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

[Kevin Venzke]

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).

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

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.

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?

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.

Comments or corrections...


Kevin Venzke
stepjak at yahoo.fr

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