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

Juho Laatu juho4880 at yahoo.co.uk
Mon Jul 2 07:58:04 PDT 2012

```On 2.7.2012, at 13.58, Raph Frank 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.  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.
>
> 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.
>
> This pretty much has the same effect as a threshold, but at least votes can be reassigned.  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.

If there are too many small parties, or if they strategically split to gain more sets thanks to the generocity of the first divisor of Sainte-Laguë, one approach would be to limit the number of parties that can get a seat with less than one quota of votes (e.g. max one party). That would still keep the threshold for new and small parties low (around 1/2 quota), but would put some limits to how many of them are allowed to grow at one time.

>
> 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.
>
> 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 simulation.

That could be a reasonable approach (if the rounding errors are considered to be a big enough problem to require a fix). Surely that approach would improve the results. We just need to agree what measure to use as an indicator of "bias" in each case (each house size).

Juho

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