[EM] Hare and Droop, d'Hondt and Sainte-Lague

[Olli Salmi]

At 07:11 +0200 26.7.2003, Kevin Venzke wrote:
>I started reading about methods of proportional seat allocation.  I 
>have a couple
>of questions...
>
>First, what is IRV's relation to Hare (quota of (votes/seats))?  It 
>looks to me
>like it could just as easily be related to Droop (you need 50%+1 to 
>be elected).

I don't understand the question. If you use Hare with IRV you are in 
effect forcing a unanimous decision. With Droop only an absolute 
majority is required (>50%)

>And second, in "remainder" methods, what happens when, after giving seats for
>quotas, there are more seats left to be allocated than parties?

I've understood that this case doesn't arise, at least with the Hare quota.

>The various pages I've looked at suggest that Hare and Sainte-Lague are more
>proportional than Droop and d'Hondt, respectively.  But I did some 
>examples and
>I'm a little concerned.  I wonder if someone will humor me and have a look at
>this.
>
>Let's say we're in Chile, so this is a two-member district:
>Party A: 21,000 votes, 67.74%
>Party B: 10,000 votes, 32.26%
>total: 31,000
>
>Hare: Quota is 15500.  A has 1 and B has 0.  Once you take away that 
>quota from
>A, B has the largest remainder to A gets 1 seat and B gets 1 seat.
>
>Sainte-Lague: A gets a seat, and votes are reduced to (21000 / 3) or 
>7000 votes,
>which means B gets the other one.

Usually Sainte-Lagu‘ gives the same result as Hare, but it doesn't 
have the paradoxes.

Sainte-Lagu‘ and Hare don't favour big parties.

>Droop: Quota is (31000/(2+1))+1 or 10335 (rounded up).  Only A has a quota.
>Once you subtract that, party A has (21000-10335) or 10665 votes, 
>which is more
>than B, so A gets both seats.
>
>d'Hondt: A gets a seat, and A's votes drop to (21000/2) or 10500 
>votes.  That's
>more than B has, so A gets both seats.
>
>My thought: Although it would be nice to give a seat to a party that 
>got nearly a
>third of the vote, wouldn't it be unfair to penalize party A for not 
>splitting into
>two equal fragments?

This is the reason why I don't fully support Sainte-Lagu‘. With 
Sainte-Lagu‘ (like Hare) a minority can, with good luck, get a 
majority of the seats. In Germany there's a special rule that if one 
party gets a majority of the votes but not the majority of the seats, 
it is to be given one extra seat. I think this is only relevant when 
there are three parties.

If parties or fractions present a common list, under d'Hondt they 
have about 50% chance of gaining a seat, but under Sainte-Lagu‘ the 
chance is around zero. In any one election they can gain or lose, so 
apparentements are not very useful in general elections. But if you 
know the number of votes you can exploit this. It just occurred to me 
that this may be why Sweden and Denmark base their committee 
elections on d'Hondt.

>Incidentally I think Chile effectively uses d'Hondt...  The top 
>party gets both
>seats unless the second-place party gets at least half the top party's votes.
>Personally I can't see a flaw with this.

This may be the reason why d'Hondt is used in many countries. The 
countries that use Sainte-Lagu‘ have a legal threshold which of 
course favours big parties. So first you use a fair method and then 
an exceptional rule to cancel the fairness.

In Modified Sainte-Lagu‘ the first divisor is 1.4 instead of 1. In a 
Swedish commission repor considered the posibility of using 1.5 as 
the first divisor, so that the first two divisors (1.5:3) would have 
the same proportion as the first divisors in d'Hondt (1:2). This also 
makes it more difficult for small parties.

Olli Salmi