[EM] PRfavoringracialminorities

[Kristofer Munsterhjelm]

Raph Frank wrote:
> On 8/25/08, Kristofer Munsterhjelm <km-elmet at broadpark.no> 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.