[EM] PR solutions

[Juho Laatu]

On 9.6.2012, at 1.46, Michael Ossipoff wrote:

> I don't know what you mean by "minimize violation of opinions".

It is just one natural way to measure delta to full proportionality. I don't claim that this is the only one or the absolutely correct one, but it is natural and it respects the philosophy of Largest Remainder, as appropriate when I try to seek justification to how LR works.

The approach is simply to count how many quotas of votes did each group get, and how many seats did they get, and then count the sum of differences. If the vote counts are 1 and 2, there are two seats, and both groups get one seat, and the quota is votes / seats. In this case the quota is 1.5, the groups have 1/1.5 (=2/3) and 2/1.5 (=4/3) quotas and are entitled to as many seats, but since we can not give them fractional seats we give them 1 and 2 seats, and we violate the rightful decision or "violate the opinions" by 1/3 + 1/3 = 2/3 quotas.

You migh say that I used the LR definition to justify that LR is right. But the idea of the parties having right to 2/3 and 4/3 seats respectively is very natural and maybe would be used if we were able to allocate fractional seats. (Maybe some representative body would give the two representatives 2/3 and 4/3 votes of voting power to make proportional representation as exact as possible. That would also cancel the paradoxical influences of the Alabama paradox, if measured in voting power.)

> I would just point out that if you give 5% of the seats to a party because
> 5% of the voters like that party, and 95% of the voters dislike them, then I
> would say that you're violating a whole lot of opinions. It would seem that
> PR is inconsistent with minimizing violation of opinions.

If I got you right, then 95% of the voters might feel that the 5% marginal group should not get any seats. Giving that small group 5% of the seats would be a violation of majority opinion. But that would not violate proportional representation. Opinions can thus be violated in at least two ways. And there are at least two (incompatible) ways to respect the opinion of the voters.

In PR systems the proportional represenative bodies typically make majority (or supermajority or consensus) decisions. The system thus still makes majority decisions that may violate the opinion of 49% of the voters (or their proportionally elected representatives), but when compared to majority oriented elections, that problematic phase has just been pushed one level higher, to occur within the representative body, instead of when electing the representative body.

> But if _proportionality_ is the goal of PR, then Sainte-Lague, and not
> Largest-Remainder supports that goal.

I'm not sure. Note also that bias in favouring large or small parties and violations in giving all groups their proportional share of voting power are two slightly differing criteria. The ability of highest average style allocation methods (Sainte-Laguë, D'Hondt) to elect representatives serially for all sizes of representative groups can be seen as an additional requirement that may work against some other criteria.

> STV can be justified because some people prefer voting for individuals, and
> because STV gets rid of the small amount of split-vote problem that remains
> even with good list systems.

Yes, STV allows voting individuals and even voting different individuals from different parties. But what is the split-vote problem?

> I have to say that I can't find any justification of Largest Remainder,
> other than the claim that it's simpler to justify to people who aren't
> familiar with proportionality--at the cost of an unaesthetic parting-of-ways
> with proportionality as soon as the remainder seats begin to be allocated.
> When the remainder seats begin to be allocated, proportionality is out the
> window.

I don't know if it violates proportionality (maybe depending on how you define proportionality), but violations of the Alabama paradox could be seen to be unaesthetical (although maybe fair too, from another viewpoint).

Btw, I have one merciful definion of proportionality that I often use to classify fully proportional methods. The idea is that if the method allocates the full seats correctly, that's enough to be "fully proportional". From this point of view, what happens with the fractional seats is a minor problem that we need not care that much (assuming that the number of seats is not very small). Maybe one could say that such methods allocate full seats proportionally.

> Anyway, as a practical matter, all of the PR systems and methods are really
> alright.

There are many working approaches. I guess most real life PR systems have however problems and/or strange features. Many of them violate also also PR more than marginally, i.e. more than just using D'Hondt or some other allocation algorithm that can be considered not to be accurate. But lso biased systems often work "well enough", i.e. with just the normal amount of problems that PR systems tend to have.

Juho