[EM] PRfavoringracialminorities

[Kristofer Munsterhjelm]

Raph Frank wrote:
> 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.

True. I just gave it as an option for the perfectionists who aren't 
satisfied with Webster, or for the case where the election system is so 
complex that adding the calculation wouldn't be noticed in theg rand 
scheme of things (and where every little bit helps).

>>  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.

For any ranked method, you could have a "new election" option, being 
shorthand for "I'd rather have a new election with the status quo going 
on in the meantime, than elect any of those listed below this option". 
Then, in the social ordering, if this option ranks first, there's a new 
election (and all the candidates of the previous election are barred 
from participating in the next one). If it doesn't rank first, whoever 
wins wins.

For multiwinner elections, you could either redo the entire election, or 
if one of the seats go to "new election", give those who were elected 
prior to this their seats and then elect the remaining seats anew. The 
latter option would be very complex, however, because you'd make sure 
that it retains proportionality. The obvious way to do so is to retain 
weights, but then you have to match those up with the voters, and doing 
that while keeping the secret ballot secret would be very difficult indeed.

>>  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.

Almost all party-neutral proportional representation methods are 
nonsummable. I say "almost all" because Warren claims that Forest solved 
this (that is, made a summable PR method), but I don't have the 
rangevoting.org password and I don't want to join, at least not yet.

What I found of Forest discussing summability in 2007 was this: 
http://lists.electorama.com/pipermail/election-methods-electorama.com/2007-April/020081.html 
. It seems to say, in essence, that since voters first k preferences are 
what count (for some small k), you can store them and average out the 
rest to make "standard ballots" that won't lose much from reality.

I think this may be iffy; there are no hard rules for how much 
proportionality you lose, and if there are more than k seats, the 
averaging could upset things.

> 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.

It works *if* all parties run what is in essence vote management: they 
have to divide votes so that no allied candidate gets too many nor too 
few votes. The same careful allocation has to happen within each party, 
and this can encourage hierarchical systems where those high up 
apportion votes in the direction of a candidate in return for the 
candidate allying with the higher levels (both inside and outside of 
parties).

But at least it's proportional if parties do this. Majoritarian Borda or 
Condorcet (elect the first n in the social ordering) isn't even that.

> 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.

The election system here in Norway is somewhat like this. In the 
national election, you vote for a party (closed list PR). For each 
district, candidates are allocated to the parliament according to 
modified Sainte-Laguë. In some cases, this leads to a (slight) 
disproportionality, so after the district seats have been filled, top-up 
seats ("leveling seats") are used to move the assembly back to 
proportionality. However, parties with less support than the threshold 
get no top-up seats, so they have to rely on district seats alone.

Because all votes are by party, and the same counts are used for 
district and top-up calculations, decoy lists are impossible.

>>  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.

One extreme is that the candidates have no party loyalty, and the other 
extreme is when all within a single party vote as one. Most real-world 
situations would be somewhere in between, and it'd seem that to have the 
assumption of power proportional to number of seats hold, it should be 
closer to the "no loyalty" extreme than to the other extreme; however, 
if one goes too far, there's no party to speak of to have political 
power. Also, it's advantageous to parties in power if they coordinate 
closely. The corollary is that the opposition can survive being 
fragmented more than the parties in power can, because the various 
subgroups of the opposition can then compromise in differing ways, 
trying to get the parties in power closer to their points of view on at 
least some of the issues.

>>  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).

Yes. I wonder if this way of thinking could link proportional 
representation to vector quantization. Something like: Each candidate 
(and voter) has a (presumably symmetric) distribution giving the 
preference to various opinions on an N-dimensional issue continuum. 
Ballots, in a way, give the distance between the distributions of the 
voters and the candidates. Given only the distances, figure out the sum 
of k distributions (for k seats), divided by k, that would most closely 
model the sum of all distributions, divided by the number of voters.

For that method to work, it would have to make assumptions about the 
shape of the distributions, since those aren't available. All we have is 
the distances of the distributions, and the method would also have to 
make a reasonable guess as to what the distance operator is. Finally, 
"closest possible" would be defined in a way that doesn't turn into 
minisum (majority rule).

>>  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.
> 

Okay, I'll explain score-scaled. Election methods may return a winner 
only, a ranked social order, or a set of scores. The latter of the three 
  is what I've been calling "aggregated scored ballot", since one may 
consider the methods as algorithms that produce a "synthetic" plurality, 
rank, or ratings ballot (respectively).

By the transformation I've talked about earlier, we can turn any method 
that returns an aggregated scored ballot into a multiwinner party list 
PR system. The voters rank (or rate, depending on the method) the 
parties, and the output is a set of scores. Say, for instance, that the 
output is:

0.46799: Party A
0.23457: Party B
0.17780: Party C
0.64003: Party D.

To turn this into party list PR, we run Webster on it:

Party A gets round(0.46799 * p) seats.
Party B gets round(0.23457 * p) seats.
Party C gets round(0.17780 * p) seats.
Party D gets round(0.64003 * p) seats.

Say that the parliament is of size 100. Then p is 65.5 and the result is

Party A: 31 seats
Party B: 15 seats
Party C: 12 seats
Party D: 42 seats

You can do this no matter the election method, as long as it returns a 
set of scores. Ordinary party list PR uses Plurality. A better choice 
might be Range (Cardinal Ratings), or some extension of a Condorcet 
method, where that extension lets it return an aggregated scored ballot.

But let's say there's a Condorcet method that does return scores. If the 
scores are to make any sense, a candidate that would have ranked higher 
in the social ordering must have a higher score than a candidate that 
would have ranked lower.

Thus, if there's a party X that's the Condorcet Winner, it must have the 
highest score of all the "candidates" (parties). Thus, no matter the 
number of seats, a member from X must be part of the assembly. However, 
by using the Left-Right-Center example above, we see that this is not a 
good idea for an assembly of even size.
Moreover, we see that, in the example above, for an assembly of size 2, 
Left and Right have a Droop quota each. This means Center must not be 
elected. But if we use a Condorcet method that returns a set of scores, 
then the Condorcet winner, which is Center, must get more seats than 
either Left or Right. That's a contradiction, so adapting a Condorcet 
method in this way must fail Droop proportionality.

The same goes for any method that returns a set of scores and also gives 
Center the highest score. Plurality doesn't.

(Incidentally, while looking around on the web, I found a paper 
describing a method that is mostly Condorcet and returns a set of 
scores. http://mat.uab.cat/~xmora/articles/crating.pdf . It's very 
complex, though, involving quadratic programming and the likes.)