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

Michael Ossipoff email9648742 at gmail.com
Mon Jul 2 17:39:57 PDT 2012

```On Mon, Jul 2, 2012 at 6:21 AM, Juho Laatu <juho4880 at yahoo.co.uk> wrote:

> On 2.7.2012, at 8.16, Michael Ossipoff wrote:
>
> > That's _big_ bias in favor of large parties, and against small parties.
>
> Maybe so, if you count the s/v values for D'Hondt. If you count the seats,
> the bias will be less than one seat per party. That's maybe not a "_big_
> bias". (Sainte-Laguë is however even less biased on average, and stays
> below the one seat bias limit in most cases.)
> [endquote]
>

That brings us back to the fact that we must agree to disagree abouts the
matter of whether or not people have a right to equal representation.

I do count s/v. You see, I think that s/v should be equal, as nearly as
possible. That's what equal representation per person means.

Sainte-Lague is completely unbiased if we assume that there is equally
likely to be party with final quotient anywhere between N and N+1, where N
is an integer, and where N to N+1 is the interval of interest. Though that
assumption isn't strictly correct, Sainte-Lague is only very slightly
large-biased.

> > 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 parties.
>
> You said:
>
>
> I simply summed up the expected D'Hondt biases of the multiple districts.
> The biases of small districts may easily sum up to multiple seats per party
> (= higher than with one large district).
>
>
>
[endquote]

You're using "bias" with a different definition that its usual
definition. This reply isn't the place to clarify the definition of bias.
I'll explain that in a subsequent posting, hopefully posted tonight.

You said:

Although D'Hondt in some sense allows large parties to get seats easier in
one large district

[endquote]

The more seats, the more bias, with d'Hondt. d'Hondt's  bias in an at-large
allocation is greater than its bias in a small district PR allocation.

You said:
,
splitting the districts in several small districts is probably
strategically even better for them.
[endquote]

Not if you're judging the benefit to them in terms of their s/v as compared
to other parties' s/v.

In a small district, very small parties will be excluded, who wouldn't be
excluded in an at-large allocation. But the big party will get more seats
in the at-large allocation too.

And in the at-large allocation, the expected s/v of a party whose final
quotient could equally likely be anywhere in the range of N to N+1 will be
more than the expected s/v of a party whose final quotient could equally
likely be anywhere in the range of 0 to 1 by a much greater factor, than it
would be if the allocation were instead done in a small district.

In other words, in comparison to a small-district allocation, the at-large
allocation advantages the big party more in comparison to the small party,
in terms of s/v.

>
> > 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).
> >
> > [endquote]
> >
> > 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.
>
> Many competitive voters hate also other competing large parties and every
> seat they get. Some of the small parties could be even more disliked. But
> personally I'd welcome almost any such representative to the parliament.
> There have been arguments about the risk of fragmenting the parliament if
> one lets all the small groups in. But at least in my home country I can't
> see any harm done if one would allow one person from the "elders' party"
> and one from some far left communist party. No harm done. Better
> proportionality. All voters (with one quota of supporters) would be
> represented as they want to be represented.
>

[endquote]

Actually I don't know if a party with a Hare quota could ever fail to get a
seat in SL.

You said that you welcome small parties, provided that their inclusion is
in keeping with proportionality. I agree.

But there's no need for an extra rule letting someone in if they have a
Hare quota. SL would almost surely let them in anyway, by its allocation
rule, if they have a Hare quota. And, if it didn't, then you'd be
letting them in preferentially, in violation of the rule that allocated
everyone else's seats; and that wouldn't be good.

No need for a special rule to let a party in if it has a Hare quota.

>
> > The inhibition against honest voting, with d'Hondt is similar to that in
> FBC-failing single-winner methods.
>
> But isn't there also a risk when voting for small parties in Sainte-Laguë?
> (just smaller and not in favour of large parties) I mean that it is not
> easy to extend FBC and keep the definition exact but make it such that it
> would cover D'Hondt but not Sainte-Laguë.
>

[endquote]

It goes without saying that, especially in small districts, there is a
split-vote problem that could inhibit someone from voting for their
favorite party. That's why we discussed remedies for that, such as listing
an alternate party to get your vote if your main party doesn't get in. As I
said, I liked the ideas that you suggested for that.

But I'd mentioned an additional problem in d'Hondt. Even if your favorite
party gets in, with several seats, small parties have a far smaller s/v
expectation than big parties, in d'Hondt. That is not true in Sainte-Lague.
It means that, in d'Hondt, you have strategic incentive to vote for
a bigger compromise party instead of for your favorite, because, in that
way, you're adding more seats to parliament that would favor a coalition
helping the big party. In SL there is no such incentive to abandon your
favorite party to help a bigger party. That's because small parties can
expect just as much s/v as big parties.

Mike Ossipoff

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