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

Michael Ossipoff email9648742 at gmail.com
Wed Jul 4 12:25:03 PDT 2012

On Mon, Jul 2, 2012 at 6:58 AM, Raph Frank <raphfrk at gmail.com> wrote:

> Another possibility is "alternative-vote" based PR.
> You rank up to 2 parties.  Something like,
> Use divisors 2, 3, 5, 7, 9, ...
> This is Websters but is d'Hondt-like for the first seat.
> The seats would be allocated using that rule, and any party which got no
> seats would be "eliminated" and the votes given to the alternative party.
> I don't think it matters if you use normal or the modified version of
> Webster for the 2nd stage.  This eliminates "micro" parties getting seats
> due to the round up from 0.5 to 1.


Why eliminate the proportional inclusion of small parties, in keeping with
Sainte-Lague's putting each party as close as possible to its correct
proportional share, and allocating seats without bias (given the flat
probability distribution assumption)?

>   If 0.5 to 1.0 sized parties get a boost, then parties would try to aim
> for those sizes (splitting if needed), so it breaks the uniform
> distribution assumption.

With most any PR system or method, parties that can accurately guess their
support could split or coalesce, in order to maximize their seats. That's
unavoidable,and there's no reason to bother trying to make it impossible. I
wouldn't worry about it. It won't create more disproportionality than the
system is capable of anyway.

> For example, 26 parties at 1.5% and one party at 61% for a 49 seat
> parliament would split the seats, 20 for the large party and 29 for split
> between the micro parties.  The micro parties get 59% of the seats for 39%
> of the vote.
> With ordinary Sainte-Lague. True. I certainly wouldn't like that if I were
a preferrer of a large party. I guess that's one reason for thresholds.
Your suggestion of making the first seat more difficult, with a
Sainte-Lague divisor of 2 instead of 1, would help that problem. And, as
you said, the ability to transfer one's vote to a 2nd choice party would
mitigate the unfairness to small parties. That sounds like a fair solution
to the problem that you brought up.

You referred to that as "Modified Sainte-Lague", when the "2" replaces
Sainte-Lague's "1". Is that in use somewhere?

You wrote:

> This pretty much has the same effect as a threshold, but at least votes
> can be reassigned.

Right. It sounds fairer than ordinary Sainte-Lague. That problem hadn't
occurred to me, because (in recent times)I've just begun looking at PR.
When I looked at it before, it was purely from a small-party standpoint,and
I disregarded that problem because it's only unfair to large parties. But
now I realize that when people vote for what they really like, and if they
have good judgement, the best will be the biggest.

You continued:

> You could also have a random threshold.  For example, if there was 100
> seats, then the threshold could be a random number between 1% and 2% of the
> vote.  This would make it hard to game the threshold system.

Sure, but I don't know if people would accept anything that involved any

You continued:

> You could also go down the IRV path, and keep eliminating the weakest
> party one at a time, until all remaining parties get at least 1 seat.  The
> ranked ballot could also have more than 2 slots, but 2 slots is probably
> enough.  The voters would be recommended to pick a party with > 2-3 seats
> for their alternative choice.

Someone could ask, why not, instead, just use IRV? The answer would be that
the system would still have the proportionality advantages of Sainte-Lague,
but would have the deluxe way of dealing with small party non-lnclusion,
with STV at the bottom end only. It seems to me that that suggestion came
up in discussions that I was involved in a long time ago. I don't know if
it was I, or one of the others, who suggested it.

You wrote:

> Also, has anyone look into picking the number of seats in a range, so as
> to minimise bias.  Use Websters, but pick a house size +/- 10 from nominal
> and have

some measure.  Does that add or remove bias?  That might require a


Are you referring to just rounding off each party's number of Hare quotas,
to the nearest whole number, and assigning to it that number of seats,
regardless of the resulting house-size? Sure, I and others have considered
that. It would be fine. But people don't seem to like variable house-size.
Maybe it's because parties and states hate it when they lose a seat, for
any reason, and perceive it as a loss, even if others lose seats too.

And, like your Modified Sainte-Lague suggestion, the 1st seat could be a
d'Hondt seat, where no one gets their 1st seat unless they have a full Hare

As for bias, it wouldn't change anything from Sainte-Lague/Webster (or
Modified Sainte-Lague, if you make the 1st seat a d'Hondt seat). The method
would still have Sainte-Lague/Webster's unbias (except for that 1st d'Hondt

Mike Ossipoff
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