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

Juho Laatu juho4880 at yahoo.co.uk
Fri Jul 13 00:36:32 PDT 2012

On 13.7.2012, at 2.24, Michael Ossipoff wrote:

> Juho:
> You said:
>> Btw, this strategy is much less risky when we talk about splitting
>> districts, since the population of districts is very stable when compared to
>> possible risky changes in party support.
> I don't know if U.S. states are allowed to split. Are Finnish PR
> districts allowed to split?

In Finland the government is currently planning to join some districts. I believe they are planning that partially for strategic reasons (larger D'Hondt districts vs. country level proportionality). In the U.S. state splitting is probably not easy, but to my understanding gerrymandering of the smaller districts could be possible. You know better.

> But remember that, in order for that strategy to really gain anything,
> they'd have to split to, say, a size that barely rounds up to 1 seat.
> They'd become single-member districts. Or 2-member districts at the
> most. I just can't believe that California would split into about 53
> states, even if allowed to, for apportionment advantage. Each new
> state, then, would be the population-size of barely over half of a
> House of Representatives district.

I agree that the strategy is not easy, but it is easier to estimate the impact of splitting areas than the impact of splitting parties.

A favourable (multi-member) environment for the startegy could be one where districts have only few respresentatives, and where different areas support different parties / interest groups. In such an environment successful gerrymandering could be quite doable.

One problem in this type of gerrymandering is that if one simply splits just one district or joins two districts, and as a result the total number of seats in this area changes, people and media may see the strategy too easily. If one rearranges all districts at one go, the intended effects are more difficult to spot.

One concrete example set-up where also the (Sainte-Laguë / Webster) splitting strategy may work, is one where a stronghold area of a party (or the home region of some strong political players) will be split in smaller districts to get extra seats. Since the amount of population in different municipalities is well known, the startegy may work also with higher number of representatives than one. In practice the strategists may generate numerous natural looking districting alternatives and then pick the one that gives highest number of seats to those regions where the strategists want to have more seats (this may include splitting some areas in smaller districts but of course also any other kind of fluctuation in the results will help the strategists). (The strategic planning could optionally include also estimates on how strong each party is in each district of each districting alternative.)

This kind of gerrymandering can be done also with other methods than Sainte-Laguë / Webster. The strategy is just somewhat different for different methods. In S-L/W the fluctuation that sometimes favours small and sometimes large parties may make it possible to keep the average size of the districts at the same level, but just change them so that the "right" areas will get the most seats.

> Note that during the years during which we used Webster, California
> didn't split into lots of HR-district-size states.
>> But what if it isn't the result of splitting strategy? What if those are the
>> natural spontaneous parties and their vote totals? Does the result look
>> wrong? It isn't wrong. SL, by doing what it does, is minimizing the
>> deviation of each party's s/q from the ideal equal s/q value.
>> It might _look_ wrong at first glance, because it "violates quote", but it
>> isn't wrong,in terms of fair s/q.
>> Yes, some people might look at the s/q values
> Some people?   But not you. :-)

I would check the s/q values right after I have checked that each party got at least close to the number of seats that their proportion of the votes entitles them to. :-)

> Remember, I tried to agree to disagree about whether people have a
> right to equal representation. You refused to disagree about that. You
> said that you agree that people have a right to equal representation.
> Equal representation means the same representation for everyone. The
> same representation for everyone means the same representation per
> person. The same representation per person means equal s/q.

But is that what people usually mean when they talk about equal representation?

> So, do you or do you not agree that people have a right to equal
> representation?.

Equal representation, yes. Byt s/q is to me just one mathematical formula (out of many) that can be used to measure different properties of the results of an election.

> If you do, then I have good news for you: Sainte-Lague/Webster puts
> each party's or district's s/q as close as possible to the ideal equal
> s/q.
> You said:
>> , but I'd expect someone to
>> notice also the unfair use of the quotas / votes.
> What unfair use of the quotas/votes?

Here I referred to the 8 quotas and 8 seats of one party in the bad example (no strategies assumed). People who think that n% of the votes should entitle them to n% of the seats are the ones that may find deviations from this principle unfair. In Sainte-Laguë / Webster the problem is that in principle (not usually in practice) it can deviate from this target not only in how the fractional seats are allocated but by multiple seats.

> Are your referring to splitting
> strategy in SL? I addressed that. I said that, if there turned out to
> be a splitting strategy, and if it remained even when SL's 1st
> denominator is raised from 1 to 2, then Largest Remainder would be the
> solution.
> If you aren't referring to splitting strategy, then what are you referring to.

See above.

>>> . In the S1+N seats case the large party gets 43.48% of the seats with 61%
>>> of the votes. Or in other words, all 20 seats with only 12.2 quotas (7.8
>>> extra seats), or only 20 seats with 28.06 quotas (8.06 seats too little).
>> [endquote]
>> That's ok if the parties are genuine, natural and not the result of
>> splitting strategy. As I described above.
>> I'm afraid some people might get upset if they think they were entitled to 8
>> seats more but will get none
> Undoubtedly. But thinking that they're entitled to 8 seats, and being
> entitled to 8 seats aren't quite the same thing.

In that example there was a party that got 61% of the voters. Its supporters may feel that they are entitled to approximately 61% of the seats (assuming good proportionality). The total number of seats was 46. If we want to give them 61% of the 46 seats, that would make 28.06 seats. But they got only 20 seats. Maybe they expected 28.06 to be rounded to 28, or maybe to 27 due to some possible additional noise in the calculations, but not to 20. One may have different kind of agreements on what each party is entitled to, but even without any such agreements people might get upset with if they get only 20 seats in a system that is supposed to be proportional.

> , and will lose a very clear (28 seats vs. 18
>> seats) majority. There are thus many approaches to measuring the fairness of
>> the results, and the quota based approach may be a very natural one to check
>> first.
> You're espousing a fairness-measure that is different from equal
> representation for all, one that is in conflict with equal
> representation for all.

I understand that you want to use a different measure.

> You speak of "the quota-based approach", as if you think that the Hare
> quota is the only divisor to use, or has some privileged status among
> divisors.

Maybe the idea of getting approximately n% of the seats with n% of the votes in a good proportional system is close to what I was thinking of.

> Dividing the parties' votes by the same divisor, any common
> divisor, and rounding off the quotients to the nearest whole number,
> will put the parties s/q as close as possible to the ideal equal s/q.
> If you use the Hare quota as the divisor, for that procedure, you'll
> often get a total number of seats different from the desired
> house-size. So you use a different divisor. Don't be wedded to the
> Hare quota.
> If we allow a variable house size, then we could say: Divide each
> party's votes by the Hare quota (based on some most preferred
> house-size), and round off the quotients to the nearest whole number.
> That rounded off quotient is the number of seats to assign to each
> party. That would be a fine method.
> But the fact that that divisor is a "Hare quota" based on some
> preferred (but not required) house-size doesn't make it special or
> privileged. How can you think that is somehow fairer to use that
> divisor instead of some other divisor?

I think that was your theory, not mine.


> Mike Ossipoff
> ----
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