[EM] Sainte-Lague vs d'Hondt for party list PR

Michael Ossipoff email9648742 at gmail.com
Sun Jul 1 22:16:57 PDT 2012

On Sun, Jul 1, 2012 at 7:34 PM, Juho Laatu <juho4880 at yahoo.co.uk> wrote:

> On 2.7.2012, at 1.51, Michael Ossipoff wrote:
> > I always advocatred SL (Sainte-Lague) over dH (d'Hondt) for party list
> PR, because, if you're using PR it's because you want proportionality,  and
> if you want proportionality, then you want SL.
> >
> > Then, more recently, I said that, since I don't think that we need PR
> anyway (though I have nothing against PR), d'Hondt would be fine,
> especially since it guarantees a seat majority to a vote majority.
> >
> > But now I feel that I was mistaken to say that. For two reasons:
> >
> > 1. For fair inclusion, there should be no threshold. d'Hondt will
> disproportionately exclude small parties. That matters, because PR can only
> be justified, in comparison to a good single-winner method, if there's no
> significant split-vote problem. You shouldn't have to worry that you need
> to vote for a compromise because your favorite party might not have enough
> votes to win a seat. That problem is, of course, worse in d'Hondt than in
> Sainte-Lague.
> >
> > 2. In PR, the idea is that you don't have to compromise in your voting,
> because you can just elect representatives (members of parliament
> congress-members, etc.) of your party to parliament or congress, and _they_
> can do the compromising, when necessary--but only when necessary.
> >
> > But how true is that in d'Hondt? Not very.
> >
> > Say your favorite party is significantly smaller than the ones that are
> in major contention in parliamentary voting. If you vote for your party,
> and it's a small party, d'Hondt will give it _significantly_ less
> representation per person, as compared to the larger parties.
> D'Hondt favours large parties. But if you assume that PR will be
> calculated at national level, D'Hondt favours large parties only in the
> allocation of the last fractional seats (the last possible seat for each
> party).

Word it how you want. Referring to the small party and the big party that I
referred to in my previous posting:

Say there's a small party whose final quotient (quotient by the final
divisor, the divisor that results in the desired number of seats) is
equally likely to be anywhere between 1 and 2 (and certain to be in that
range). Suppose there's large party whose final quotient is equally likely
to be anywhere between 53 and 54 (and certain to be in that range). The
large party's expected s/v is about 1.5 times greater than the small
party's expected s/v.

That's _big_ bias in favor of large parties, and against small parties.

You said:

If the results are counted separately for each district, the bias in favour
of large parties becomes bigger.


No, the factor by which the large party's expected s/v is greater than that
of the small party is greater when there can be a large factor by which the
parties' final quotients can differ from eachother--That's when there are a
lot of seats to allocate.

I'm only talking about when we compare a final quota of 1 to 2, to a a
final quota of A to B, consecutive integers much greater than 2.

That is a big bias problem at _national_ level, where there are a lot of
seats in the allocation.

But yes, in small districts, the smallest parties might not get a seat at
all. But that isn't usually what is meant when bias is spoken of. The small
parties' greater difficulty of winning any seats in a small district is a
whole other problem, having less to do with d'Hondt's bias, and much to do
with the large number of votes needed to get a final quotient qualifying
for even one seat--due to the smaller number of seats. You know what I'm
talking about. If there are only 3 seats in the district, then a party with
only 5 or 10 percent of the vote in that district isn't going to do well.
That isn't a bias problem. It's a small district problem. It will be a
problem in SL too, in that small district. Yes, even in that small
district, d'Hondt's bias will of course make things worse for small
parties. But d'Hond't effect will be less in the small district, even as
the small district problem makes things worse, in its own way, for small

You said:

If you want to get rid of the problem of voting for a party that will not
get any representatives, you could allow the vote to be inherited by some
other party one way or another (e.g. second preference in the ballot, or
tree structure of the parties).


Yes, I like those solutions. I guess their disadvantage is that they
complicate the electoral law being proposed, and they don't have precedent.
But yes, I'm for those improvements.

You said:

But for most purposes already methods that guarantee a small party its
first seat if it gets 1/N of the total votes (where N is th number of
seats) may be good enough (people may not fear too much losing their vote
when they vote for the small parties).


I didn't know that. Guaranteeing a seat for a Hare quota, no matter what
the party's divisor-quotient is, would help avoid the split vote problem.
On the other hand, suppose that the small party that thereby gets in
happens to be the most abominable party there is, from your point of view.
Do you really want to give them a seat by a special rule that violates the
PR rule that allocated the other parties' seats? Do you really want to give
that maximally abominable party a significantly higher s/v than your party,
and the other ok parties? I don't think so. l don't like that, and neither
would you.

You said:

Most real life electoral systems have higher bias anyway for various other
reasons like thresholds or not counting PR at national level.


The small district exclusion of small parties isn't about bias. As I said,
d'Hondt's bias is _less_ in a small district. And referring to that unliked
party I mentioned above, I only object to letting them in when it violates
the other parties' allocation rule and gives them a significantly,
unnecessarily, higher s/v.

As for theresholds, I said above that I oppose them, because they, too,
violate the allocation rule, for no good reason.

> So your favorite party won;t have many seats with which to support
coalitions. If compromising, coalition-support, are necessary, then you'd
do better, in the d'Hondt PR election, to give your vote to a big party, so
that you can thereby add more seats to the coalition that you want to
> That's no good. d'Hondt fails FBC, if FBC were extended to PR methods.
You asked:

> What would that extended definition say?


I don't know. I haven't written one. I don't suppose that a precise one is
needed for PR. The precise ones are only needed for single-winner methods.

Why not just say that your power to help a compromise party in
voting-coalition strength, shouldn't be reliably better if you vote for
that party, instead of for your favorite (which is sure to be seated).

In SL, you can expect to help just as much by voting for Small, because
your vote is worth just as much when you give it to Small. And Small can
vote in a coalition with Large. In d'Hondt, that isn't so. Your vote for
Small is worth less, in terms of seats, and so you'd do better to vote for
Large instead, for the purpose of helping Large in coalitions.

The inhibition against honest voting, with d'Hondt is similar to that in
FBC-failing single-winner methods.

Mike Ossipoff

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