Raph Frank wrote:
On 8/25/08, Kristofer Munsterhjelm <[EMAIL PROTECTED]> wrote:
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.
Right, I was thinking more about fairness. If all parties are
expected to get 2+ seats, then there isn't that much of a difference
between the two.
However, for the initial distribution, I think d'Hondt is better as it
rounds downwards, this forces parties to get 2 full seats before being
considered.
This would be more important if the threshold was 1 seat though (as
Webster's would allow parties with 0.5 seats worth of votes to get a
seat, and that is potentially open to abuse).
Websters is fairer as it has much less of a bias between large and
small parties. There were posts on this list comparing bias in
Webster's and d'Hondt. The conclusion was very slight bias for
Websters and much larger bias for d'Hondt.
My view would be that as long as all the parties are expected to get a
reasonable number of seats, the Webster's is better. If there is a
possibility of single seat parties, then d'Hondt is better.
This is what modified Sainte-Lague tries to achieve with its larger
first divisor. Ofc, that means voting for a small party can be
throwing your vote away.
That kind of constraint can also be added to any divisor method (of the
floor(votes_for_this/votes_in_total * p + q) sort, where q is a
constant between 0 and 1 inclusive for the method in question, and p is
set so that the sum equals the assembly size). Before rounding down,
check if the result is less than x (where x is 1, or 2, or whatnot). If
it is, act as if that number is 0 instead.
If you want even less bias, you could use Warren's adjusted divisor method,
since in party list PR,
Is that modified Sainte-Lague?
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.
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%.
Another option would be to have 2 votes, one is a 'vote of support'
and the other is your real vote.
However, that is probably better implemented using a ranked party
system, even if only allowing 2 ranks.
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.
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.
Have you read about Fair Majority Voting?
http://www.mathaware.org/mam/08/EliminateGerrymandering.pdf
This is similar to MMP, but it doesn't assign any extra seats. What
happens is that each party gets a multiplier. This multiplier is
multiplied by the number of votes each party member receives and the
candidate with the highest total wins each constituency.
The multipliers are selected so that each party receives the correct
number of seats nationwide.
If a party gets to many seats, it would receive a low multiplier and
thus would lose a few marginal seats to a party which has to few.
The paper shows that under reasonable conditions, there is also a
solution and it is unique.
I am not sure if it could be applied to multiseat constituencies.
PR-STV would be especially hard as a central office wouldn't be able
to work out who would win as it tries new multipliers. Also, the
non-monotonic nature of PR-STV could play havoc with the algorithm
even if the central station could recalculate the results on the fly.
Increasing a party's multiplier could result in it getting fewer
seats.
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. 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?
Also, it still has the problem dealing with independent candidates and
also, assumes that parties are primary over voting for individual
candidates.
True; the latter takes it away from party neutrality (though MMP does so
to some extent as well), while the former reduces its advantage over
MMP, even assuming we can make it work with multi-winner methods.
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.
I still think that PR-STV with the ability to transfer exhausted
ballots to the national count is the best way to go. This means that
each vote (or fraction of a vote) is either used to elect a local
candidate or to elect a national candidate. By making the quota the
same in both cases, the count is completely fair. It also allows
voters who just want to vote party list to do so and ones who want to
rank all their local candidates to do so and both methods give an
equal ratio of representation to vote.
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.
Have you considered PR-STV with Condorcet loser elimination. Rather
than eliminating the weakest candidate, the condorcet loser is
eliminated.
This has the effect of discriminating against candidates who are not
near the centre. Also, the condorcet winner is immune from
elimination.
Another option is to directly centre bias the election method.
For example, you could have 5 seater constituencies, and give the
condorcet winner a 'free' seat and then use the ballots to elect 4
using PR-STV.
This would give a centerist party a disproportionally large seat total.
This was an attempt at trying to use the score to party list
transformation with a Condorcetian method. It would work on any method
that returns a score, and the method would determine its centrist bias.
Thus PR-STV wouldn't fit very well inside this, though giving a vote (or
casting vote if one wants to be more fair) to a single-member winner
could work.
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.
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.
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.
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.
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.
Well, with a 2 seat assembly, the Droop PR rule says that any faction
with more than 1/3 of the votes must be a seat. I think this is
almost the definition of a PR method. If a PR method doesn't meet
that criteria, then it is only semi-PR at best.
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.
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