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

Michael Ossipoff email9648742 at gmail.com
Tue Jul 3 04:44:22 PDT 2012

On Tue, Jul 3, 2012 at 4:03 AM, Juho Laatu <juho4880 at yahoo.co.uk> wrote:

> On 3.7.2012, at 3.39, Michael Ossipoff wrote:
>
> > 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.
>
>
> I used word "bias" in its general English meaning, in this case referring
> to how D'Hondt favours large parties.
>
>
[endquote]

Fair enough. I just meant that even the unbiased (with flat probability
distribution) Sainte-Lague will give a small party less s/v, when it
doesn't give that party any seats. But, say that a small party is equally
likely to have its final quotient anywhere between 0 and 1 (and certain to
have it in that range); and that a large party is equally likely to have
its final quotient  anywhere between 99 and 100 (and certain to be in that
range). With Sainte-Lague, the small party and the large one have exactly
equal expected s/v. That's what I mean when I say that Sainte-Lague is
unbiased. The expected s/v is equal, in the way that i described, for all
intervals.

(again, assuming a flat probability distribution, for finding a state at
various population-sizes.)

>
>
> 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.
>
>
> If the party leaders are allowed to decide between getting nice s/v values
> or getting more seats, I guess they will choose the latter.
>
>
[endquote]

But, with a given number of voters, a higher s/v means more seats.

>
>
> 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.
>
>
> Do you have an example (or a definition) where (in D'Hondt) large parties
> are likely to get more seats when a country is divided in larger districts?
>
>
[endquote]

No, but it's an unquestionable fact. For two intervals between consecutive
integers, n to n+1, and N to N+1, the bigger N is, in comparison to n, the
greater is the factor by which the N interval party's expected s/v is
greater than the n party's expected s/v.

AT large, or in large districts, N can be greater than n by a greater
amount, meaning that d'Hondt's bias is greater. That gives more seats to a
large party.

Mike Ossipoff

>
>
> Juho
>
>
>
>
>
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>
>
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