[EM] PRfavoringracialminorities

[Kristofer Munsterhjelm]

Raph Frank wrote:
> On Sun, Aug 24, 2008 at 10:44 PM, Kristofer Munsterhjelm
> <km-elmet at broadpark.no> wrote:
>> There are some limits to the transformation: for instance, you can't have
>> representation below 1/(assembly size), thus the "power constraint" caveat
>> of the transformation. Similarly, power is in steps of 1/(assembly size),
>> and you can't have a sum power (over all representatives) higher than 1
>> (which is to say, the assembly can't hold more reps than its size).
> 
> Right, it could work as
> 
> 1) Voter votes for one party + maybe other info
> 2) Assign seats using d'Hondt's method
> 3) Eliminate any party with fewer than 2 seats
> 4) If any eliminated, redistribute votes of eliminated parties and goto 2)
> 
> The redistribution could be ballot based (voters rank the parties) or
> party based (parties rank the parties prior to the election).
> 
> The method for deciding how the seats should be assigned in the party
> is another issue.
> 
> I set the threshold at 2 as this reduces the effects of the
> Webster/d'Hondt choice.  Maybe the final distribution should use
> Webster's.

The divisor method choice differs not just when you're by the threshold, 
but also at the "discontinuity points" of their respective rounding. 
Also, I think that if you're going to use a divisor method, there's no 
point in not using Webster instead of D'Hondt or Adams -- that is, 
unless you think the large/small party bias is desirable.

If you want even less bias, you could use Warren's adjusted divisor 
method, since in party list PR, the number of parties are known in 
advance. It may have some ambiguity still, though: would only parties 
that exceed the threshold count? I think only those would, because 
they're the only ones that would make a difference to the composition of 
the assembly.

>> But if it's true that a simple "FPTP then pick the n best" is a bad system
>> for electing representatives with different power, and I'm right about the
>> transformation, then it follows that ordinary list PR (which is just a FPTP
>> vote for parties) can be a bad system as well.
> 
> Right.  Votes for parties that don't hit the threshold (5-10% in some
> countries) are effectively thrown away.  It is surprising that a
> bigger issue isn't made of this.
> 
> I guess people do complain about thresholds, but never about the risk
> it poses to the voter.  If your party has 5% support and the threshold
> is 5%, then there is a risk of throwing your vote away if you vote for
> that party.

Or, for that matter, if it's 4% and you want to show that the party has 
support. Electoral support numbers can encourage parties by themselves, 
I think - for parties on their own, or for coalitions. If the method has 
at least some strategy, and we know that no method is absolutely free of 
strategy, then knowing that there's support for a party may make others 
who think that "it only has 3% support, voting for it is definitely a 
waste" reconsider when they see that it really has 4.9%.

>> If constituencies are too small and there's no national compensation, then
>> list PR could suffer from the same problems as exist with FPTP applied to
>> candidates: vote splitting and the familiar "worst of many evils" situation.
>> Party list PR elections usually lead to multiparty democracy, though, so I
>> am guessing that this effect isn't significant for real world party list
>> districts. It can still be annoying, in particular to voters who are
>> dissatisfied with existing parties but know that voting for a new party is
>> "just throwing one's vote away".
> 
> If there are transfers, then this should be less of an issue.
> 
> If there are small constituencies, then PR-STV is a better choice.

True. I think that a party neutral multiwinner method is preferrable to 
party list in any case, but with many parties, voters can suffer a sort 
of information overload having to check which candidates are worth it to 
rank, and in which order. Obviously this would be diminished in small 
constituencies and with fewer parties.

Part of what I'm trying to achieve when considering MMP methods based on 
PR-STV (not necessarily STV though) is of making the resulting method 
immune from negative campaigns on the basis that the PR-STV base 
produces an effective threshold that's higher than what was the case for 
the party list method, and so one should return to party list.

>>> Voters would be recommended to vote for a candidate who is likely
>>> to get elected as their 2nd choice.
>> I seem to remember past posts on this list about so-called "three slot
>> methods" that would have only two ranks, but approval-like ordering within
>> each rank.
> 
> You mean equal ranks allowed ?

Yes, in the sense that Approval is an "equal ranks allowed but only two 
ranks" method.

>> Condorcet could also be used as a weighted-power method, but only if it
>> gives scores and not just ranking for its social ordering. Perhaps an
>> eigenvector method?
> 
> Not sure how you would work that.  Do you still mean that voters would
> rank the parties?

Yes, again. The method would be Condorcet, accepting rank ballots over 
the parties. Then it returns a scoring order - n pairs of party and 
score - and the number of representatives are given according to the 
relative score of the party in number, using a divisor method.

This generalized transformation could be used for any method that 
provides not just a social order (aggregate ranked ballot) but a score 
set (aggregate scored ballot).

With a sufficiently large assembly, the left-center-right case wouldn't 
be a problem either. With a ballot like

20: Left > Center > Right
20: Right > Center > Left
  1: Center > Left = Right

and a fair scoring function, you'd probably get a center party that 
(since it's the CW) gets somewhat more power than either Left and Right, 
with the Left and Right parties being of equal power and taking the 
remainder. For the case I've given, this may cause a problem with Center 
being a kingmaker, but I think that's more a problem with the assumption 
that power is directly proportional to the number of seats, than with 
the election method in general.

> What about something like PR-STV instead of a divisor method
> 
> 1) Count votes
> 2) If party with most votes exceeds quota
> - assign additional seat to party
> - Remove one quota of vote from party (Remove random ballots or just
> do normal PR-STV reweighting)
> 3) If no party is above quota, eliminate party with fewest votes and
> reassign them to other parties
> 4) Goto 1) until all seats assigned to some party
> 
> I am not sure if the elimination rule is fair.  Maybe it should be
> eliminate the party with the fewest seats and use currently held
> points as tie break.  However, that is biased towards big parties.

If you have PR-STV, you can just "emulate" party list by altering a vote 
for a single party to a vote for the entire list, in the order the list 
has been set up (for closed list) or in the order the voter specified 
(for open list).

That is, if you have a ballot of the form:

PartyA > PartyB > PartyC

you get

PACand1 > PACand2 > ... > PACandN > PBCandA > PBCandB > ... > PBCandN > 
PCCand1 > ...

Since IRV is cloneproof, the length of the list shouldn't make a 
difference, except when compared to a list that's too short for the 
number of seats the party should rightly have. I say IRV because STV 
isn't cloneproof - for the simple reason that adding clones to a list 
that has too few candidates should (and does) alter the outcome in favor 
of that party.

This emulation is like the candidate proxy method I wrote about in a 
reply to Jonathan Lundell, only with lists (that are constrained within 
the party) instead of candidate proxy ballots.


If we go further on this path of reasoning, it seems we can unify 
single-winner and multiwinner methods, if vaguely. Ideally (with 
differing power), one could construct a scored social order and then 
give each representative differin power, as above. Party list PR lets us 
do this, by the earlier equivalence. However, if we're party-neutral and 
can't have unequal power weights, then we can't do that. So the power 
must go to someone else, and since the method is party-neutral, the only 
way of determining such is to use the ballots as an indication of where 
that power should go.

But that only works for systems in the spirit of divisor methods. For 
instance, for the Condorcet election above, Center is ranked above Left 
and Right in the social order, but I think that the correct assembly of 
two is one of Left and one of Right. Still, it's a step towards 
understanding multiwinner methods.