting score-scaled.

However, you are right, if you want the condorcet winner to be
elected, the constituency must elect an odd number of members.