[EM] PRfavoringracialminorities

[Raph Frank]

On Wed, Aug 27, 2008 at 7:59 PM, Kristofer Munsterhjelm
<km-elmet at broadpark.no> wrote:
> 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).

Someone would probably call you on it :).  You would have to justify
what the particular method is best.

> 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.

Well, I guess it depends on the method.  However, if it was IRV, I
think there is a reasonable case for making the NOTA option not be
subject to elimination.

> 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.

One option is to use Asset voting for that situation.

Your vote can designate a named candidate as responsible for voting
for you if a NOTA option wins a seat.

This might be a separate column.  You rank the candidates in one
column and then mark one of them as your NOTA delegate.

> 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.

I don't entirely agree with that policy either :).

IIRC, Warren posted it on the Rangevoting yahoo group.

It is something like

Each voter picks one candidate as their favourite.

Each voter rates all the candidates (may have to give favourite max).

The constituency then reports for each candidate the sum of the scores
received for all of the candidates where that candidate was marked as
favourite.

For example,

Assuming 1000 voters and each voter rating from 0 to 10.

Sum on ballots where candidate A1 is favourite
A1: 3000
A2: 2500
B: 200

Sum on ballots where candidate A2 is favourite
A1: 2500
A2: 2200
B: 100

Sum on ballots where candidate B is favourite
A1: 500
A2: 100
B: 4500

These grids can be combined at the national level.

Once that is done, they are converted into N effective ballots.
(N=number of candidates).

1) A1: 3000, A2: 2500, B: 200
2) A1: 2500, A2: 2200, B: 100
3) A1: 500, A2: 100, B: 4500

These are range ballots and as such RRV can be used to work out the winner.

This is proportional because if a group names their candidate as
favourite and rates him max and all others min, they are guaranteed a
seat if they exceed the Droop quota.

> 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.

Hmm, this looks like a more general case.  However, I think you would
maintain proportionality as long as you meet the Droop criteria.

If all voters from a group vote for their candidate first choice, then
they are guaranteed a seat (assuming the group has a Droop quota).

The only effect is on lower rankings.

One issue is that if a party expects to get more than 3 seats, then
there could be issues.  However, even then it mightn't be a major
problem.

Abuse would require that the abusers vote 1,2,3 for the party and then
try to mess up their 4th rank.  I think that this is likely to
increase the number of votes received by that faction rather than
decrease it.

>> I really don't like PR-SNTV, but it would work.
>
> It works *if* all parties run what is in essence vote management:

Yes.  However, vote management strips voters of their power to choose.
 They can't bottom rank a disliked party candidate (without the party
losing a seat).

> 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.

I guess that is sorta like what I was saying.

I would have implemented the district seats as open list election.

Ofc, it uses a MMP like top-up seats rather than Fair Majority Voting
reversal of low margin victories to return to balance.

> However, parties with
> less support than the threshold get no top-up seats, so they have to rely on
> district seats alone.

Not entirely fair.

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

They can also be made impossible in MMP (and Fair Majority Voting),
if your party vote is inferred from your local vote.

> 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;

I think the voting system matters a lot for this.

PR-STV combines difficulty in getting re-elected with the inability of
parties to prevent their members from running as independents.

This gives little power to parties to discipline their members by
threatening to kick them out of the party, while giving voters lots of
power to remove representatives who don't represent them well.

> 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.

In Ireland, the governing coalition always votes as a bloc.  They have
effectively "signed up" to the program for government document that
they publish at the start of each new term.

A party which pulls out of government without a good reason may have
difficulty in being trusted at a later time.  Also, if the government
tries to pass legislation and fails, that is an automatic motion of no
confidence, which can trigger an election (which no politician wants).

> 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).

I think PR-STV actually does something like this.

It is in effect (to an approx at least)

Assign each voter to an elected representative (same number per
elected representative)

Find the set of representatives and voters that minimises the distance
between the voters and their representatives

Declare elected that set of representatives.

> 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).

Ahh, I see.

>
> 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

Right, I guess it ultimately depends on the scoring function.

> 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.

Condorcet is fundamentally linked to rankings.

What about something like

Sn = score for candidate who is in nth place in the condorcet ranking

Sn = Sn-1 * (1 - ( ( margin of victory for (n-1)th candidate of nth
candidate )/(votes cast) ) )

S1 = 1000 (or some constant)

So if when comparing the first and 2nd place candidate the result was
55% to 45%, then

S1 = 1000
S2 = 1000 * ( 1 - ( 10 / 100 ) ) = 900

This gives scores for all the candidates based on how well they
compared to the candidate higher than them.  Also, it ranks the
candidates in condorcet order.

It has issues handling circular ties. Maybe all in a tie should get equal score.

> 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.

Right.  I think it is fundamentally different to trying to find a PR method.

Condorcet is a centerist finding method.  PR is designed to spread the
seats evenly between all the voters.

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

That is a fault with plurality.

A single seat method should aim for the centre as that means that
everyone is best represented rather than representing one side of the
electorate.

> (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.)